Ergodicity of Some Open Systems with Particle-Disk Interactions

We consider steady states for a class of mechanical systems with particle-disk interactions coupled to two, possibly unequal, heat baths. We show that any steady state that satisfies some natural assumptions is ergodic and absolutely continuous with respect to a Lebesgue-type reference measure and conclude that there exists at most one absolutely continuous steady state.     

Sub-exponential Mixing of Open Systems with Particle–Disk Interactions

We consider a class of mechanical particle systems with deterministic particle–disk interactions coupled to Gibbs heat reservoirs at possibly different temperatures. We show that there exists a unique (non-equilibrium) steady state. This steady state is mixing, but not exponentially mixing, and all initial distributions converge to it. In addition, for a class of initial distributions, the rates of converge to the steady state are sub-exponential.     

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities

We introduce a multidimensional peridynamic formulation for transient heat-transfer. The model does not contain spatial derivatives and uses instead an integral over a region around a material point. By construction, the formulation converges to the classical heat transfer equations in the limit of the horizon (the nonlocal region around a point) going to zero. The new model, however, is suitable for modeling, for example, heat flow in bodies with evolving discontinuities such as growing insulated cracks. We introduce the peridynamic heat flux which exists even at sharp corners or when the isotherms are not smooth surfaces. The peridynamic heat flux coincides with the classical one in simple cases and, in general, it converges to it in the limit of the peridynamic horizon going to zero. We solve test problems and compare results with analytical solutions of the classical model or with other numerical solutions. Convergence to the classical solutions is seen in the limit of the horizon going to zero. We then solve the problem of transient heat flow in a plate in which insulated cracks grow and intersect thus changing the heat flow patterns. We also model heat transfer in a fiber-reinforced composite and observe transient but steep thermal gradients at the interfaces between the highly conductive fibers and the low conductivity matrix. Such thermal gradients can lead to delamination cracks in composites from thermal fatigue. The formulation may be used to, for example, evaluate effective thermal conductivities in bodies with an evolving distribution of insulating or permeable, possibly intersecting, cracks of arbitrary shapes.     

Existence of Nonequilibrium Steady State for a Simple Model of Heat Conduction

This paper contains rigorous results for a simple stochastic model of heat conduction similar to the KMP (Knipnis–Marchiori–Presutti) model but with possibly energy-dependent interaction rates. We prove the existence and uniqueness of nonequilibrium steady states, their relation to Lebesgue measure, and exponential convergence to steady states from suitable initial conditions.     

A variational Bayesian method to inverse problems with impulsive noise

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback–Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm.     

Stabilization of the Soliton Transported Bio-energy in Protein Molecules in the Improved Model

We study the stabilization of the soliton transported bio-energy by the dynamic equations in the improved Davydov theory from four aspects containing the feature of free motion and states of the soliton at the long-time motion and at biological temperature 300 K and behaviors of collision of the solitons by Runge-Kutta method and physical parameter values appropriate to the $\alpha$-helix protein molecules. We prove that the new solitons can move without dispersion at a constant speed retaining its shape and energy in free and long-time motions and can go through each other without scattering. If considering further influence of the temperature effect of heat bath on the soliton, it is still thermally stable at biological temperature 300 K and in a time as long as 300 ps and amino acid spacings as large as 400, which shows that the lifetime of the new soliton is at least 300 ps, which is consistent with analytic result obtained by quantum perturbation theory. These results exhibit that the new soliton is a possible carrier of bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.     

Two superconducting phases in the d=3 Hubbard model

The phase diagram of the d=3 Hubbard model is calculated as a function of temperature and electron density 〈n_i〉, in the full range of densities between 0 and 2 electrons per site, using renormalization-group theory. An antiferromagnetic phase occurs at lower temperatures, at and near the half-filling density of 〈n_i〉= 1. The antiferromagnetic phase is unstable to hole or electron doping of at most 15%, yielding to two distinct“τ" phases: for large coupling U/t, one such phase occurs between 30–35% hole or electron doping, and for small to intermediate coupling U/t another such phase occurs between 10–18% doping. Both τ phases are distinguished by non-zero hole or electron hopping expectation values at all length scales. Under further doping, the τ phases yield to hole- or electron-rich disordered phases. We have calculated the specific heat over the entire phase diagram. The low-temperature specific heat of the weak-coupling τ phase shows an exponential decay, indicating a gap in the excitation spectrum, and a cusp singularity at the phase boundary. The strong-coupling τ phase, on the other hand, has a critical exponent α≈-1, and an additional peak in the specific heat above the transition temperature possibly indicating pair formation. In the limit of large Coulomb repulsion, the phase diagram of the tJ model is recovered.     

