Deviations from minimum entropy production at steady states of reacting chemical systems arbitrarily close to equilibrium

Our analysis of reacting systems displaced from equilibrium by a matter flux across the boundaries has shown that the state of minimum entropy production differs from the steady state, even in the near equilibrium regime. When the displacement δ from equilibrium is small, the derivative of the dissipation at the steady state and the dissipation itself are both of order δ². The state of least dissipation is displaced from the steady state by terms of order δ² in the species concentrations. The theorem of minimum entropy production may be derived by first truncating the series expansions for the reaction rates, affinities and dissipation assuming that δ is small, and then differentiating to locate the minimum of the dissipation within the resulting idealized model. For chemical systems with an arbitrarily small but macroscopic displacement from equilibrium, this truncation procedure establishes that the dissipation is comparatively small in a neighborhood of the steady state; but it causes large relative errors in the values of the concentration derivatives and time derivatives of the dissipation within that neighborhood, because the operations of series truncation and differentiation do not commute near the steady state, when δ is small but nonzero. Near the steady state, the concentration derivative of the term of order δ³ in the dissipation is comparable to or larger than the derivative of the δ² term.     

On dissipation mechanisms in micromagnetics

Within the framework of a dynamic version of micromagnetics [1,2], the space-time evolution of magnetization in a rigid, saturated ferromagnet is governed by the following equation: γ^-1 = ×( + + div ), where the interaction couple × and the couple stress are to be constitutively specified. Under constitutive assumptions for , , and the free energy ψ, that allow for equilibrium response and viscosity out of equilibrium and agree with the dissipation principle - ^. + ^. ∇ - ≥ 0, the above evolution equation yields a broad generalization of the standard Gilbert equation. In particular, while the standard Gilbert equation only incorporates relativistic dissipation, it is shown that the dissipation mechanisms compatible with the generalized Gilbert equation include exchange dissipation [2], dry-friction dissipation [3], and others. It is also shown that the additional term proposed in [4] to account for exchange dissipation, rather than having a genuine dissipative nature, modifies instead the nature of possible equilibria; and that such a modification is an automatic side effect when dry-friction dissipation is incorporated in the manner of [3]. Received 31 October 2000     

Temperature gradient spectra and temperature dissipation rate in a turbulent convective flow

Determining mixing coefficients in oceanographic flows relies on the form of temperature gradient spectra in turbulent water flows at large wavenumbers. Several recent investigations concluded that these spectra are best described by the functional form proposed by Kraichnan rather than by the Batchelor form, more commonly used in oceanography. In this study, we provide additional support for this conclusion using laboratory measurements of the temperature gradient spectra in a Rayleigh–Bénard convective cell, in order to avoid difficulties inherent in oceanographic field measurements. The range of Rayleigh numbers in experiments is between Ra = 3×10⁷ and Ra = 5×10⁹. In addition to a traditional method of traversing thermistors, a novel optical technique recently introduced for oceanic measurements was used to obtain the spectra; comparison between these two methods serves as a validation test for the new optical technique. The temperature measurements were also augmented by 2D particle image velocimetry (PIV) observations. The measured dependence of the Nusselt number on the Rayleigh number followed Nu ∝ Ra^0.29 at Pr = 6 and was consistent with the literature data. We observed the temperature dissipation rate to vary by an order of magnitude over a horizontal transect at Ra > 10⁹. The temperature dissipation spectra obtained by both methods were in agreement over the Ra interval considered. The location of the temperature dissipation peaks was also consistent with PIV measured energy dissipation rates. Our data suggest increasing importance of top/bottom boundaries for the momentum and the temperature dissipation with increasing Ra number. Applied to oceanic upper ocean convection, our results imply that most of the dissipation occurs close to the air–sea boundary. Thus, attempts to parameterise or measure air–sea turbulent convective fluxes have to reflect the dominant role of near boundary dissipation at large Ra.     

Casimir energy dissipation in media at rest

From classical electrodynamics the energy dissipation per unit volume in a dispersive nonmagnetic medium is known to be equal to ωϵ″(ω) 〈E²〉, where ϵ″ denotes the imaginary part of the permittivity. The present work calculates the energy dissipation per unit surface area when two semi-infinite homogenous slabs are separated by a gap a. Only the gap-induced part of the dissipation is taken into account, so that the effect may be called a Casimir dissipative effect. Subtracting off the formal T = 0 expression the net dissipation is found to be negative. This reflects the fact that the dissipation in the presence of a gap is less than it would be in the case of a single homogeneous medium (i.e., a = ∞).     

