Self-Organized Criticality Theory Model of Thermal Sandpile

A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on the slow time scale. The main characteristics of the model are that both particle and energy avalanches of sand grains are considered simultaneously. Properties of intermittent transport and improved confinement are analyzed in detail. The results imply that the intermittent phenomenon such as blobs in the low confinement mode as well as edge localized modes in the high confinement mode observed in tokamak experiments are not only determined by the edge plasma physics, but also affected by the core plasma dynamics.

Cornwall-Jackiw-Tomboulis Effective Potential for Quark Propagator in Real-Time Thermal Field Theory and Landau Gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A（p^2） in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics （QCD）, we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.

Explicit Proof of Equivalence of Two—Point Functions in the Two Formalisms of Thermal Field Theory

We give an explicit proof of equivalence of the two-point function to one-loop order in the two formalisms of thermal theory based on the expressions in the real-time formalism and indicate that the key point of completing the proof is to separate carefully the imaginary part of the zero-temperature loop integral from relevant expressions and this fact will certainly be very useful for examination of the equivalent problem of two formalisms of thermal field theory in other theories, including the one of the propagators for scalar bound states in an NJL model.

Building imaginary-time thermal field theory with artificial neural networks

In this paper,we introduce a novel approach in quantum field theories to estimate actions using artificial neural networks(ANNs).The actions are estimated by learning system configurations governed by the Boltzmann factor,e^(-s),at different temperatures within the imaginary time formalism of thermal field theory.Specifically,we focus on the 0+1 dimensional quantum field with kink/anti-kink configurations to demonstrate the feasibility of the method.Continuous-mixture autoregressive networks(CANs)enable the construction of accurate effective actions with tractable probability density estimation.Our numerical results demonstrate that this methodology not only facilitates the construction of effective actions at specified temperatures but also adeptly estimates the action at intermediate temperatures using data from both lower and higher temperature ensembles.This capability is especially valuable for detailed exploration of phase diagrams.

Interpretation of living tissue's temperature oscillations by thermal wave theory

The fact that the temperature of living tissue may respond oscillatorily to externalheating has been a classical difficulty in the field of bioheat transfer for a long time.Roemer et al. have carefully discussed this in their serial articles, but experiments did notsupport their conclusions, Tharp et al. have artificially made a time-delay differential equs-tion to describe this phenomenon, but their model is short of a strict theoretical founda-

A continuum thermal stress theory for crystals based on interatomic potentials

This paper presents a new continuum thermal stress theory for crystals based on interatomic potentials.The effect of finite temperature is taken into account via a harmonic model.An EAM potential for copper is adopted in this paper and verified by computing the effect of the temperature on the specific heat,coefficient of thermal expansion and lattice constant.Then we calculate the elastic constants of copper at finite temperature.The calculation results are in good agreement with experimental data.The thermal stress theory is applied to an anisotropic crystal graphite,in which the Brenner potential is employed.Temperature dependence of the thermodynamic properties,lattice constants and thermal strains for graphite is calculated.The calculation results are also in good agreement with experimental data.

Study on thermal wave based on the thermal mass theory

The conservation equations for heat conduction are established based on the concept of thermal mass.We obtain a general heat conduction law which takes into account the spatial and temporal inertia of thermal mass.The general law introduces a damped thermal wave equation.It reduces to the well-known CV model when the spatial inertia of heat flux and temperature and the temporal inertia of temperature are neglected,which indicates that the CV model only considers the temporal inertia of heat flux.Numerical simulations on the propagation and superposition of thermal waves show that for small thermal perturbation the CV model agrees with the thermal wave equation based on the thermal mass theory.For larger thermal perturbation,however,the physically impossible phenomenon pre-dicted by CV model,i.e.the negative temperature induced by the thermal wave superposition,is eliminated by the general heat conduction law,which demonstrates that the present heat conduction law based on the thermal mass theory is more reasonable.

Thermal performance analysis of non-uniform height rectangular fin based on constructal theory and entransy theory

A model of non-uniform height rectangular fin, in which the variation of base's thickness and width are taken into account, is established in this paper. The dimensionless maximum thermal resistance(DMTR) and the dimensionless equivalent thermal resistance(DETR) defined based on the entransy dissipation rate(EDR) are taken as performance evaluation indexes. According to constructal theory, the variations of the two indexes with the geometric parameters of the fin are analyzed by using a finite-volume computational fluid dynamics code, the effects of the fin-material fraction on the two indexes are analyzed. It is found that the two indexes decrease monotonically as the ratio between the front height and the back height of the fin increases subjected to the non-uniform height rectangular fin. When the model is reduced to the uniform height fin, the two indexes increase first and then decrease with increase in the ratio between the height of the fin and the fin space. The fin-material fraction has no effect on the change rule of the two indexes with the ratio between the height of the fin and the fin space. The sensitivity of the DETR to the geometric parameters of the fin is higher than that of the DMTR to the geometric parameters. The results obtained herein can provide some theoretical support for the thermal design of rectangular fins.

