Optimal configuration for a finite high-temperature source heat engine cycle with the complex heat transfer law

The optimal configuration of a heat engine operating between a finite high-temperature source and an infinite low-temperature reservoir is derived by using finite time thermodynamics based on a complex heat transfer law, including Newtonian heat transfer law, linear phenomenological heat transfer law, radiative heat transfer law, Dulong-Petit heat transfer law, generalized convective heat transfer law and generalized radiative heat transfer law, q ∝ (ΔT ⁿ ). In the engine model the only irreversibility of finite rate heat transfer is considered. The optimal relation between the power output and efficiency of the heat engine is also derived by using an equivalent temperature of the hot reservoir. The obtained results include those obtained in recent literature and can provide some theoretical guidance for the designs of practical engines. Supported by the Program for New Century Excellent Talents in University of China (Grant No. 20041006) and the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)     

Optimal configuration of a class of endoreversible heat engines for maximum efficiency with radiative heat transfer law

Optimal configuration of a class of endoreversible heat engines with fixed duration, input energy and radiative heat transfer law (q ∝ Δ(T ⁴)) is determined. The optimal cycle that maximizes the efficiency of the heat engine is obtained by using optimal-control theory, and the differential equations are solved by the Taylor series expansion. It is shown that the optimal cycle has eight branches including two isothermal branches, four maximum-efficiency branches, and two adiabatic branches. The interval of each branch is obtained, as well as the solutions of the temperatures of the heat reservoirs and the working fluid. A numerical example is given. The obtained results are compared with those obtained with the Newton’s heat transfer law for the maximum efficiency objective, those with linear phenomenological heat transfer law for the maximum efficiency objective, and those with radiative heat transfer law for the maximum power output objective.     

Maximum power output of a class of irreversible non-regeneration heat engines with a non-uniform working fluid and linear phenomenological heat transfer law

Maximum power output of a class of irreversible non-regeneration heat engines with non-uniform working fluid, in which heat transfers between the working fluid and the heat reservoirs obey the linear phenomenological heat transfer law [q ∝ Δ(T ⁻¹)], are studied in this paper. Optimal control theory is used to determine the upper bounds of power of the heat engine for the lumped-parameter model and the distributed-parameter model, respectively. The results show that the maximum power output of the heat engine in the distributed-parameter model is less than or equal to that in the lumped-parameter model, which could provide more realistic guidelines for real heat engines. Analytical solutions of the maximum power output are obtained for the irreversible heat engines working between constant temperature reservoirs. For the irreversible heat engine operating between variable temperature reservoirs, a numerical example for the lumped-parameter model is provided by numerical calculation. The effects of changes of reservoir’s temperature on the maximum power of the heat engine are analyzed. The obtained results are, in addition, compared with those obtained with Newtonian heat transfer law [q ∝ Δ(T)].     

Fundamental optimal relation of a generalized irreversible Carnot heat pump with complex heat transfer law

The fundamental optimal relation between heating load and coefficient of performance (COP) of a generalized irreversible Carnot heat pump is derived based on a new generalized heat transfer law, which includes the generalized convective heat transfer law and generalized radiative heat transfer law, q ∝ (ΔT ⁿ ) ^m . The generalized irreversible Carnot heat pump model incorporates several internal and external irreversibilities, such as heat resistance, bypass heat leakage, friction, turbulence and other undesirable irreversibility factors. The added irreversibilities besides heat resistance are characterized by a constant parameter and a constant coefficient. The effects of heat transfer laws and various loss terms are analysed. The heating load vs. COP characteristic of a generalized irreversible Carnot heat pump is a parabolic-like curve, which is consistent with the experimental result of thermoelectric heat pump. The obtained results include those obtained in many literatures and indicated that the analysis results of the generalized irreversible Carnot heat pump were more suitable for engineering practice than those of the endoreversible Carnot heat pump.     

