Abstract

This paper deals with radiation’s contribution to thermal insulation. The mechanism by which a stack of absorbers limits radiative heat transfer is examined in detail both for black-body shields and grey-body shields. It shows that radiation energy transfer rates should be much faster than conduction rates. It demonstrates that, for opaque screens, increased reflectivity will dramatically reduce the rate of heat transfer, improving thermal insulation. This simple model is thought to contribute to the understanding of how animal furs, human clothes, rockwool insulators, thermo-protective containers, and many other passive energy-saving devices operate.

© 2014 Optical Society of America

1. Introduction

Fur or pelage is unique to mammals. In addition to thermal insulation, it serves to protect the skin from abrasion or harmful ultraviolet radiation, to communicate with other species – signalling or concealing – or to gain information about its environment by sensing its surroundings. Mammalian hair can vary in form from straight to curly: there is a correlation between this geometry and the form (circular to flattened) seen in the hair’s cross-section. For aquatic mammals, the hair shape will allow an air layer to be maintained within the fur during submersion, increasing its water-repelling function [1]. It should be noted that furs generally contain two kinds of hair: ground hair (shorter, denser and often curly) and guard hair (longer, straighter and coloured). A similar distinction is found in birds’ feathers.

 

Fig. 1 Warm-blooded animals like mammals and birds have hairs or feathers which serve multiple functions. One of them is camouflage, when the coloration or pattern of coloration matches the background to make the animal less conspicuous. However, a more ancient function must have been thermal insulation. A good example is the polar bear (Ursus maritimus), where the thick white hair clearly needs to serve these functions. Alan D. Wilson, Polar Bear (Sow), Kaktovik, Barter Island, Alaska, with permission.

Download Full Size | PPT Slide | PDF

The colouration of a mammal’s guard hair is usually cryptic, matching its surrounding landscape (Fig. 1). In the form of specialised vibrissae, guard hair can also function as a tactile sensor. Taken as a whole, hair makes up a complex system; it grows from pits (follicles) in the skin. A sebaceous gland next to the hair root delivers a conditioning substance and tiny muscles can temporarily modify their implantation angle [2].

The most important purpose of the pelt is to thermally insulate the body in high or low temperatures and improve thermoregulation. Heat conservation is the chief function of ground hair [3, 4, 5]. This hair grows continuously forming a woolly layer. They are shed in a process called moulting (continuous or seasonal) and is periodically replaced. Thermal insulation may not have been its original function in mammals, as only full-grown dense fur insulates effectively. Sensing the environment may have been the earliest evolutionary advantage it provided. Hair is usually not preserved in fossils, but its presence on a therapsid (mammal’s ancestor) from the Cretaceous period may be inferred from the presence of characteristic pits, usually associated with vibrissae, on the rostrum of this fossilised animal [6]. It is highly probable that the earliest mammals already had hair: their very small size indicates a high surface-to-volume ratio, which would result in a high risk of heat loss [7]. It is difficult to imagine that such small animals would not have had the protection of a substantial layer of hair.

Surprisingly little is known about the detailed physical mechanism of thermal insulation in structured material, such as criss-crossed fibres. Several studies have, albeit experimentally, investigated thermal insulation in penguin feathers [8, 9, 10]. Their shape has evolved into a very short, stiff and lance-shaped form with a long afterfeather, giving a general two-layer fibrous layout resembling a mammal’s hair. Moreover, the packing of penguin’s feathers on the skin is densely and evenly distributed, increasing thermal insulation [9].

Thermal insulation most often refers to thermal conduction by air trapped between the hairs or feathers – and standard measurement techniques often favour this point of view – [9, 10]. Nevertheless, it is a fact that the thermal conduction can (and often must) also be driven by convection and radiation [11, 12]. Thermal insulation mainly depends on fibre density and length. Measurements on the two-layer fur of rock squirrels (Spermophilus variegatus) show an abrupt decrease in transmission through the inner, dense coat in comparison to the outer coat [12]. Insulation is further improved by skin coloration underneath [13]. However no precise mechanism is proposed for thermal insulation. Studying this mechanism in order to understand how warm-blooded animals keep their heat in cold or hot environments is interesting, but in terms of biomimetism, the importance of such a study brings up further questions on thermal insulation in other biological areas [14] and in material science, which have implications for energy-saving habitation design, textiles for clothes, automobile and more.

In this paper, we address the question of the contribution of far-infrared radiation to the thermal conductance of what we call an “interfacial material”, by which we mean a solid material made of at least two different media separated by interfaces distributed throughout its volume. In such materials, the physical properties are closely linked to the configuration of these internal surfaces. In this case, the distance travelled by the radiation exchanged between the interfaces is greater than its wavelength. At temperatures on most locations on the planet, this means, in application of Wien’s law [15], distances larger than 9 μm (+50°C) or 13 μm (−50°C). In this paper, we only consider simple one-dimensional models, leaving forthcoming publications to examine more complete three-dimensional transcriptions, as well as experimental comparisons for more specific insulating systems.

2. Importance of radiation

When two bodies at different temperatures, say Ta > Tb, are separated by still air, the heat transfer from a to b takes place via two mechanisms: conduction and radiation. In this instance, there is no convection. Conduction refers to energy transfer through the boundary between two bodies and radiation concerns energy transferred by means of electromagnetic waves. As the rate of heat transferred is directly linked to insulation capability, it makes sense to compare which process will result in the most rapid losses.

The rate of energy transfer (W, in joule units) by conduction can easily be estimated by using the expression

dWdt=(KSL)(TaTb).
In this expression, L is the distance between the two bodies, S is the area of their emitting and absorbing surfaces and K is the thermal conductivity of air which slightly depends on temperature, as follows [16],
K={0.0204W/mK(50°C)0.0243W/mK(0°C)0.0257W/mK(20°C)0.0271W/mK(40°C)0.0285W/mK(60°C)
Let us consider the case of a polar bear, with a body temperature of 37°C (Ta = 310 K) and an atmosphere temperature of −40°C (Tb = 233 K). Assuming a woolly fur layer with a thickness L = 5 cm, the rate of heat transfer is:
1SdWdt37.4W/m2.