Effect of tensor force on dissipation dynamics in time-dependent Hartree-Fock theory

The role of tensor force on the collision dynamics of ¹⁶O+¹⁶O is investigated in the framework of a fully three-dimensional time-dependent Hartree-Fock theory. The calculations are performed with modern Skyrme energy functional plus tensor terms. Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions. The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom. We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets. The fusion cross section without tensor force overestimates the experimental value by about 25%, while the calculation with tensor force T11 has good agreement with experimental cross section.     

Kink with Allowance for the Energy Dissipation and Pumping

In the present work, the (1+1)-dimensional nonlinear equation of motion of ϕ⁴ scalar theory is examined with simultaneous allowance for the processes of energy dissipation and pumping in the system. The energy dissipation is described in the equation by a linear term, and the energy pumping is described by a squared time derivative of the field. A single-kink solution is constructed for the given problem. It is demonstrated that a scalar field expansion in the inflationary model can occur with balanced energy dissipation and pumping. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 40–42, May, 2005.     

Sound radiation due to unsteady dissipation in turbulent flows

The radiation of sound from free turbulence is known to be dominated at sufficiently low Mach numbers by the unsteady dissipation of temperature or composition gradients, where these are present in the flow. Scaling laws for dissipation noise are developed, with particular application to jet mixing. Existing noise measurements on hot air jets at velocities down to 0·25c₀ appear to be better explained by a dipole mechanism (with intensity proportional to U⁶ than by unsteady thermal dissipation (for which the predicted intensity varies as U⁴).     

Analog of Kelvin-Helmholtz instability on a free surface of a superfluid liquid

We analyze the analog of the Kelvin-Helmholtz instability on the free surface of a superfluid liquid. This instability is induced by the relative motion of superfluid and normal components of the same liquid along the surface. The instability threshold is found to be independent of the value of viscosity, but turns out to be lower than in the absence of dissipation. The result is similar to that obtained for the interface between two sliding super-fluids (with different mechanisms of dissipation) and confirmed by the first experimental observation of the Kelvin-Helmholtz instability on the interface between ³He-A and ³He-B by Blaauwgeers et al. (cond-mat/0111343).     

On the steady motions of a flat domain wall in a ferromagnet

A new derivation is presented of Walker's exact solution to Gilbert equation, a solution which mimicks the travelling-wave motion of a flat domain wall at 180^°. It is shown that a process during which the working of the applied magnetic field exactly compensates dissipation (the Walker condition) exists both under the constitutive circumstances considered in the standard Gilbert equation and when either the internal free-energy or the dissipation, or both, are generalized by the introduction of higher-gradient terms; but that such a process cannot solve the generalized Gilbert equation. It is also shown that, when dry-friction dissipation is considered and a suitable magnetic field is applied, the associated Gilbert equation has a Walker-type solution mimicking a flat wall, at 90^° this time, which however does not satisfy the Walker condition. Received 16 November 2001     

对流层晴空湍流耗散率的风廓线雷达测量及特征

从Airda16000低平流层风廓线雷达的谱宽出发,扣除非湍流因素引起的谱宽加宽,得到湍流对谱宽的贡献,并计算出湍流耗散率。对对流层湍流耗散率的变化特征进行了分析,得出结论:对流层以下耗散率的量级在10-6~10-2m2.s-3之间,并且随高度增加而减小。在3 km以下,晴空湍流耗散率具有明显的日变化特征,中午逐渐增大,在夜间和清晨偏小,并且随着高度增加,日变化规律随时间向后延迟;3 km以上则不具有明显的日变化规律。耗散率的季节变化很突出,不同季节耗散率随高度递减的程度有差异,2008年夏季耗散率随高度的递减率为5.67%;冬季耗散率随高度递减率为14.7%;秋季分别为12.5%;而09年春季递减率为11.5%。耗散率的变化可以反映出雷达的探测高度,夏季雷达探测高度可达12 km;冬季雷达探测高度很低,仅为7 km;春秋两季探测高度为8~10 km。     

千瓦级双包层光纤激光器冷却方案设计理论和实验研究

尽管双包层光纤激光器的散热性能好于传统的固体激光器的散热性能,光纤激光器中的热沉积仍然是限制提高其输出功率的重要因素.以双端抽运的400 W双包层光纤激光器为实例,定量分析了光纤内的热沉积分布.根据所建立的散热模型,为了确保千瓦级双包层光纤激光器安全稳定的运行,抽运端附近的对流换热系数应大于2.8×10^-2W·cm^-2K^-1.据此设计出高功率双包层光纤激光器抽运端冷却装置并成功应用在激光系统中,获得了千瓦级的激光输出. 关键词： 热沉积 散热 双包层光纤激光器     

Excitation-energy sharing in uranium induced dissipative collisions

Strongly damped collisions were studied in uranium induced reactions on¹¹⁰Pd and¹²⁴Sn target nuclei near the barrier. The excitation-energy splitting was deduced from binary reaction yields and those in which the heavy fragment undergoes sequential fission. For systems with 87≦Z≦95 for the heavy fragment, the excitation energy is concentrated in the lighter nucleus, at best shared equally. The results indicate a non-equilibrated energy dissipation, and support nucleon exchange based on average single-particle strength functions as the underlying dissipation mechanism at the barrier.     