Periodic thermodynamics of laser-driven molecular motor

Operation of a laser-driven nano-motor inevitably generates a non-trivial amount of heat, which can possibly lead to instability or even hinder the motor＇s continual running. This work quantitatively examines the overheating problem for a recently proposed laser-operated molecular locomotive. We present a single-molecule cooling theory, in which molecular details of the locomotive system are explicitly treated. This theory is able to quantitatively predict cooling efficiency for various candidates of molecular systems for the locomotive, and also suggests concrete strategies for improving the locomotive＇s cooling. It is found that water environment is able to cool the hot locomotive down to room temperature within 100 picoseconds after photon absorption. This cooling time is a few orders of magnitude shorter than the typical time for laser operation, effectively preventing any overheating for the nano-locomotive. However, when the cooling is less effective in non-aqueous environment, residual heat may build up. A continuous running of the motor will then lead to a periodic thermodynamics, which is a common character of many laser-operated nano-devices.     

DFT study on the effect of relative positions of methyl-, nitro- and N→oxide groups on the molecular structure,thermal/kinetic stability,crystal density,heat of decomposition and performance characteristics of triazolones

Methyl-, nitro- and N→oxide substituted triazolones are of interest in the contest of high-energy density compounds and have been found to have true local energy minima at the B3LYP/aug-cc-pVDZ level. The optimised structures, harmonic frequencies and thermodynamic values for all the model molecules have been obtained in their ground state. The velocity of detonation (D) and detonation pressure (P) have been evaluated by the Kamlet–Jacob equations using the crystal density and the heat of explosion. The estimated performance properties are higher (D = 9.92–10.27 km/s, P = 48.10–52.52 GPa) compared with 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (D = 9.20 km/s, P = 42.0 Gpa). The higher densities are possibly due to the intramolecular hydrogen bonds and the layered structures in the crystal lattice. We speculate that the calculated heat of explosion and the density are for the gas phase compounds and in the reality they should be for the solid phase which would diminish the magnitude of the calculated values. The –N→O and –NO₂ group leads to the desirable consequences of higher heat of explosion and diminished sensitivities. The substituting of N–H hydrogen atom(s) of triazolones for a –CH₃ group decreases melting point, heat of formation and density; however, the methyl group increases the thermal stability.     

Anisotropic effect of Cd and Hg doping on the Pauli limited superconductor CeCoIn5

We studied the effect of impurity on the first order superconducting (SC) transition and the high field-low temperature (HFLT) SC state of CeCoIn5 by measuring the specific heat of CeCo(In1-xCdx)_{5} with x=0.0011, 0.0022, and 0.0033 and CeCo(In1-xHgx)_{5} with x=0.000 16, 0.000 32, and 0.000 48 at temperatures down to 0.1 K and fields up to 14 T. Cd substitution rapidly suppresses the crossover temperature T0, where the SC transition changes from second to first order, to T=0 K with x=0.0022 for H parallel[100], while it remains roughly constant up to x=0.0033 for H parallel[001]. The associated anomaly of the proposed FFLO state in Hg-doped samples is washed out by x=0.000 48, while remaining at the same temperature, indicating high sensitivity of that state to impurities. We interpret these results as supporting the nonmagnetic, possibly FFLO, origin of the HFLT state in CeCoIn5.     

Heat capacity of a current carrying superconductor

We present an analysis of the heat capacity of a superconductor carrying a constant applied electric current. We find that the heat capacity diverges with an exponent of 0.5 at a depressed transition temperature. This result is similar to a recent calculation of the heat capacity of superfluid helium under an applied heat current.     

Low temperature specific heat of diethyl-morpholinium ditetracyanoquino-dimethane [DEM (TCNQ)2]

Specific heat measurements are reported for 0.5 K<T<50 K. Anomalous effects are observed near T = 30 K, which possibly can be attributed to a spin-Peierls transition. At low temperatures the specific heat contains a term linear in T indicating that one half of the TCNQ stacks is still in its unpertubed state.     

Spectral energy balance in dry convective boundary layers

Three-dimensional large-eddy simulations (LES) of the convective boundary layer over a domain of approximately 6 km are performed with the UCLA LES model. Simulations are forced with a constant surface heat flux and prescribed subsidence, and are run to equilibrium. Sub-grid scale fluxes are parameterised with the Smagorinsky–Lilly scheme. A range of grid spacings from 40 down to 5 m are employed. Kinetic energy spectra and the various terms in the kinetic energy spectral budget – heat flux, nonlinear transfer, pressure, and dissipation – are computed using two-dimensional discrete Fourier transforms at every vertical level. Despite the fact that isotropic grid spacings of down to 5 m (grid sizes of 1152²×400) were used, an inertial range with a ?5/3 spectrum is not obtained. Rather, shallower energy spectral slopes that are closer to ?4/3 are found. The shallower spectra are shown to possibly result from the injection of kinetic energy over a wide range of scales via a very broad heat flux spectrum. Only with the highest resolution (Δx = 5 m) does the total heat flux begin to converge and the possibility of local isotropy emerge at small scales. Dependence on surface heat flux and domain size is considered. Preliminary sub-grid scale sensitivity results are obtained through comparison with the turbulent kinetic energy sub-grid scale model.     