Let us now look at radiation losses. The emissivity of the skin of a polar bear in the mid- and far-infrared is close to unity, as it is for most non-metallic surfaces. The atmosphere is assumed not to reradiate the emitted power, so we consider that the skin and the atmosphere are black bodies exchanging thermal energy. The net heat transfer rate is given by Stefan-Boltzmann’s law,

dWdt=σS(Ta4Tb4).
With the value of the Stefan constant σ = 5.67 × 10−8 W/m2K4, we get
1SdWdt356.5W/m2.
It shows that the heat transfer rate by radiation is much faster than by conduction. Radiation’s contribution in thermal conductance must then be considered in seeking to explain the insulation properties of low-density fibrous materials. Qualitative arguments on the mechanism for thermal insulation of materials such as rock or glass wool mention convection blockage or reduced thermal conductance more frequently than the reduction of radiation. This suggests however that radiation should be the first mechanism to address when working on thermal insulation improvements. In a high vacuum (such as in interplanetary space), radiation would often be the only energy transfer mechanism to take into account.

3. Black-body shields

In order to introduce a “radiative” insulator, we will consider a fibrous material which fills the space between two black-body thermostats at different temperatures. The aim of this study is to determine the energy exchange rate as a function of the number of radiative shields. The idea is that each thermostat emits and absorbs heat, which will be absorbed and re-emitted by interposed absorbing reflectors. Even if three-dimensional absorbing scatterers are more realistic, one-dimensional reflectors will be considered, because they lead to exact analytic results and contain the necessary physical components. Fig. 2a shows the geometry of the simple model we will study first.

 

Fig. 2 a) A simple model for the “radiative insulator” described in section 3. A hot black body thermostat at temperature Ta faces a cold black body thermostat at temperature Tb. The exchange of energy between these thermostats is only radiative. The insulator is a set of n black or grey sheets interposed between the thermostats. b) Energy exchanges between two neighboring sheets, say sheets i and i + 1, are denoted Ii+ and Ii+1, for energy travelling to sheet i + 1 and to sheet i, respectively.

Download Full Size | PPT Slide | PDF

In this geometry, two semi-infinite black-body media, at temperatures Ta > Tb, are considered. Their surfaces are parallel and normal to the horizontal (z) direction. When considering radiative energy transfer, the distance between the surfaces is unimportant and the rate of heat transfer per unit surface is:

R0=1SdWdt=σ(Ta4Tb4).
In what follows, this heat current density will be our reference heat transfer rate, to which currents through insulators will be compared.

Our first model radiative insulator is a series of n equidistant sheets, parallel to the thermostat surfaces. The sheets are black bodies, with an emissivity ε = 1, which corresponds to an absorptivity a = 1. Each sheet – for example sheet number i (i = 1, 2,...n) – absorbs and emits energy to and from neighbouring sheets i − 1 and i + 1 and equilibrates at a temperature of Ti. For convenience, the high-temperature thermostat at a temperature of Ta can be viewed as sheet number 0 and the low-temperature thermostat at a temperature of Tb can be viewed as sheet number n + 1. As shown in Fig. 2(b), the power per unit area transferred from sheet i to sheet i + 1 is denoted by Ii+ and the power per unit area transferred in the opposite direction, from sheet i +1 to sheet i is denoted by Ii+1. For convenience, the power emitted from sheet i in one direction will be written:

wi=σTi4.

With all black bodies, these energy transfers depend only on the temperature of the sheets, as follows:

Ii+=Ii=wi.
The energy emitted by the high-temperature thermostat is:
I0+=σTa4=wa.
and the energy emitted by the cold thermostat is:
In+1=σTb4=wb.
The unknowns here are the n values of the temperature of the sheets, or equivalently the n values of wi. The n constraints arise because we require all sheets to reach thermal equilibrium which means that for each sheet, the ingoing energy must be exactly balanced by the outgoing energy:
Ii+Ii+=Ii1++Ii+1.
Note that Eq. 11 also means that:
Ii+Ii+1=Ii1+Ii,
which (see Fig. 2(b) expresses that the net heat energy exchange between two successive sheets is constant and equal to the net global energy exchanged between the thermostats.

A practical solution to this very simple equilibrium problem is given by the following system of n linear equations, with n unknowns, obtained by rewriting equation 11 in the following form: for i = 2, 3, 4,...n − 1

wi12wi+wi+1=0
while, for i = 1,
2w1+w2=wa
and, for i = n,
wn12wn=wb.
The linear system is tridiagonal. When solving for the radiative terms wi, we gain access to the equilibrium temperatures of the sheets. For instance, if (as can be assumed for a polar bear fur) one side (body) is at the constant temperature Ta = 37°C and the other side (outer polar atmosphere) at Tb = −40°C, we find the distribution of temperatures shown in Fig. 3(b). The change of temperature in the thickness of the “fur” is almost, but not exactly, linear.

 

Fig. 3 a) Distribution of the equilibrium temperatures of 100 black-body sheets, shielding thermostats at 37°C and −40°C. b) Base 10 logarithm of the energy attenuation factor as a function of the number of black-body shielding sheets, for thermostats at 37°C and −40°C. Only radiative energy exchanges are included in the model.

Download Full Size | PPT Slide | PDF

The purpose of this analysis is also to determine the effect of interposing black-body sheets on the global energy transfer between the thermostats. Quantitatively, this can be determined by calculating the ratio η(n) of the energy transfer in presence of n black-body sheets to the corresponding energy transfer R0 (see Eq. 6 and previous discussion)

η(n)=Ii+Ii+1R0=I0+I1R0.
This ratio will be referred to as the “energy exchange reduction factor”. This factor has been calculated, again for Ta = 37°C and Tb = −40°C, for a varying number of black-body shields.

The result of this calculation is shown in Fig. 3(b). n = 0 is the reference system, so that the energy exchange factor is η(0) = 1. The energy exchange decreases rapidly as new sheets are added. With about 10 sheets, the energy transfer is reduced by one order of magnitude while, with a hundred sheets, we gain two orders of magnitude. The rapid decrease in heat transfer rate with the increasing number of intermediate absorbers means that the radiative exchange results in an efficient thermal insulation mechanism. In the next section, we use a slightly more elaborate model, using grey-body shields, to show that black bodies may not be the best conceivable absorber sheets.