Radiative energy loss of high-energy quarks in finite-size nuclear matter and quark-gluon plasma

The induced gluon radiation of a high-energy quark in a finite-size QCD medium is studied. For a sufficiently energetic quark produced inside a medium we find the radiative energy loss ΔE _q∝L ², where L is the distance traveled by quark in the medium. It has a weak dependence on the initial quark energy E _q. The L ² dependence turns to L ¹ as the quark energy decreases. Numerical calculations are performed for a cold nuclear matter and a hot quark-gluon plasma. For a quark incident on a nucleus we predict ΔE _q ≈0.1E _q (L/10fm) ^β , with β close to unity. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 585–589 (25 April 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Specific heat of the harmonic oscillator within generalized equilibrium statistics

Summary Within the generalized equilibrium statistics recently introduced by Tsallis (p _n ∝[1−β(q−-1) _εn ]^1/(q−)), we calculate the thermal dependence of the specific heat corresponding to a harmonic-oscillator-like spectrum, namely ε _n ω(n−α) (∀ω>0,n=0,1,2,...). The influences ofq and α are exhibited. Physically inaccessible and/or thermally frozen gaps are obtained in the low-temperature region, and, forq>1, oscillations are observed in the high-temperature region. The specific heat of the two-level system is also shown.     

δ/γ transformation in non-equilibrium solidified peritectic Fe-Ni alloy

Through phase transformation kinetic analysis and experimental observation, the δ/γ transformation occurring in the non-equilibrium peritectic Fe-4.33at.%Ni alloys was systematically investigated. According to JMA solid-state transformation kinetic theory, the Time-Temperature-Transformation (TTT) curves of the δ/γ transformation in peritectic Fe-Ni alloy were calculated. On this basis, the physical correlation between the δ/γ transformation and the initial undercooling of melt (△T) was elucidated. The results indicate that the change of △T can alter not only the overall δ/γ transformation pathways but also the transformation fraction with respect to each transformation mechanism.     

A simple theory of condensation

A simple assumption of the emergence in gas of small atomic clusters consisting of c particles each leads to a phase separation (first-order transition). It reveals itself by the emergence of a “forbidden” density range starting at a certain temperature. Defining this latter value as the critical temperature predicts the existence of an interval with the anomalous heat capacity behavior c _p ∝ ΔT ^−1/c . The value c = 13 suggested in the literature yields the heat capacity exponent α = 0.077.     

Fractal simulation of the resistivity and capacitance of arsenic selenide

The temperature dependences of the ac resistivity R and ac capacitance C of arsenic selenide were measured more than four decades ago [V. I. Kruglov and L. P. Strakhov, in Problems of Solid State Electronics, Vol. 2 (Leningrad Univ., Leningrad, 1968)]. According to these measurements, the frequency dependences are R ∝ ω^{−0.80±0.01} and ΔC ∝ ω^{−0.120±0.006} (ω is the circular frequency and ΔC is measured from the temperature-independent value C ₀). According to fractal-geometry methods, R ∝ ω^1−3/h and ΔC ∝ ω^−2+3/h , where h is the walk dimension of the electric current in arsenic selenide. Comparison of the experimental and theoretical results indicates that the walk dimensions calculated from the frequency dependences of resistivity and capacitance are h _R = 1.67 ± 0.02 and h _C = 1.60 ± 0.08, which are in agreement with each other within the measurement errors. The fractal dimension of the distribution of conducting sections is D = 1/h = 0.6. Since D < 1, the conducting sections are spatially separated and form a Cantor set.     

Magnetoresistance and magnetic ordering in praseodymium and neodymium hexaborides

The magnetoresistance Δρ/ρ of single-crystal samples of praseodymium and neodymium hexaborides (PrB₆ and NdB₆) has been measured at temperatures ranging from 2 to 20 K in a magnetic field of up to 80 kOe. The results obtained have revealed a crossover of the regime from a small negative magnetoresistance in the paramagnetic state to a large positive magnetoresistive effect in magnetically ordered phases of the PrB₆ and NdB₆ compounds. An analysis of the dependences Δρ(H)/ρ has made it possible to separate three contributions to the magnetoresistance for the compounds under investigation. In addition to the main negative contribution, which is quadratic in the magnetic field (−Δρ/ρ ∝ H ²), a linear positive contribution (Δρ/ρ ∝ H) and a nonlinear ferromagnetic contribution have been found. Upon transition to a magnetically ordered state, the linear positive component in the magnetoresistance of the PrB₆ and NdB₆ compounds becomes dominant, whereas the quadratic contribution to the negative magnetoresistance is completely suppressed in the commensurate magnetic phase of these compounds. The presence of several components in the magnetoresistance has been explained by assuming that, in the antiferromagnetic phases of PrB₆ and NdB₆, ferromagnetic nanoregions (ferrons) are formed in the 5d band in the vicinity of the rareearth ions. The origin of the quadratic contribution to the negative magnetoresistance is interpreted in terms of the Yosida model, which takes into account scattering of conduction electrons by localized magnetic moments of rare-earth ions. Within the approach used, the local magnetic susceptibility χ_loc has been estimated. It has been demonstrated that, in the temperature range T _N < T < 20 K, the behavior of the local magnetic susceptibility χ_loc for the compounds under investigation can be described with good accuracy by the Curie-Weiss dependence χ_loc ∝ (T − Θ _p )⁻¹.     

