Exploring the operation of a tiny heat engine

We model a tiny heat engine as a Brownian particle that moves in a viscous medium in a sawtooth potential (with or without load) assisted by alternately placed hot and cold heat baths along its path. We find closed form expression for the steady-state current as a function of the model parameters. This enables us to deal with the energetics of the model and evaluate either its efficiency or its coefficient of performance depending upon whether the model functions either as a heat engine or as a refrigerator, respectively. We also study the way current changes with changes in parameters of interest. When we plot the phase diagrams showing the way the model operates, we not only find regions where it functions as a heat engine and as a refrigerator but we also identify a region where the model functions as neither of the two.     

Spin-boson thermal rectifier

Rectification of heat transfer in nanodevices can be realized by combining the system inherent anharmonicity with structural asymmetry. We analyze this phenomenon within the simplest anharmonic system-a spin-boson nanojunction model. We consider two variants of the model that yield, for the first time, analytical solutions: a linear separable model in which the heat reservoirs contribute additively, and a nonseparable model suitable for a stronger system-bath interaction. Both models show asymmetric (rectifying) heat conduction when the couplings to the heat reservoirs are different.     

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.     

Abstract models for heat engines

We retrospect three abstract models for heat engines which include a classic abstract model in textbook of thermal physics, a primary abstract model for finite-time heat engines, and a refined abstract model for finite-time heat engines. The detailed models of heat engines in literature of finite-time thermodynamics may be mapped into the refined abstract model. The future developments based on the refined abstract model are also surveyed.     

Anomalous energy diffusion and heat conduction in one-dimensional system

We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in one-dimensional hard-point model. For diatom model, we find an anomalous energy diffusion as $\langle x^2 \rangle\sim t^\beta$ with $\beta=1.33$, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be $\alpha=0.33$, which is confirmed by a simple numerical calculation.     

Heat conduction in the Frenkel-Kontorova model

Heat conduction is an old yet important problem. Since Fourier introduced the law bearing his name almost 200 years ago, a first-principle derivation of this simple law from statistical mechanics is still lacking. Worse still, the validity of this law in low dimensions, and the necessary and sufficient conditions for its validity are far from clear. In this paper we will review recent works on heat conduction in a simple nonintegrable model called the Frenkel-Kontorova model. The thermal conductivity of this model has been found to be finite. We will study the dependence of the thermal conductivity on the temperature and other parameters of the model such as the strength and the periodicity of the external potential. We will also discuss other related problems such as phase transitions and finite-size effects. The study of heat conduction is not only of theoretical interest but also of practical interest. We will show various recent designs of thermal rectifiers and thermal diodes by coupling nonlinear chains together. The study of heat conduction in low dimensions is also important to the understanding of the thermal properties of carbon nanotubes.     

Size dependence of efficiency at maximum power of heat engine

We perform a molecular dynamics computer simulation of a heat engine model to study how the engine size difference affects its performance. Upon tactically increasing the size of the model anisotropically, we determine that there exists an optimum size at which the model attains the maximum power for the shortest working period. This optimum size locates between the ballistic heat transport region and the diffusive heat transport one. We also study the size dependence of the efficiency at the maximum power. Interestingly, we find that the efficiency at the maximum power around the optimum size attains a value that has been proposed as a universal upper bound, and it even begins to exceed the bound as the size further increases. We explain this behavior of the efficiency at maximum power by using a linear response theory for the heat engine operating under a finite working period, which naturally extends the low-dissipation Carnot cycle model [M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)]. The theory also shows that the efficiency at the maximum power under an extreme condition may reach the Carnot efficiency in principle.     

以一维谐振子势阱中的单粒子为工质的量子热机性能分析

建立了以一维谐振子势阱中的单粒子为工质的量子热机模型.当势阱壁宽度和粒子的量子态缓慢改变时, 该热机类似于经典卡诺热机对外做功.假设势阱壁移动速度非常缓慢并且考虑热漏, 推导出量子热机循环的输出功率和效率等重要性能参数的一般表达式.通过优化分析, 获得了热机循环中各主要性能参数的最佳优化值和优化区间.     

Directional region control of the thermal fractal diffusion of a space body

We present a directional region control(DRC) model of thermal diffusion fractal growth with active heat diffusion in three-dimensional space. This model can be applied to predict the space body heat fractal growth and study its directional region control. When the nonlinear interference term and the inner heat source term are generalized functions, the relationship between the particle aggregation probability and the interference terms can be obtained using the norm theory. We can then predict the aggregation form of particles in different regions. When the nonlinear interference terms in the model are expressed as a trigonometric function and its composite function, our simulations show that the DRC method of thermal fractal diffusion is effective and has reference value for the directional control of actual fractal growth systems.     

非平衡涨落问题的微观唯象分析理论(Ⅱ)——物理系统中的非平衡涨落与由信息理论所求得的热传导精确结果的比较

本文将文献[10]所建立的非平衡涨落统计的微观唯象分析理论与对一般的涨落-耗散表示式的修正方法,直接应用于一、二与三维光子热传导与金属中的电子热传导的研究中,并将所得结果与由信息理论方法所建立的线性谐振子链的非平衡涨落的精确模型所求得的精确结果进行了比较,两者相当符合。从而证实了文献[10]所建立的非平衡涨落统计的微观唯象分析理论是正确的。     