4. Grey-body shields

In this second model, we keep exactly the same geometry as in the previous section, with full half-space thermostats at temperatures Ta and Tb, but we replace black-body planar shielding sheets by grey-body sheets. With grey bodies, Stefan’s radiation law must be modified by introducing an emissivity ε which has been shown by thermodynamics to be equal to the absorptivity a = 1 − tr of the emittor. The absorptivity a, the reflectivity r and the transmittivity t are new parameters which characterise the grey shield. Even if this one-dimensional geometry is kept simple, the problem is now made more complicated by the fact that the sheets have some degree of transparency, so that the light emitted by any sheet can be reabsorbed by any other, and long-range coupling can take place, not just nearest neighbour coupling as in the case of black-body shields. An incoherent multiple-reflection/transmission picture is needed.

Fortunately, this can be examined analytically. In fact, the scheme of energy exchange depicted in Fig. 2(b) can be maintained, with the following changes to the energy transfers,

Ii+=11r2j=0i1(t1r2)jwij+r1r2j=1ni(t1r2)j1wi+j+(t1r2)iwa+r(t1r2)niwb
and
Ii=r1r2j=1i1(t1r2)j1wij+11r2j=0ni(t1r2)jwi+j+r(t1r2)i1wa+r(t1r2)ni+1wb.
Notable exceptions to these expressions are for the energy transfers involving one of the thermostats:
I0+=wa
I1=j=1n(t1r2)j1wj+rwa+t(t1r2)n1wb
and
In+1=wb
In+=j=1n(t1r2)j1wn+1j+rwb+t(t1r2)n1wa.
We note that, with r = t = 0 (black body limit) we recover the expressions given in section 3. The equilibrium conditions are exactly the same as those given by Eq. 11, with the forward and backward energy transfers given above, which leave us with a set of n linear equations for the n unknown temperatures. At this stage, this approach does not restrict the value of shield transparency, as all terms in a multiple incoherent-scattering expansion have been taken into account.

Even if the following case is not realistic, it is interesting to consider: if the transmission becomes perfect (t = 1), we force the reflectivity and the absorptivity to vanish and the energy attenuation factor takes the maximum value η(n) = 1. In this case, the equilibrium equation leads to the values wi = 0 for all shields, which means that all shield temperatures are zero: the shields are effectively discoupled from the thermostats, being unable to absorb energy from them. This is not advisable if we seek a strong thermal insulation effect, so, for the purposes of illustration, we will turn to the opposite case: a weak transmission value. The energy touching one of the screens is distributed in the reflected and absorbed parts and we can describe the effect for varying absorptivities, from a ≈ 0 to a ≈ 1.

The case t = 0 leads to a remarkably simple situation, as second nearest neighbors sheets are optically shielded by the first nearest neighbors. Indeed, we see that

I0+=wa
In+=wn+rwb
and, otherwise,
Ii+=11r2wi+r1r2wi+1
and
I1=w1+rwa
In+1=wb
and, otherwise,
Ii=r1r2wi1+11r2wi.

The result, for increasing reflectances, is shown in Fig. 4. The distribution of shields’ temperatures is identical for all values of reflectances and, as expected, corresponds to the black-body case. The energy attenuation factor is shown in Fig. 4(b). The curve which corresponds to the highest value has been calculated for a reflectance r = 0 – and then a = 1 – which corresponds to the use of black-body shields, as in section 3. With increasing reflectivity, the rate of transfer is dramatically reduced for any number of shields. It is clear that the use of a very small absorption with high reflectances improves overall thermal insulation. Photonic crystals which produce, without absorption, a total reflection in the far infrared (more specifically with wavelengths around 10 μm) would be ideal in the present model. Other very good insulation candidates involve the stack of metallic layers, in vacuum.

 

Fig. 4 a) Distribution of the equilibrium temperatures of 100 grey-body sheets with increasing reflectances: r = 0.0 (black-body result, in blue), 0.2, 0.4, 0.6, 0.8 and 0.99 (magenta), shielding thermostats at 37°C and −40°C. b) Base 10 logarithm of the energy attenuation factor as a function of the number of grey-body shielding sheets, for thermostats at 37°C and −40°C. The shields are assumed opaque to far infrared radiation (t = 0). The upper curve is the black-body shields result and simply repeats the results shown in Fig. 3. The lower ones, from top down, correspond to increasing reflectances: r = 0.2, 0.4, 0.6, 0.8 and 0.99.

Download Full Size | PPT Slide | PDF

5. Three-dimensional thermal inhomogeneous insulators

One of the important points underlined by the above one-dimensional models is that the thermal transparency of the structure decreases rapidly when more shields are interposed between the thermostats. The exact distance between the shields is not important. In the case of a complex three-dimensional structure filling the space, the number of multiple reflections can increase very rapidly when the internal surface per unit volume becomes larger than the inverse of the distance between the thermostats. The decrease in transferred energy with the number of shields can be interpreted as a decrease if the distance between the thermostats is a given constant. This decrease with depth can be understood in approximate terms as a series of black-body shields between a hot “transmitter” thermostat and a zero-temperature “receiver”. The first shield, close to the hot thermostat, fully absorbs the energy provided but, at equilibrium, re-emits it in the form of radiation in both directions. For one half, back to the hot thermostat and for the other half, to the next shield. Neglecting multiple re-emission, a second shield will further halve the transmitted energy, and so on for the third and other shields. The resulting exponential decrease is only approximately observed in the decays shown in Fig. 3(b) for a few thermostats, because the multiple re-emission tends to slow down the decrease. The observed decay is typical of a tendency to enhanced retro-diffusion. Such a classic weak light localisation [17, 18] can arguably explain the large backscattering of light from white diffusing structures: the base of thick clouds can be quite dark, in spite of the fact they contain few absorbing materials. The top of the same clouds redistribute nearly all the incidental light they receive to higher altitudes, providing a high albedo value. The decay of the light with the depth towards the cloud base is caused, in this case, by multiple scattering on spherical droplets.

Given that the distance between the diffusing elements is often large, structured layers providing a visible white appearance and efficient thermal insulation in the far infrared can often be found. This is particularly useful to animals, such as mammals and birds which live in snowy areas. White color matching that of the snow, is a camouflage useful both to prey and predators. But, at the same time, the same snowy areas are obviously very cold environments, from which the warm-blooded animals need protection. The structure of polar bear or snow fox fur is actually multifunctional, providing both visual camouflage and good thermal insulation.

From this multifunctional point of view, the white peacock is an interesting example of the absence of melanin in an organism that should have inherited a coloring structure. The white peacock is assumed to result from a genetic mutation of a recent ancestor of the Indian blue peacock Pavo cristatus [19] which migrated to the North of Europe, where it forms a stable variation, easily reproduced in captivity. This type of peacock and peahen is entirely white and their offspring are white peafowls. This variation is usually referred to as Pavo cristatus mut. alba. They should not be confused with albino birds: in the alba variation, pigments are systematically found in the eyes and on the feet. The white peacock mutant can still be bred with Pavo cristatus, resulting in a pied bird perfectly able to reproduce.