Potts Model on Infinite Graphs and the Limit of Chromatic Polynomials

 Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy per site W _r (𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe ³ /q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated in [16 and 19], based on which a sufficient condition for W _r (𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice. Received: 16 January 2002 / Accepted: 17 October 2002 Published online: 18 February 2003 RID="*" ID="*" Partially supported by CNPq (Brazil) RID="**" ID="**" Partially supported by CNR, G.N.F.M. (Italy) Communicated by H. Spohn     

Pore size distribution in porous glass: fractal dimension obtained by calorimetry

By differential Scanning Calorimetry (DSC), at low heating rate and using a technique of fractionation, we have measured the equilibrium DSC signal (heat flow) J _q ⁰ of two families of porous glass saturated with water. The shape of the DSC peak obtained by these techniques is dependent on the sizes distribution of the pores. For porous glass with large pore size distribution, obtained by sol-gel technology, we show that in the domain of ice melting, the heat flow J_q is related to the melting temperature depression of the solvent, ΔT _m , by the scaling law: J _q ⁰∼ΔT _m ^{- (1 + D)}. We suggest that the exponent D is of the order of the fractal dimension of the backbone of the pore network and we discuss the influence of the variation of the melting enthalpy with the temperature on the value of this exponent. Similar D values were obtained from small angle neutron scattering and electronic energy transfer measurements on similar porous glass. The proposed scaling law is explained if one assumes that the pore size distribution is self similar. In porous glass obtained from mesomorphic copolymers, the pore size distribution is very sharp and therefore this law is not observed. One concludes that DSC, at low heating rate ( q? 2^°C/min) is the most rapid and less expensive method for determining the pore distribution and the fractal exponent of a porous material. Received 23 July 1999 and Received in final form 16 February 2001     

Prior probabilities and thermal characteristics of heat engines

The thermal characteristics of a heat cycle are studied from a Bayesian approach. In this approach, we assign a certain prior probability distribution to an uncertain parameter of the system. Based on that prior, we study the expected behaviour of the system and it has been found that even in the absence of complete information, we obtain thermodynamic-like behaviour of the system. Two models of heat cycles, the quantum Otto cycle and the classical Otto cycle are studied from this perspective. Various expressions for thermal efficiences can be obtained with a generalised prior of the form Π(x) ∝ 1/x ^b . The predicted thermodynamic behaviour suggests a connection between prior information about the system and thermodynamic features of the system.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Thermal conductivity of solid cyclohexane in orientationally ordered and disordered phases

Thermal conductivity Λ _P of solid cyclohexane is measured at a pressure P = 0.1 MPa in the temperature range from 80 K to the melting point, which covers the ranges of low-temperature orientationally ordered phase II and high-temperature orientationally disordered phase I. Thermal conductivity Λ _V is measured at a constant volume in orientationally disordered phase I. The thermal conductivity measured at atmospheric pressure decreases with increasing temperature as Λ _P ∝ T ^−1.15 in phase II, whereas Λ _P ∝ T ^−0.3 in phase I. As temperature increases, isochoric thermal conductivity Λ _V in phase I increases gradually. The experimental data are described in terms of a modified Debye model of thermal conductivity with allowance for heat transfer by both phonons and “diffuse” modes.     