INFRARED RADIATION OF SF6 AND ITS APPLICATION TO GAS-FILLED DOUBLE-PANE WINDOWS

Interest in using sulfur hexafluoride (SF₆ as a gas-fill in multipane windows has raised questions concerning the calculation of heat transfer rates through such windows. The infrared absorption characteristics of this gas make the heat transfer analysis much more complicated. In order to account for the absorption effect, we measured the spectral absorptivity of several infrared-active bands of sulfur hexafluoride at low resolution and a temperature of 298 K. We correlated the spectral absorption data with the Edwards exponential wide-band model and with the Elsasser narrow-band model, and incorporated the wide-band model into a one-dimensional, finite-element heat transfer model. The finite-element heat transfer model considered combined conduction and radiation effects in a double-pane window, and was used to evaluate the overall heat transfer coefficients of double-pane windows filled with SF₆; CO₂, or air. The numerical results show good agreement with the experimental results     

Time-dependent thermodynamic properties of the Ising model from damage spreading

The relationship between damage spreading and static thermodynamic properties in the Ising model developed by Coniglioet al. is here extended to include time-dependent thermodynamic quantities. We exploit this new result to measure the time-dependent spin correlation function from damage spreading in the Ising model with heat bath and Glauber dynamics. Until now, only static thermodynamic quantities have been correctly determined from damage spreading, and even then, only with heat bath dynamics. We also show that there are significant differences between the kinetics of damage spreading as found in heat bath and Glauber dynamics.     

Heat transistor: demonstration of gate-controlled electronic refrigeration

We present experiments on a superconductor-normal-metal electron refrigerator in a regime where single-electron charging effects are significant. The system functions as a heat transistor; i.e., the heat flux out from the normal-metal island can be controlled with a gate voltage. A theoretical model developed within the framework of single-electron tunneling provides a full quantitative agreement with the experiment. This work serves as the first experimental observation of Coulombic control of heat transfer and, in particular, of refrigeration in a mesoscopic system.     

Temperature dependence of heat conduction coefficient in nanotube/nanowire networks

Studies on heat conduction are so far mainly focused on regular systems such as the one-dimensional(1D) and twodimensional(2D) lattices where atoms are regularly connected and temperatures of atoms are homogeneously distributed.However, realistic systems such as the nanotube/nanowire networks are not regular but heterogeneously structured, and their heat conduction remains largely unknown. We present a model of quasi-physical networks to study heat conduction in such physical networks and focus on how the network structure influences the heat conduction coefficient κ. In this model,we for the first time consider each link as a 1D chain of atoms instead of a spring in the previous studies. We find that κ is different from link to link in the network, in contrast to the same constant in a regular 1D or 2D lattice. Moreover, for each specific link, we present a formula to show how κ depends on both its link length and the temperatures on its two ends.These findings show that the heat conduction in physical networks is not a straightforward extension of 1D and 2D lattices but seriously influenced by the network structure.     

Isolated quantum heat engine

We present a theoretical and numerical analysis of a quantum system that is capable of functioning as a heat engine. This system could be realized experimentally using cold bosonic atoms confined to a double well potential that is created by splitting a harmonic trap with a focused laser. The system shows thermalization, and can model a reversible heat engine cycle. This is the first demonstration of the operation of a heat engine with a finite quantum heat bath.     

Mathematical simulation of hydrocarbon fuel conversion in heat-protection elements of hypersonic aircrafts

We consider a mathematical model of hydrocarbon fuel conversion in a thermochemical reactor as an element of heat protection of a hypersonic aircraft. The application of this model has made it possible to enrich information obtained in experimental studies.     

Regular network model for the sea ice-albedo feedback in the Arctic

The Arctic Ocean and sea ice form a feedback system that plays an important role in the global climate. The complexity of highly parameterized global circulation (climate) models makes it very difficult to assess feedback processes in climate without the concurrent use of simple models where the physics is understood. We introduce a two-dimensional energy-based regular network model to investigate feedback processes in an Arctic ice-ocean layer. The model includes the nonlinear aspect of the ice-water phase transition, a nonlinear diffusive energy transport within a heterogeneous ice-ocean lattice, and spatiotemporal atmospheric and oceanic forcing at the surfaces. First results for a horizontally homogeneous ice-ocean layer show bistability and related hysteresis between perennial ice and perennial open water for varying atmospheric heat influx. Seasonal ice cover exists as a transient phenomenon. We also find that ocean heat fluxes are more efficient than atmospheric heat fluxes to melt Arctic sea ice.     

Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics

We continue the study of a model for heat conduction [6] consisting of a chain of non-linear oscillators coupled to two Hamiltonian heat reservoirs at different temperatures. We establish existence of a Liapunov function for the chain dynamics and use it to show exponentially fast convergence of the dynamics to a unique stationary state. Ingredients of the proof are the reduction of the infinite dimensional dynamics to a finite-dimensional stochastic process as well as a bound on the propagation of energy in chains of anharmonic oscillators. Received: 12 March 2001 / Accepted: 5 August 2001     

Current progress on heat conduction in one-dimensional gas channels

We give a brief review of the past development of model studies on one-dimensional heat conduction. Particularly, we describe recent achievements on the study of heat conduction in one-dimensional gas models including the hard-point gas model and billiard gas channel. For a one-dimensional gas of elastically colliding particles of unequal masses, heat conduction is anomalous due to momentum conservation, and the divergence exponent of heat conductivity is estimated as α≈0.33 in k ∼ L ^α . Moreover, in billiard gas models, it is found that exponent instability is not necessary for normal heat conduction. The connection between heat conductivity and diffusion is investigated. Some new progress is reported. A recently proposed model with a quantized degree of freedom to study the heat transport in quasi-one dimensional systems is illustrated in which three distinct temperature regimes of heat conductivity are manifested. The establishment of local thermal equilibrium (LTE) in homogeneous and heterogeneous systems is also discussed. Finally, we give a summary with an outlook for further study about the problem of heat conduction.