Feathers are composed of a keratin hollow shaft, the rachis, which support a number of side branches called barbs. The barbs themselves support finer sub-branches called barbules. In the white peacock, the barbs contain a three-dimensional array of large polyhedral cells of about 20 μm extent (see Fig. 6), with thin keratin membranes (about 300 nm width) which can diffuse both visible and thermal radiation. In its blue ancestor, the same polyhedral structure is found but walls and cortex are filled with melanin, absorbing considerable amounts of light and decreasing the white coloration [20]. White peacock barbules have evolved to lose the coloring structure of its ancestor [20, 21] and modify its outer structure. They appear as a flat, bulky blade, and, in contrast to the blue peacock, with longitudinal segmentation and long appendages (Fig. 5) which add to its ability to diffuse visible and far-infrared radiation. Lacking melanin, the whole white peacock feather system produces a bright white color, mainly coming from barbs, as seen in Fig. 6. A dense fleece of down fluffy feathers with segmented barbules close to the skin may provide, like for penguins, very effective thermal insulation.The genetic mutations that lead to the loss of all structural coloration of Pavo cristatus does not appear to be a complex morphological modification, as it results from the loss of melanin [22]. The change of barbule’s form does, however, have an impact on thermal regulation and, probably, increases a discoloration which happens to be also very beneficial, making it inconspicuous in the Scandinavian snowy winter. A detailed study taking into account the full 3D barb foam geometry would need to be further investigated in order to determine the influence of melanin on thermal insulation.

 

Fig. 5 a) External shape of blue peacock Pavo cristatus feather’s barbules. b) External shape of white peacock Pavo cristatus mut. alba feather’s barbules. The segments, visible on most birds, are here terminated by long appendages, which add the capacity to diffuse light and thermal radiation.

Download Full Size | PPT Slide | PDF

 

Fig. 6 Feather’s barb from the train of a white peacock. a) scanning electron microscopy cross-section. The barbs, by contrast to the uniformly solid barbules, are structured by large polyhedral cells. b) Optical microscope view. The white coloration is identified coming from the barb polyhedral cells. Barbules are seen as transparent with diffusing white at their appendages.

Download Full Size | PPT Slide | PDF

The considerations here are also important for artificial insulating layers, which are needed for passive thermal regulation of future human habitats. Insulation can help to avoid energy consumption, both in summer and winter. It is already known that woolly materials such as rock or glass wool can be very good thermal insulators when their layer is thick enough (modern specifications tend to recommend a thickness of about 50 cm for roof insulation in Northern European countries). This thickness requirement is directly correlated to the increase of the number of interfaces for multiple scattering of far infrared.

Consideration of heat transfer by radiation is mandatory in certain cases, where vacuum layers are involved. We know of structures such as Dewar bottles [23] where highly reflective metal-coated glass, separated by evacuated space, act to slow down heat transfer. These are a special case of the structures studied here. They have important applications in science, medicine and everyday use.

Other important areas where radiative thermal insulation is vital are spatial applications, outside the Earth’s atmosphere. No conduction or convection through air can occur there, and the only cooling or heating mechanism uses radiation. Satellites would be a good place to use the physical principles examined in the present work. Here, there are difficult challenges posed by some instruments, firstly, because the temperature differences between the parts exposed to the Sun and those in the dark are extremely high. In some cases, the active parts must be maintained at a temperature of 0.1 K, while the rest of the instrument is exposed to high and fluctuating temperatures [24]. The design of a challenging thermal shield protecting the radiometers was crucial: the designers came up with multiple V-grooved reflector able to provide passive cooling to the level of 50 K.

6. Conclusion

Because of their efficient scattering power, criss-crossed fibrous materials are effective localisers of thermal radiation. Starting from the one-dimensional models presented here, new tracks for functional optimization can certainly be found. Guided by the the results from Fig. 4, a stack of thin metal layers, separated by thin homogeneous or fibrous spacing layers might provide an insulating system that can be as efficient or even outperform actual systems, while keeping the thickness to a much more manageable minimum [25]. Reports have been published showing that insulating layers with such a structure can be 3 to 5 times thinner than standard woolly layers, with similar performances [26].

Natural selection means that organisms gradually change when exposed to extreme conditions. Polar bear fur contains several different sizes of hair, with a large density of interfaces. This produces the scattering needed to retrodiffuse heat. A polar bear (Ursus maritimus) does not produce a strong thermal image against snow. The same structure also gives it its white color because the illuminating daylight is effectively scattered over the fur. The slight greenish coloration of these bears is actually related to the presence of marine algae that develop in the fur and absorb blue light as most plant forms. The dromedary (Camelus dromedarius) has to deal with a different challenge: keeping heat out of his body. Here again, a double layer of hair, with a strong melanin concentration reduction, provides the necessary multiple scattering of solar radiation, from the outside, to help in blocking heat absorption. It should be observed here that the scattered radiation corresponds to the solar spectrum, which only contains visible, some UV and near infrared rays. The thermal insulation here is then directly related to the visual appearance of the animal and the elimination of thermal absorption is directly visible in the luminosity and the desaturation of the color of the dromedary fur.

This work, which wants to contribute to the understanding of thermal insulation in living systems, suggests that radiative thermal transfer provides a better view of thermal insulation than the more frequent approach based on the low thermal conductance of air. Structures like furs and arrays of feathers do slow down air convection, but radiation seems to be much faster than conductance to provide thermal leaks. So, the control of thermal radiation seems to be the dominant factor for biological adaptation in organisms like mammals and birds living in very high or cold environments and which need to control heat exchange efficiently.

Acknowledgments

P. Simonis acknowledges S. Upton for helpful comments on the manuscript. The project was partly funded by the “Actions Concertées” (ARC), Grant No 10/15-033 from the Belgian Federation Wallonia-Brussels. This research used resources of the ”Plateforme Technologique de Calcul Intensif (PTCI)” (http://www.ptci.unamur.be) located at the University of Namur, Belgium, which is supported by the F.R.S.-FNRS. The PTCI is member of the ”Consortium des Equipements de Calcul Intensif (CECI)”.