Heat conductivity of a nonlinear β-FPU lattice

In this work, we propose a new approach to the computation of heat conductivity in nonlinear systems. The total heat conductivity process is decomposed into two parts: one part is an equilibrium process at the same temperature T of either end of the lattice, which does not transfer energy and the other is a nonequilibrium process at temperature ΔT of one end and a zero temperature of the opposite end of the lattice. This approach makes it possible to somewhat reduce the time of computation of heat conductivity at ΔT → 0. The threshold temperature T _thr is found to behave as T _thr ∼ N ⁻³, where N is the lattice length. The threshold temperature conventionally separates two mechanisms of heat conductivity: at T < T _thr, phonon heat conductivity is dominant; at T > T _thr, the contribution of soliton heat conductivity increases with increasing temperature. The problem of the computation of heat conductivity in the limit ΔT → 0 reduces to the heat conductivity of a harmonic lattice with time-dependent bond rigidities determined by an equilibrium process at temperature T. An exact expression for the temperature dependence of sound velocity in a lattice with a β-FPU potential at T < 10 is derived. A numerical experiment confirmed the existence of solitons and breathers that correspond to a modified Korteweg-de Vries (KdV) equation. The problem of the quantitative contribution of solitons and breathers to heat conductivity requires further study.     

Experimental study and mathematical modelling of heat transfer processes in heat accumulating media

Experimental results on reversing non-stationary heat transfer are presented for filtration of an air flow through an immobile heat accumulating medium consisting of lead (D = 2.0, 3.5, and 4.5 mm) and glass (D = 3.2 mm) balls. The studied device imitated the cyclic modes of heat regeneration in the ventilation system for domestic and office rooms. Dependency between the time of flow switching and Re number was measured. The mathematical model describing heat transfer between a gas flow and an immobile layer of balls was developed. Good correspondence between the experimental data and calculation results is observed for high Reynolds numbers. For low Re numbers the effect of heat losses is considerable, and experimental time of flow switching is shorter than the calculation one. The work was financially supported by the President of the Russian Federation (Grant No. NSh 6526.2006.3), Russian Foundation for Basic Research (Grant No. 06-08-00982), Foundation “Global energy” and Program “Energy saving of SB RAS”.     

Two-particle dispersion in model two-dimensional velocity fields

We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v ²(r) ∝r ^α and the corresponding correlation time scales as τ(r) ∝r ^β, and fix α = 2/3, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For α/2 + β < 1 the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, α/2 + β > 1, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation. In this case, depending on the particular parameters of the flow, the dispersion behavior can be rather diffusive or rather ballistic. Received 13 March 2001     

Fitting Cosmological Data to the Function <Emphasis Type="Italic">q</Emphasis>(<Emphasis Type="Italic">z</Emphasis>) from GR Theory: Modified Chaplygin Gas

In the Friedmann cosmology, the deceleration of the expansion q plays a fundamental role. We derive the deceleration as a function of redshift q(z) in two scenarios: ΛCDM model and modified Chaplygin gas (MCG) model. The function for the MCG model is then fitted to the cosmological data in order to obtain the cosmological parameters that minimize χ ². We use the Fisher matrix to construct the covariance matrix of our parameters and reconstruct the q(z) function. We use Supernovae Ia, WMAP5, and BAO measurements to obtain the observational constraints. We determined the present acceleration as q ₀ = − 0.65 ±0.19 for the MCG model using the Union2 dataset of SNeIa, BAO, and CMB and q ₀ = − 0.67 ±0.17 for the Constitution dataset, BAO and CMB. The transition redshift from deceleration to acceleration was found to be around 0.80 for both datasets. We have also determined the dark energy parameter for the MCG model: Ω _X0 = 0.81 ±0.03 for the Union2 dataset and Ω _X0 = 0.83 ±0.03 using the Constitution dataset.     

The exclusive reaction of pion quasi-elastic knockout from nucleon <Emphasis Type="Italic">p(e,e′ π)B</Emphasis> to various states of the final baryon-spectator <Emphasis Type="Italic">B</Emphasis> and the quark models for the pion cloud of nucleon

The pion momentum distributions (MDs) in four channels of virtual decay p→B+π, B = N, Δ, N _1/2-(1535), N _1/2+(1440) are calculated in two models, the microscopic model of ³ P ₀ scalar q−q fluctuation with the pion as a composite q−q-system and the chiral semi-microscopic model of πq interaction with the pion as a structureless Goldstone boson. The results of the above models are similar for the baryon states B = N, Δ, N _1/2-(1535) but are rather different for the Roper resonance N _1/2+(1440) which corresponds to excitation of two oscillator quanta in the nucleon. The experimental investigation of pion MDs by means of the reaction of quasi-elastic knockout of pion by an electron of a few GeV energy p(e, e′ π)B may be very suitable for Jefferson Laboratory, Virginia (JLab).