Linear response theory temperature

Figure 5 Typical velocity relationship of kinetic friction for a sliding contact in which friction is from adsorbed layers confined between two incommensurate walls. The kinetic friction F is normalized by the static friction Fs. At extremely small velocities v, the confined layer is close to thermal equilibrium and, consequently, F is linear in v, as to be expected from linear response theory. In an intermediate velocity regime, the velocity dependence of F is logarithmic. Instabilities or pops of the atoms can be thermally activated. At large velocities, the surface moves too quickly for thermal effects to play a role. Time-temperature superposition could be applied. All data were scaled to one reference temperature. Reprinted with permission from Ref. 25. 

The dependencies of the signal-to-noise ratio S on the temperature parameter a-1 = T/KVm obtained are shown in Figures 4.14 and 4.15. Note that within the framework of the linear response theory, our approach removes all the... 

One can then try to extend the linear response theory with the help of an effective temperature [5,6]. 

In an out-of-equilibrium environment, no well-defined thermodynamical temperature does exist. Since, in an out-of-equilibrium regime, even if stationary, the FDTs are not satisfied, one can try to rewrite them in a modified way, and thus to extend linear response theory, with the help of a (frequency-dependent) effective temperature. 

Transport coefficients of molecular model systems can be calculated by two methods [8] Equilibrium Green-Kubo (GK) methods where one evaluates the GK-relation for the transport coefficient in question by performing an equilibrium molecular dynamics (EMD) simulation and Nonequilibrium molecular dynamics (NEMD) methods. In the latter case one couples the system to a fictitious mechanical field. The algebraical expression for the field is chosen in such a way that the currents driven by the field are the same as the currents driven by real Navier-Stokes forces such as temperature gradients, chemical potential gradients or velocity gradients. By applying linear response theory one can prove that the zero field limit of the ratio of the current and the field is equal to the transport coefficient in question. 

Prom statistical linear response theory, the infrared spectrum of a sample at temperature T is ... 

At T 0 the sharp lines corresponding to the harmonic modes are broadened by anharmonic effects until, at high temperature, the simple relationship between vibrational density of states and dynamical matrix is lost. In this regime, and especially for large aggregates, MD is the most suitable tool to compute the vibrational spectrum. Standard linear response theory within classical statistical mechanics shows that the spectrum f(co) is given by the Fourier transform of the velocity-velocity autocorrelation function... 

One of the most important principles of linear response theory relates the system s response to an externally imposed perturbation, which causes it to depart from equilibrium, to its equilibrium fluctuations. Indeed, the system response to a small perturbation should not depend on whether this perturbation is a result of some external force, or whether it is just a random thermal fluctuation. Spontaneous concentration fluctuations, for instance, occur all the time in equilibrium systems at finite temperatures. If the concentration c at some point of a liquid at time zero is (c) + 3c(r, t), where (c) is an average concentration, concentration values at time t + 8t dXt and other points in its vicinity will be affected by this. The relaxation of the spontaneous concentration fluctuation is governed by the same diffusion equation that describes the evolution of concentration in response to the external imposition of a compositional heterogeneity. The relationship between kinetic coefficients and correlations of the fluctuations is derived in the framework of linear response theory. In general, a kinetic coefficient is related to the integral of the time correlation function of some relevant microscopic quantity. 

Zwanzig (65) considered a lattice model of dipoles reorienting by rotational diffusion and coupled by electrostatic dipole-dipole interaction energy. He was able to obtain results by a high temperature expansion of the Boltzmann factor in the linear response theory correlation... 

There is also a step-based equivalent technique founded on linear-response theory. This has been presented by Schick and co-workers [19] and is formally equivalent to the real and imaginary heat capacities generated by modulation at a single frequency. In principle, it is therefore possible to apply a Fourier transform to step-scan type data and break down the overall response into heat flow responses to a series of sinusoidal temperature modulations. 

According to the theory of linear response the transverse dielectric tensor of a crystal at temperature T = 0 is determined by the relation... 

UHMWPE specimens subjected to very small strains, while exploration of hyperelasticity theory led to the conclusion that it is often safer to use a more sophisticated constitutive model when modeling UHMWPE. The use of linear viscoelasticity theory led to a reasonable prediction for the response of the material during a uniaxial compression test however, even small changes to the strain rate rendered the previously identified material parameters unsatisfactory. Isotropic J2-plasticity theory provided excellent predictions under monotonic, uniaxial, constant-strain rate, constant-temperature conditions, but it was unable to predict reasonable results for a cyclic test. The augmented Hybrid Model was capable of predicting the behavior of UHMWPE during a uniaxial tension test, a cyclic uniaxial fully... 

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