References and links

1. H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, and T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012). [CrossRef]  

2. B.J. Teerink, Hair of West-European Mammals (Cambridge University, 1991).

3. P. R. Morrison and W. J. Tietz, “Cooling and thermal conductivity in three small Alaskan mammals,” J. Mammal. 38(1), 78–86 (1957). [CrossRef]  

4. C. F. Herreid and B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967). [CrossRef]   [PubMed]  

5. G. S. Bakken, “Wind speed dependence of the overall thermal conductance of fur and feather insulation,” J. Therm. Biol. 16(2), 121–126 (1991). [CrossRef]  

6. J. C. McLoughlin, Synapsida: A New Look into the Origin of Mammals (Viking, 1980).

7. R. J. G. Savage and M. R. Long, Mammal Evolution, an Illustrated Guide (Facts On File Inc., 1986).

8. P. F. Scholander, R. Hock, V. Walters, and L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950). [CrossRef]   [PubMed]  

9. C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, and P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999). [CrossRef]   [PubMed]  

10. C. D. Stahel and S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).

11. L. B. Davis and R. C. Birkebak, “Convective energy transfer in fur,” in Perspectives in Biophysical Ecology, Vol. 12 of Ecological Studies (Springer, 1975), pp. 525–548. [CrossRef]  

12. G. E. Walsberg, “The significance of fur structure for solar heat gain in the rock squirrel, Spermophilus variegatus,” J. Exp. Biol. 138, 243–257 (1988). [PubMed]  

13. G. E. Walsberg, “Consequences of skin color and fur properties for solar heat gain and ultraviolet irradiance in two mammals,” J. Comp. Physiol. B 158(2), 213–221 (1988). [CrossRef]   [PubMed]  

14. C. Skowron and M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).

15. G. Rybicki and A. P. Lightman, Radiative Processes in Astrophysics, (Wiley-Interscience, 1979).

16. K. Stephan and A. Laesecke, “The thermal conductivity of fluid air,” J. Phys. Chem. Ref. Data 14(1), 227–234 (1985). [CrossRef]  

17. C. M. Soukoulis, Photonic Band Gaps and Localization Nato ASI series B 308(Plenum, 1993). [CrossRef]  

18. A. Langendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009). [CrossRef]  

19. R. G. Somes Jr. and R. E. Burger, “Inheritance of the white and pied plumage color patterns in the Indian peafowl (Pavo cristatus),” J. Hered 84(1), 57–62 (1993).

20. S. Yoshioka and S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).

21. J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, and R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003). [CrossRef]   [PubMed]  

22. I. M. Weiss and H. O. K. Kirchner, “The peacock’s train (Pavo cristatus and Pavo cristatus mut. alba) I. Structure, mechanics, and chemistry of the tail feather,” J. Exp. Zool. A Ecol. Genet. Physiol. 313, 690–703 (2010). [CrossRef]   [PubMed]  

23. R. Soulen, “James Dewar, his flask and other achievements,” Phys. Today 49(3), 32–37 (1996). [CrossRef]  

24. F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, and L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001). [CrossRef]  

25. U. Sivert and A. Heidi, “Thermal insulation performance of reflective material layers in well insulated timber frame structures,” in Proceedings of 8th Symp. Building Physics in the Nordic Countries1, 1–8 (2008).

26. T. I. Ward and S. M. Doran, “The thermal performance of multi-foil insulation,” U. K. Government Building Regulation Report, (2005).

References

  • View by:
  • |
  • |
  • |

  1. H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
    [CrossRef]
  2. B.J. Teerink, Hair of West-European Mammals (Cambridge University, 1991).
  3. P. R. Morrison, W. J. Tietz, “Cooling and thermal conductivity in three small Alaskan mammals,” J. Mammal. 38(1), 78–86 (1957).
    [CrossRef]
  4. C. F. Herreid, B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967).
    [CrossRef] [PubMed]
  5. G. S. Bakken, “Wind speed dependence of the overall thermal conductance of fur and feather insulation,” J. Therm. Biol. 16(2), 121–126 (1991).
    [CrossRef]
  6. J. C. McLoughlin, Synapsida: A New Look into the Origin of Mammals (Viking, 1980).
  7. R. J. G. Savage, M. R. Long, Mammal Evolution, an Illustrated Guide (Facts On File Inc., 1986).
  8. P. F. Scholander, R. Hock, V. Walters, L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
    [CrossRef] [PubMed]
  9. C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
    [CrossRef] [PubMed]
  10. C. D. Stahel, S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).
  11. L. B. Davis, R. C. Birkebak, “Convective energy transfer in fur,” in Perspectives in Biophysical Ecology, Vol. 12 of Ecological Studies (Springer, 1975), pp. 525–548.
    [CrossRef]
  12. G. E. Walsberg, “The significance of fur structure for solar heat gain in the rock squirrel, Spermophilus variegatus,” J. Exp. Biol. 138, 243–257 (1988).
    [PubMed]
  13. G. E. Walsberg, “Consequences of skin color and fur properties for solar heat gain and ultraviolet irradiance in two mammals,” J. Comp. Physiol. B 158(2), 213–221 (1988).
    [CrossRef] [PubMed]
  14. C. Skowron, M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).
  15. G. Rybicki, A. P. Lightman, Radiative Processes in Astrophysics, (Wiley-Interscience, 1979).
  16. K. Stephan, A. Laesecke, “The thermal conductivity of fluid air,” J. Phys. Chem. Ref. Data 14(1), 227–234 (1985).
    [CrossRef]
  17. C. M. Soukoulis, Photonic Band Gaps and Localization Nato ASI series B 308(Plenum, 1993).
    [CrossRef]
  18. A. Langendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
    [CrossRef]
  19. R. G. Somes, R. E. Burger, “Inheritance of the white and pied plumage color patterns in the Indian peafowl (Pavo cristatus),” J. Hered 84(1), 57–62 (1993).
  20. S. Yoshioka, S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).
  21. J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
    [CrossRef] [PubMed]
  22. I. M. Weiss, H. O. K. Kirchner, “The peacock’s train (Pavo cristatus and Pavo cristatus mut. alba) I. Structure, mechanics, and chemistry of the tail feather,” J. Exp. Zool. A Ecol. Genet. Physiol. 313, 690–703 (2010).
    [CrossRef] [PubMed]
  23. R. Soulen, “James Dewar, his flask and other achievements,” Phys. Today 49(3), 32–37 (1996).
    [CrossRef]
  24. F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
    [CrossRef]
  25. U. Sivert, A. Heidi, “Thermal insulation performance of reflective material layers in well insulated timber frame structures,” in Proceedings of 8th Symp. Building Physics in the Nordic Countries1, 1–8 (2008).
  26. T. I. Ward, S. M. Doran, “The thermal performance of multi-foil insulation,” U. K. Government Building Regulation Report, (2005).