First-Principles Study of the High-Temperature Behaviors of the Willemite-Ⅱ and Post-Phenacite Phases of Silicon Nitride

The structural and elastic properties of the recently-discovered wⅡ- and δ-Si3N4 are investigated through the plane-wave pseudo-potential method within ultrasoft pseudopotentials.The elastic constants show that wⅡ- and δ-Si3N4 are mechanically stable in the pressure ranges of 0-50 GPa and 40-50 GPa,respectively.The α→wⅡ phase transition can be observed at 18.6 GPa and 300 K.The β→δ phase transformation occurs at pressures of 29.6,32.1,35.9,39.6,41.8,and 44.1 GPa when the temperatures are100,200,300,400,500,and 600 K,respectively.The results show that the interactions among the N-2s,Si-3s,3p bands（lower valence band） and the Si-3p,N-2p bands（upper valence band） play an important role in the stabilities of the wⅡ and S phases.Moreover,several thermodynamic parameters（thermal expansion,free energy,bulk modulus and heat capacity） of δ-Si3N4 are also obtained.Some interesting features are found in these properties.δ-Si3N4 is predicted to be a negative thermal expansion material.The adiabatic bulk modulus decreases with applied pressure,but a majority of materials show the opposite trend.Further experimental investigations with higher precisions may be required to determine the fundamental properties of wⅡ- andδ-Si3N4.

Gap Equations and Effective Potentials at Finite Temperature and Chemical Potential in D—Dimensional Four—Fermion Models

We have proven the general relations between the gap equations obeyed by dynamical fermion mass and thecorresponding effective potentials at finite temperature and chemical potential in D-dimensional four-fermion interactionmodels. This gives an easy approach to get effective potentials directly from the gap equations. We find out explicitexpressions for the effective potentials at zero temperature in the cases of D = 2,3, and 4 for practical use.

A Brief Overview of Hard-Thermal-Loop Perturbation Theory

The poor convergence of quantum field theory at finite temperature has been one of the main obstacles in the practical applications of thermal QCD for decades.Here we briefly review the progress of hard-thermal-loop perturbation theory (HTLpt) in reorganizing the perturbative expansion in order to improve the convergence.The quantum mechanical anharmonic oscillator is used as a simple example to show the breakdown of weak-coupling expansion,and variational perturbation theory is introduced as an effective resummation scheme for divergent weak-coupling expansions.We discuss HTLpt thermodynamic calculations for QED,pure-glue QCD,and QCD with N f=3 up to three-loop order.The results suggest that HTLpt provides a systematic framework that can be used to calculate both static and dynamic quantities for temperatures relevant at LHC.

Propagators for Scalar Bound States at Finite Temperature in an NJL Model

We re-examine physical causal propagators for scalar and pseudoscalar bound states at finite temperature in a chiral NJL model, defined by four-point amputated functions subtracted through the gap equation, and prove that they are completely equivalent in the imaginary-time and real-time formalisms by separating carefully the imaginary part of the zero-temperature loop integral. It is shown that the same thermal transformation matrix of the matrix propagators for these bound states in the real-time formalism is precisely the one of the matrix propagator for an elementary scalar particle and this fact shows the similarity of thermodynamic property between a composite and elementary scalar particle. The retarded and advanced propagators for these bound states are also given explicitly from the imaginary-time formalism.

Thermal reffusivity： uncovering phonon behavior, structural defects, and domain size

To understand the relation between different nanostructures and thermal properties, a simple yet effective model is in demand for characterizing the underlying phonons and electrons scattering mechanisms. Herein, we make a systematic review on the newly developed thermal reffusivity theory. Like electrical resistivity which has been historically used as a theory for analyzing structural domain size and defect levels of metals, the thermal reffusivity can also uncover phonon behavior, structure defects and domain size of materials. We highlight that this new theory can be used for not only metals, but also nonmetals, even for amorphous materials. From the thermal reffusivity against temperature curves, the Debye temperature of the material and the ideal thermal diffusivity of single perfect crystal can be evaluated. From the residual thermal reffusivity at the 0 K limit, the structural thermal domain （STD） size of crystalline and amorphous materials can be obtained. The difference of white hair and normal black hair from heat conduction perspective is reported for the first time. Loss of melanin results in a worse thermal protection and a larger STD size in the white hair. By reviewing the different variation of thermal reffusivity against decreasing temperature profiles, we conclude that they reflected the structural connection in the materials. Ultimately, the future application of thermal reffusivity theory in studying 2D materials and amorphous materials is discussed.

Hard-thermal-loop QED thermodynamics

The weak-coupling expansion for thermodynamic quantities in thermal field theories is poorly convergent unless the coupling constant is tiny.We discuss the calculation of the free energy for a hot gas of electrons and photons to three-loop order using hard-thermal-loop perturbation theory （HTLpt）.We show that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling,e ～ 2.The reorganization is gauge invariant by construction,and due to the cancellations among various contributions,we obtain a completely analytic result for the resummed thermodynamic potential at three loops.

Photon polarization tensor in a magnetized plasma system

We investigate the photon polarization tensor at finite temperatures in the presence of a static and homogeneous external magnetic field.In our scheme,the summing of the Matsubara frequency is performed after Poisson resummation,which is easily completed and converges quickly.Moreover,the behaviors of finite Landau levels are presented explicitly.It shows a convergence while summing infinite Landau levels.Consequently,there is no necessity to truncate the Landau level in a numerical estimation.At zero temperature,the lowest Landau level(LLL)approximation is analytically satisfied for the vacuum photon polarization tensor.However,we examine that the LLL approximation is not enough for the thermal polarization tensor.The thermal tensor obtains non-trivial contributions from the finite-n Landau levels.And,photon spectra gains a large imaginary contribution in thermal medium,which is the so-called Landau damping.Finally,it is argued that the summation of Matsubara frequency is not commuted with Landau level ones,such conjecture is excluded in our calculations.