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The focus of this paper is on topology optimization of continuum structures subject to thermally induced buckling. Popular strategies for solving such problems include Solid Isotropic Material with Penalization (SIMP) and Rational…
A model for comminution processes in ball mills is presented. The model provides an empirical approach using the physically realistic modelization of the ball mill system, but also deployes the statistical method to extract relevant…
In safety-critical applications a probabilistic model is usually required to be calibrated, i.e., to capture the uncertainty of its predictions accurately. In multi-class classification, calibration of the most confident predictions only is…
In this paper, we review the set of rules specific to the calculation of the imaginary part of a Green's function at finite temperature in the real-time formalisms. Emphasis is put on the clarification of a recent controversy concerning…
We describe a method for computing the response of an insulator to a static, homogeneous electric field. It consists of iteratively minimizing an electric enthalpy functional expressed in terms of occupied Bloch-like states on a uniform…
Finite temperature correlation functions in integrable quantum field theories are formulated only in terms of the usual, temperature-independent form factors, and certain thermodynamic filling fractions which are determined from the…
In this work, we present a compact analytical approximation for the quantum partition function of systems composed of quantum oscillators. The proposed formula is general and applicable to an arbitrary number of oscillators described by a…
Providing students of introductory thermal physics with a plot of the heat capacities of many low density gases as a function of temperature allows them to look for systematic trends. Specifically, large amounts of heat capacity data allow…
We present a method based on Mueller calculus to calibrate linear polarimetric observations. The key advantages of the proposed way of calibration are: (1) that it can be implemented in a data reduction pipeline, (2) that it is possible to…
Molecular dynamics simulations of a three dimensional relativistic gas with a soft potential are conducted with different interactions and particle masses. For all cases the velocity distribution agrees numerically with the J\"uttner…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
Thermodynamic functions of the ideal Fermi gas at arbitrary temperatures are calculated using the standard Fermi-Stoner functions. The properties of the Fermi-Stoner functions are analyzed. The limiting cases of low-temperature and…
We construct, using fermionic functional integrals, thermodynamic Green's functions for a weakly coupled fermion gas whose Fermi energy lies in a gap. Estimates on the Green's functions are obtained that are characteristic of the size of…
The holographic product formula is used to determine the general form taken by holographic spectral functions in the near-extremal hydrodynamic regime, with energy $\omega$, momentum $k$ and temperature $T$ much smaller than a hard scale…
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions.…
Temperature fluctuations of a finite system follows the Landau bound $\delta T^2 = T^2/C(T)$ where $C(T)$ is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system…
We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second order Casimir differential equations and have integral representations…
Sound attenuation and internal friction coefficients are calculated for a realistic model of amorphous silicon. It is found that, contrary to previous views, thermal vibrations can induce sound attenuation at ultrasonic and hypersonic…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
A theoretical and numerical investigations of the quantum tunneling of the domain walls in ferromagnets and weak ferromagnets was performed taking into account the interaction between walls and thermal excitations of a crystal. The…