2012 (1)

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

2010 (1)

I. M. Weiss, H. O. K. Kirchner, “The peacock’s train (Pavo cristatus and Pavo cristatus mut. alba) I. Structure, mechanics, and chemistry of the tail feather,” J. Exp. Zool. A Ecol. Genet. Physiol. 313, 690–703 (2010).
[CrossRef] [PubMed]

2009 (1)

A. Langendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[CrossRef]

2003 (1)

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

2002 (1)

S. Yoshioka, S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).

1999 (1)

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

1996 (1)

R. Soulen, “James Dewar, his flask and other achievements,” Phys. Today 49(3), 32–37 (1996).
[CrossRef]

1993 (1)

R. G. Somes, R. E. Burger, “Inheritance of the white and pied plumage color patterns in the Indian peafowl (Pavo cristatus),” J. Hered 84(1), 57–62 (1993).

1991 (1)

G. S. Bakken, “Wind speed dependence of the overall thermal conductance of fur and feather insulation,” J. Therm. Biol. 16(2), 121–126 (1991).
[CrossRef]

1988 (2)

G. E. Walsberg, “The significance of fur structure for solar heat gain in the rock squirrel, Spermophilus variegatus,” J. Exp. Biol. 138, 243–257 (1988).
[PubMed]

G. E. Walsberg, “Consequences of skin color and fur properties for solar heat gain and ultraviolet irradiance in two mammals,” J. Comp. Physiol. B 158(2), 213–221 (1988).
[CrossRef] [PubMed]

1985 (1)

K. Stephan, A. Laesecke, “The thermal conductivity of fluid air,” J. Phys. Chem. Ref. Data 14(1), 227–234 (1985).
[CrossRef]

1982 (1)

C. D. Stahel, S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).

1980 (1)

C. Skowron, M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).

1967 (1)

C. F. Herreid, B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967).
[CrossRef] [PubMed]

1957 (1)

P. R. Morrison, W. J. Tietz, “Cooling and thermal conductivity in three small Alaskan mammals,” J. Mammal. 38(1), 78–86 (1957).
[CrossRef]

1950 (1)

P. F. Scholander, R. Hock, V. Walters, L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Abney, M.

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Bakken, G. S.

G. S. Bakken, “Wind speed dependence of the overall thermal conductance of fur and feather insulation,” J. Therm. Biol. 16(2), 121–126 (1991).
[CrossRef]

Bersanelli, M.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Berta, A.

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Birkebak, R. C.

L. B. Davis, R. C. Birkebak, “Convective energy transfer in fur,” in Perspectives in Biophysical Ecology, Vol. 12 of Ecological Studies (Springer, 1975), pp. 525–548.
[CrossRef]

Burger, R. E.

R. G. Somes, R. E. Burger, “Inheritance of the white and pied plumage color patterns in the Indian peafowl (Pavo cristatus),” J. Hered 84(1), 57–62 (1993).

Burigana, C.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Butler, R.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Costa, D. P.

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Davis, L. B.

L. B. Davis, R. C. Birkebak, “Convective energy transfer in fur,” in Perspectives in Biophysical Ecology, Vol. 12 of Ecological Studies (Springer, 1975), pp. 525–548.
[CrossRef]

Dawson, C.

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

Doran, S. M.

T. I. Ward, S. M. Doran, “The thermal performance of multi-foil insulation,” U. K. Government Building Regulation Report, (2005).

Forshaw, P.

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

Fu, R.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Heidi, A.

U. Sivert, A. Heidi, “Thermal insulation performance of reflective material layers in well insulated timber frame structures,” in Proceedings of 8th Symp. Building Physics in the Nordic Countries1, 1–8 (2008).

Herreid, C. F.

C. F. Herreid, B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967).
[CrossRef] [PubMed]

Hock, R.

P. F. Scholander, R. Hock, V. Walters, L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Hu, X.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Irving, L.

P. F. Scholander, R. Hock, V. Walters, L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Jeronimidis, G.

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

Kern, M.

C. Skowron, M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).

Kessel, B.

C. F. Herreid, B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967).
[CrossRef] [PubMed]

Kinoshita, S.

S. Yoshioka, S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).

Kirchner, H. O. K.

I. M. Weiss, H. O. K. Kirchner, “The peacock’s train (Pavo cristatus and Pavo cristatus mut. alba) I. Structure, mechanics, and chemistry of the tail feather,” J. Exp. Zool. A Ecol. Genet. Physiol. 313, 690–703 (2010).
[CrossRef] [PubMed]

Laesecke, A.

K. Stephan, A. Laesecke, “The thermal conductivity of fluid air,” J. Phys. Chem. Ref. Data 14(1), 227–234 (1985).
[CrossRef]

Langendijk, A.

A. Langendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[CrossRef]

Li, Y.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Lightman, A. P.

G. Rybicki, A. P. Lightman, Radiative Processes in Astrophysics, (Wiley-Interscience, 1979).

Liu, X.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Liwanag, H. E. M.

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Long, M. R.

R. J. G. Savage, M. R. Long, Mammal Evolution, an Illustrated Guide (Facts On File Inc., 1986).

Mandolesi, N.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

McLoughlin, J. C.

J. C. McLoughlin, Synapsida: A New Look into the Origin of Mammals (Viking, 1980).

Mennella, A.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Morgante, G.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Morrison, P. R.

P. R. Morrison, W. J. Tietz, “Cooling and thermal conductivity in three small Alaskan mammals,” J. Mammal. 38(1), 78–86 (1957).
[CrossRef]

Nicol, S. C.

C. D. Stahel, S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).

Rice, G.

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

Rybicki, G.

G. Rybicki, A. P. Lightman, Radiative Processes in Astrophysics, (Wiley-Interscience, 1979).

Sandri, M.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Savage, R. J. G.

R. J. G. Savage, M. R. Long, Mammal Evolution, an Illustrated Guide (Facts On File Inc., 1986).

Scholander, P. F.

