Types of evolutionary stability and the problem of cooperation.

The evolutionary stability of cooperation is a problem of fundamental importance for the biological and social sciences. Different claims have been made about this issue: whereas Axelrod and Hamilton's [Axelrod, R. & Hamilton, W. (1981) Science 211, 1390-1398] widely recognized conclusion is that cooperative rules such as "tit for tat" are evolutionarily stable strategies in the iterated prisoner's dilemma (IPD), Boyd and Lorberbaum [Boyd, R. & Lorberbaum, J. (1987) Nature (London) 327, 58-59] have claimed that no pure strategy is evolutionarily stable in this game. Here we explain why these claims are not contradictory by showing in what sense strategies in the IPD can and cannot be stable and by creating a conceptual framework that yields the type of evolutionary stability attainable in the IPD and in repeated games in general. Having established the relevant concept of stability, we report theorems on some basic properties of strategies that are stable in this sense. We first show that the IPD has "too many" such strategies, so that being stable does not discriminate among behavioral rules. Stable strategies differ, however, on a property that is crucial for their evolutionary survival--the size of the invasion they can resist. This property can be interpreted as a strategy's evolutionary robustness. Conditionally cooperative strategies such as tit for tat are the most robust. Cooperative behavior supported by these strategies is the most robust evolutionary equilibrium: the easiest to attain, and the hardest to disrupt.

Study of stability for non-linear ordinary differential equations.

"C00-1469-0118."

On the stability of elastic equilibrium

Translation of Over de stabiliteit van het elastisch evenwicht (Thesis, Polytechnic Institute of Delft, 1945)

Chemical non-equilibrium shock flow,

"Work performed for the Ballistic Systems Divisions, USAF, under Contract no. AF04(647)-617."

Effects of hydrogen-air non-equilibrium chemistry on the performance of a model scramjet thrust nozzle

Two aspects of hydrogen-air non-equilibrium chemistry related to scramjets are nozzle freezing and a process called 'kinetic afterburning' which involves continuation of combustion after expansion in the nozzle. These effects were investigated numerically and experimentally with a model scramjet combustion chamber and thrust nozzle combination. The overall model length was 0.5m, while precombustion Mach numbers of 3.1 +/- 0.3 and precombustion temperatures ranging from 740K to 1,400K were involved. Nozzle freezing was investigated at precombustion pressures of 190kPa and higher, and it was found that the nozzle thrusts were within 6% of values obtained from finite rate numerical calculations, which were within 7% of equilibrium calculations. When precombustion pressures of 70kPa or less were used, kinetic afterburning was found to be partly responsible for thrust production, in both the numerical calculations and the experiments. Kinetic afterburning offers a means of extending the operating Mach number range of a fixed geometry scramjet.

Stability for parametric implicit vector equilibrium problems

In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters is an element of and lambda respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S : Lambda(1) x A(2) -> 2(X) for such parametric implicit vector equilibrium problems. (c) 2005 Elsevier Ltd. All rights reserved.

αα'-trehalose 6,6'-dibehenate in non-phospholipid-based liposomes enables direct interaction with trehalose, offering stability during freeze-drying

Trehalose is a well known protector of biostructures like liposomes and proteins during freeze-drying, but still today there is a big debate regarding its mechanism of action. In previous experiments we have shown that trehalose is able to protect a non-phospholipid-based liposomal adjuvant (designated CAF01) composed of the cationic dimethyldioctadecylammonium (DDA) and trehalose 6,6-dibehenate (TDB) during freeze-drying [D. Christensen, C. Foged, I. Rosenkrands, H.M. Nielsen, P. Andersen, E.M. Agger, Trehalose preserves DDA/TDB liposomes and their adjuvant effect during freeze-drying, Biochim. Biophys. Acta, Biomembr. 1768 (2007) 2120-2129]. Furthermore it was seen that TDB is required for the stabilizing effect of trehalose. Herein, we show using the Langmuir-Blodgett technique that a high concentration of TDB present at the water-lipid interface results in a surface pressure around 67 mN/m as compared to that of pure DDA which is approximately 47 mN/m in the compressed state. This indicates that the attractive forces between the trehalose head group of TDB and water are greater than those between the quaternary ammonium head group of DDA and water. Furthermore, addition of trehalose to a DDA monolayer containing small amounts of TDB also increases the surface pressure, which is not observed in the absence of TDB. This suggests that even small amounts of trehalose groups on TDB present at the water-lipid interface associate free trehalose to the liposome surface, presumably by hydrogen bonding between the trehalose head groups of TDB and the free trehalose molecules. Hence, for CAF01 the TDB component not only stabilizes the cationic liposomes and enhances the immune response but also facilitates the cryo-/lyoprotection by trehalose through direct interaction with the head group of TDB. Furthermore the results indicate that direct interaction with liposome surfaces is necessary for trehalose to enable protection during freeze-drying.

Range of validity of weakly non-linear theory in Rayleigh-Bénard problem

In this paper we examine the equilibrium states of finite amplitude flow in a horizontal fluid layer with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau constants and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infinitesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighborhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable. © 2009 The Physical Society of Japan.

Range of validity of weakly non-linear theory in Rayleigh-Bénard convection

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

Memory effects in a non-equilibrium growth model

We study memory effects in a kinetic roughening model. For d=1, a different dynamic scaling is uncovered in the memory dominated phases; the Kardar-Parisi-Zhang scaling is restored in the absence of noise. dc=2 represents the critical dimension where memory is shown to smoothen the roughening front (a=0). Studies on a discrete atomistic model in the same universality class reconfirm the analytical results in the large time limit, while a different scaling behavior shows up for t

Waveguide fabrication in lithium-niobo-phosphate glasses by high repetition rate femtosecond laser:route to non-equilibrium material’s states

We study waveguide fabrication in lithium-niobo-phosphate glass, aiming at a practical method of single-stage fabrication of nonlinear integrated-optics devices. We observed chemical transformations or material redistribution during the course of high repetition rate femtosecond laser inscription. We believe that the laser-induced ultrafast heating and cooling followed by elements diffusion on a microscopic scale opens the way toward the engineering non-equilibrium sates of matter and thus can further enhance Refractive Index (RI) contrasts by virtue of changing glass composition in and around the fs tracks. © 2014 Optical Society of America.