Specific heat of graphene nanoribbons

We studied the specific heat of graphene nanoribbons (GNRs) using an extended force constant model. We found that at low temperature, the specific heat decreases, and its variation with temperature increases with increasing GNR width. However, the specific heat increases with increasing GNR width after crossing a chaotic region. Free boundary conditions, -CHOH-terminated and armchair-edge-induced phonon nondegeneracy, shift and distortion and localized vibrational modes significantly influence GNR specific heat compared with periodic boundary conditions and bare and zigzag edges in GNRs. Finally, we found a uniform expression for specific heat vs. width at every temperature except for the chaotic region.     

Reprint of : Three-terminal heat engine and refrigerator based on superlattices

We propose a three-terminal heat engine based on semiconductor superlattices for energy harvesting. The periodicity of the superlattice structure creates an energy miniband, giving an energy window for allowed electron transport. We find that this device delivers a large power, nearly twice than the heat engine based on quantum wells, with a small reduction of efficiency. This engine also works as a refrigerator in a different regime of the system's parameters. The thermoelectric performance of the refrigerator is analyzed, including the cooling power and coefficient of performance in the optimized condition. We also calculate phonon heat current through the system and explore the reduction of phonon heat current compared to the bulk material. The direct phonon heat current is negligible at low temperatures, but dominates over the electronic at room temperature and we discuss ways to reduce it.     

Normal heat conduction in a chain with a weak interparticle anharmonic potential

We analytically study heat conduction in a chain with an interparticle interaction V(x)= lambda[1-cos(x)] and harmonic on-site potential. We start with each site of the system connected to a Langevin heat bath, and investigate the case of small coupling for the interior sites in order to understand the behavior of the system with thermal reservoirs at the boundaries only. We study, in a perturbative analysis, the heat current in the steady state of the one-dimensional system with a weak interparticle potential. We obtain an expression for the thermal conductivity, compare the low and high temperature regimes, and show that, as we turn off the couplings with the interior heat baths, there is a "phase transition": Fourier's law holds only at high temperatures.     

Thermal conductivity of a kind of mesoporous silica SBA-15

Mesoporous silica SBA-15 consists of uniform hexagonal, unconnected cylindrical channels with diameters that can be tuned within a range of 1.5 nm-30 nm, and is thought to have a special thermal conductivity. The theoretical investigation of the shell thermal conductivity of the mesoporous silica is performed in the relaxation time approximation in this paper and an available one-dimensional heat transfer model is used to predict the effective thermal conductivity （ETC） of the mesoporous silica. The experimental result of the ETC is also presented for comparison. The shell thermal conductivity of the mesoporous silica decreases with mesochannel radius increasing or wall thickness decreasing, but does not strictly decrease with porosity increasing. The thermal radiation possibly plays a primary role in heat transfer at the large porosity scale. The predicted ETC of SBA-15 with only conduction considered is quite low at the large porosity, even lower than the thermal conductivity of the silica aerogels. To realize it, doping carbon or other matters which can strongly absorb infrared light into SBA-15 is a possible way.     

Theory and calculations for a spin glass

We obtain the properties of a mean-field spin-glass (in which the bonds connecting each spin to every other spin are “frozen-in” with random signs), by locating the zeros of the partition function in the complex T plane. For N = 5 and 9 spins, we obtain the relevant polynomials and zeros explicitly, and the resulting thermodynamic properties (free energy, specific heat, magnetic susceptibility, etc.). We then analyze the properties of such a system in the thermodynamic limit N → ∞, where it is impossible to obtain the polynomials directly but where the presumed location of the zeros can be usefully construed. In this limit, the thermodynamic functions are obtainable as functions of the distribution functions of monopoles, quadrupoles, and possibly higher-order poles.     

Mesoscopic description of radiative heat transfer at the nanoscale

We present a formulation of the nanoscale radiative heat transfer using concepts of mesoscopic physics. We introduce the analog of the Sharvin conductance using the quantum of thermal conductance. The formalism provides a convenient framework to analyze the physics of radiative heat transfer at the nanoscale. Finally, we propose a radiative heat transfer experiment in the regime of quantized conductance.     

Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.