P. F. Scholander, R. Hock, V. Walters, L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Sivert, U.

U. Sivert, A. Heidi, “Thermal insulation performance of reflective material layers in well insulated timber frame structures,” in Proceedings of 8th Symp. Building Physics in the Nordic Countries1, 1–8 (2008).

Skowron, C.

C. Skowron, M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).

Somes, R. G.

R. G. Somes, R. E. Burger, “Inheritance of the white and pied plumage color patterns in the Indian peafowl (Pavo cristatus),” J. Hered 84(1), 57–62 (1993).

Soukoulis, C. M.

C. M. Soukoulis, Photonic Band Gaps and Localization Nato ASI series B 308(Plenum, 1993).
[CrossRef]

Soulen, R.

R. Soulen, “James Dewar, his flask and other achievements,” Phys. Today 49(3), 32–37 (1996).
[CrossRef]

Stahel, C. D.

C. D. Stahel, S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).

Stephan, K.

K. Stephan, A. Laesecke, “The thermal conductivity of fluid air,” J. Phys. Chem. Ref. Data 14(1), 227–234 (1985).
[CrossRef]

Teerink, B.J.

B.J. Teerink, Hair of West-European Mammals (Cambridge University, 1991).

Terenzi, L.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Tietz, W. J.

P. R. Morrison, W. J. Tietz, “Cooling and thermal conductivity in three small Alaskan mammals,” J. Mammal. 38(1), 78–86 (1957).
[CrossRef]

Valenziano, L.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

van Tiggelen, B.

A. Langendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[CrossRef]

Villa, F.

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

Vincent, J. F. V.

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

Walsberg, G. E.

G. E. Walsberg, “The significance of fur structure for solar heat gain in the rock squirrel, Spermophilus variegatus,” J. Exp. Biol. 138, 243–257 (1988).
[PubMed]

G. E. Walsberg, “Consequences of skin color and fur properties for solar heat gain and ultraviolet irradiance in two mammals,” J. Comp. Physiol. B 158(2), 213–221 (1988).
[CrossRef] [PubMed]

Walters, V.

P. F. Scholander, R. Hock, V. Walters, L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Wang, X.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Ward, T. I.

T. I. Ward, S. M. Doran, “The thermal performance of multi-foil insulation,” U. K. Government Building Regulation Report, (2005).

Weiss, I. M.

I. M. Weiss, H. O. K. Kirchner, “The peacock’s train (Pavo cristatus and Pavo cristatus mut. alba) I. Structure, mechanics, and chemistry of the tail feather,” J. Exp. Zool. A Ecol. Genet. Physiol. 313, 690–703 (2010).
[CrossRef] [PubMed]

Wiersma, D. S.

A. Langendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[CrossRef]

Williams, T. M.

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Xu, C.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Yoshioka, S.

S. Yoshioka, S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).

Yu, X.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Zi, J.

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Auk (1)

C. Skowron, M. Kern, “The insulation in nests of selected North-American songbirds,” Auk 97(4), 816–824 (1980).

Biol. Bull. (1)

P. F. Scholander, R. Hock, V. Walters, L. Irving, “Adaptation to cold in artic and tropical mammals and birds in relation to body temperature, insulation and basal metabolic rate,” Biol. Bull. 99(2), 259–271 (1950).
[CrossRef] [PubMed]

Biol. J. Linn. Soc. (1)

H. E. M. Liwanag, A. Berta, D. P. Costa, M. Abney, T. M. Williams, “Morphological and thermal properties of mammalian insulation: the evolution of fur for aquatic living,” Biol. J. Linn. Soc. 106, 926–939 (2012).
[CrossRef]

Comp. Biochem. Physiol. (1)

C. F. Herreid, B. Kessel, “Thermal conductance in birds and mammals,” Comp. Biochem. Physiol. 21(2), 405–414 (1967).
[CrossRef] [PubMed]

Forma (1)

S. Yoshioka, S. Kinoshita, “Effect of macroscopic structure in iridescent color of the peacock feathers,” Forma 17, 169–181 (2002).

J. Comp. Physiol. (1)

C. D. Stahel, S. C. Nicol, “Temperature regulation in the little penguin, Eudyptula minor, in air and water,” J. Comp. Physiol. 148, 93–100 (1982).

J. Comp. Physiol. B (1)

G. E. Walsberg, “Consequences of skin color and fur properties for solar heat gain and ultraviolet irradiance in two mammals,” J. Comp. Physiol. B 158(2), 213–221 (1988).
[CrossRef] [PubMed]

J. Exp. Biol. (1)

G. E. Walsberg, “The significance of fur structure for solar heat gain in the rock squirrel, Spermophilus variegatus,” J. Exp. Biol. 138, 243–257 (1988).
[PubMed]

J. Exp. Zool. A Ecol. Genet. Physiol. (1)

I. M. Weiss, H. O. K. Kirchner, “The peacock’s train (Pavo cristatus and Pavo cristatus mut. alba) I. Structure, mechanics, and chemistry of the tail feather,” J. Exp. Zool. A Ecol. Genet. Physiol. 313, 690–703 (2010).
[CrossRef] [PubMed]

J. Hered (1)

R. G. Somes, R. E. Burger, “Inheritance of the white and pied plumage color patterns in the Indian peafowl (Pavo cristatus),” J. Hered 84(1), 57–62 (1993).

J. Mammal. (1)

P. R. Morrison, W. J. Tietz, “Cooling and thermal conductivity in three small Alaskan mammals,” J. Mammal. 38(1), 78–86 (1957).
[CrossRef]

J. Phys. Chem. Ref. Data (1)

K. Stephan, A. Laesecke, “The thermal conductivity of fluid air,” J. Phys. Chem. Ref. Data 14(1), 227–234 (1985).
[CrossRef]

J. Theor. Biol. (1)

C. Dawson, J. F. V. Vincent, G. Jeronimidis, G. Rice, P. Forshaw, “Heat transfer through penguin feathers,” J. Theor. Biol. 199, 291–295 (1999).
[CrossRef] [PubMed]

J. Therm. Biol. (1)

G. S. Bakken, “Wind speed dependence of the overall thermal conductance of fur and feather insulation,” J. Therm. Biol. 16(2), 121–126 (1991).
[CrossRef]

Phys. Today (2)

R. Soulen, “James Dewar, his flask and other achievements,” Phys. Today 49(3), 32–37 (1996).
[CrossRef]

A. Langendijk, B. van Tiggelen, D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. Zi, X. Yu, Y. Li, X. Hu, C. Xu, X. Wang, X. Liu, R. Fu, “Coloration strategies in peacock feathers,” Proc. Natl. Acad. Sci. U.S.A. 100(22), 12576–12578 (2003).
[CrossRef] [PubMed]

Other (9)

F. Villa, M. Bersanelli, C. Burigana, R. Butler, N. Mandolesi, A. Mennella, G. Morgante, M. Sandri, L. Terenzi, L. Valenziano, “The Planck telescope,” in AIP Conference Proceedings616, 224–228 (2001).
[CrossRef]

U. Sivert, A. Heidi, “Thermal insulation performance of reflective material layers in well insulated timber frame structures,” in Proceedings of 8th Symp. Building Physics in the Nordic Countries1, 1–8 (2008).

T. I. Ward, S. M. Doran, “The thermal performance of multi-foil insulation,” U. K. Government Building Regulation Report, (2005).

J. C. McLoughlin, Synapsida: A New Look into the Origin of Mammals (Viking, 1980).

R. J. G. Savage, M. R. Long, Mammal Evolution, an Illustrated Guide (Facts On File Inc., 1986).

B.J. Teerink, Hair of West-European Mammals (Cambridge University, 1991).

C. M. Soukoulis, Photonic Band Gaps and Localization Nato ASI series B 308(Plenum, 1993).
[CrossRef]

G. Rybicki, A. P. Lightman, Radiative Processes in Astrophysics, (Wiley-Interscience, 1979).

L. B. Davis, R. C. Birkebak, “Convective energy transfer in fur,” in Perspectives in Biophysical Ecology, Vol. 12 of Ecological Studies (Springer, 1975), pp. 525–548.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Warm-blooded animals like mammals and birds have hairs or feathers which serve multiple functions. One of them is camouflage, when the coloration or pattern of coloration matches the background to make the animal less conspicuous. However, a more ancient function must have been thermal insulation. A good example is the polar bear (Ursus maritimus), where the thick white hair clearly needs to serve these functions. Alan D. Wilson, Polar Bear (Sow), Kaktovik, Barter Island, Alaska, with permission.

Fig. 2
Fig. 2

a) A simple model for the “radiative insulator” described in section 3. A hot black body thermostat at temperature Ta faces a cold black body thermostat at temperature Tb. The exchange of energy between these thermostats is only radiative. The insulator is a set of n black or grey sheets interposed between the thermostats. b) Energy exchanges between two neighboring sheets, say sheets i and i + 1, are denoted I i + and I i + 1 , for energy travelling to sheet i + 1 and to sheet i, respectively.

Fig. 3
Fig. 3

a) Distribution of the equilibrium temperatures of 100 black-body sheets, shielding thermostats at 37°C and −40°C. b) Base 10 logarithm of the energy attenuation factor as a function of the number of black-body shielding sheets, for thermostats at 37°C and −40°C. Only radiative energy exchanges are included in the model.

Fig. 4
Fig. 4

a) Distribution of the equilibrium temperatures of 100 grey-body sheets with increasing reflectances: r = 0.0 (black-body result, in blue), 0.2, 0.4, 0.6, 0.8 and 0.99 (magenta), shielding thermostats at 37°C and −40°C. b) Base 10 logarithm of the energy attenuation factor as a function of the number of grey-body shielding sheets, for thermostats at 37°C and −40°C. The shields are assumed opaque to far infrared radiation (t = 0). The upper curve is the black-body shields result and simply repeats the results shown in Fig. 3. The lower ones, from top down, correspond to increasing reflectances: r = 0.2, 0.4, 0.6, 0.8 and 0.99.

Fig. 5
Fig. 5

a) External shape of blue peacock Pavo cristatus feather’s barbules. b) External shape of white peacock Pavo cristatus mut. alba feather’s barbules. The segments, visible on most birds, are here terminated by long appendages, which add the capacity to diffuse light and thermal radiation.

Fig. 6
Fig. 6

Feather’s barb from the train of a white peacock. a) scanning electron microscopy cross-section. The barbs, by contrast to the uniformly solid barbules, are structured by large polyhedral cells. b) Optical microscope view. The white coloration is identified coming from the barb polyhedral cells. Barbules are seen as transparent with diffusing white at their appendages.

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

d W d t = ( K S L ) ( T a T b ) .
K = { 0.0204 W / mK ( 50 ° C ) 0.0243 W / mK ( 0 ° C ) 0.0257 W / mK ( 20 ° C ) 0.0271 W / mK ( 40 ° C ) 0.0285 W / mK ( 60 ° C )
1 S d W d t 37.4 W / m 2 .
d W d t = σ S ( T a 4 T b 4 ) .
1 S d W d t 356.5 W / m 2 .
R 0 = 1 S d W d t = σ ( T a 4 T b 4 ) .
w i = σ T i 4 .
I i + = I i = w i .
I 0 + = σ T a 4 = w a .
I n + 1 = σ T b 4 = w b .
I i + I i + = I i 1 + + I i + 1 .
I i + I i + 1 = I i 1 + I i ,
w i 1 2 w i + w i + 1 = 0
2 w 1 + w 2 = w a
w n 1 2 w n = w b .
η ( n ) = I i + I i + 1 R 0 = I 0 + I 1 R 0 .
I i + = 1 1 r 2 j = 0 i 1 ( t 1 r 2 ) j w i j + r 1 r 2 j = 1 n i ( t 1 r 2 ) j 1 w i + j + ( t 1 r 2 ) i w a + r ( t 1 r 2 ) n i w b
I i = r 1 r 2 j = 1 i 1 ( t 1 r 2 ) j 1 w i j + 1 1 r 2 j = 0 n i ( t 1 r 2 ) j w i + j + r ( t 1 r 2 ) i 1 w a + r ( t 1 r 2 ) n i + 1 w b .
I 0 + = w a
I 1 = j = 1 n ( t 1 r 2 ) j 1 w j + r w a + t ( t 1 r 2 ) n 1 w b
I n + 1 = w b
I n + = j = 1 n ( t 1 r 2 ) j 1 w n + 1 j + r w b + t ( t 1 r 2 ) n 1 w a .
I 0 + = w a
I n + = w n + r w b
I i + = 1 1 r 2 w i + r 1 r 2 w i + 1
I 1 = w 1 + r w a
I n + 1 = w b
I i = r 1 r 2 w i 1 + 1 1 r 2 w i .

Metrics