Dissipative quantum dynamics in a multiwell system

We investigate the dynamics of a quantum particle moving in a tight-binding lattice and coupled to a heat bath environment. Using the Feynman-Vernon influence functional method, we obtain an exact series representation in powers of the tunneling matrix for the generating functional of moments of the probability distribution which is valid for arbitrary temperatures and linear dissipation. We prove that the Einstein relation between the linear mobility and the diffusion coefficient holds to any order of the expansion for Ohmic, and for a restricted region of super-Ohmic dissipation. We also compute in the Ohmic case the mobility in certain regions of the parameter space. In particular, we find that the low temperature correction to the zero temperature mobility behaves asT ², and we also determine the prefactor. Finally, the exact solution of the dynamics for any times, temperatures and bias is presented for a particular value of the damping strength in the case of strict Ohmic dissipation.     

One-body dissipation and nuclear dynamics

We discuss recent developments in the “one-body” dissipation theory described in B?ocki et al. [Ann. Phys. (N.Y.)113 (1978), 330]. The principal new result is the derivation of the functional form of the dissipation expression (the Rayleigh Dissipation Function) for a finite idealized nucleus with a diffuse surface, in the form of an expansion in powers of the dimensionless ratio of the surface diffuseness to the size, R, of the system. The leading term in such an expansion is a surface contribution, of relative order R², in the form of the “Wall Formula” of B?ocki et al. The next is a curvature correction of order R. At the next level (R⁰) there are two higher order curvature corrections and a correction for the presence of gradients in the normal velocity field specifying the motion of the surface. For simple models of the nuclear surface profile we work out analytically the coefficients in the curvature and velocity-gradient correction terms. We compare the one-body dissipation theory formulated in this way with recent linear-response and Time-Dependent Hartree-Fock treatments of the nuclear problem. The principal theme that emerges from this study is the close analogy between the problem of the nuclear macroscopic dissipation function and the problem of the nuclear macroscopic potential energy.     

Nuclear viscosity of hot rotating 240Cf

In a detailed investigation of giant dipole resonance (GDR) γ-ray yield from ²⁴⁰Cf populated in the ³²S + ²⁰⁸Pb reaction, the absolute γ-ray/fission multiplicities are extracted over a wide range of excitation energy and angular momentum. The enhanced yield of GDR decay γ rays has been analyzed within the framework of a modified statistical model containing the nuclear viscosity as a free parameter. The extracted nuclear dissipation coefficient is found to be independent of the temperature. Large constant dissipation during the saddle-to-scission path provides good fits to the γ-ray spectra.     

Problems of realizing a long pulse length, high duty cycle p-Ge landau level fir laser

The hot-hole p-Ge laser, which requires a large power density ( ≅ 10⁵ watts/cm³) for excitation, has fundamental heat dissipation and lattice temperature constraints that limit the laser pulse length and duty cycle that can be achieved. This paper presents a two-dimensional heat equation analysis of the p-Ge laser bar configuration along with consideration of constraints of resonator size, heat sink dissipation limits, and temperature cut-off limits (∼20°K). In order to realize a CW p-Ge laser, the present bar sizes (typically 3×4×50 mm), would need to be decreased by over an order of magnitude and the heat sink dissipation capability appreciably increased. The detailed graphs and equations presented provide design data for future p-Ge lasers and optimization data with respect to laser pulse length and duty cycle for existing lasers.     

Nuclear dissipation with residual interactions studied by means of the Mori formalism

We apply correlation function techniques to the calculation of nuclear friction within the framework of a linear response theory. We make use of the fluctuation dissipation theorem to relate the response function to the correlation function which is evaluated by exploiting projection operator techniques. We go beyond the one-body dissipation approximation in the sense that we have taken into account the decay of particle-hole excitations into more complicated configurations. A rather simple formula for the frequency and temperature dependence of the friction coefficient is derived which we have applied to the high energy fission of²³⁸U. The friction coefficients for deformations around the first and second minima of the fission barrier have been calculated using this approach.     

One- and two-body dissipation in heavy-ion collisions

A microscopic theory has been formulated for one- and two-body dissipation in collisions between two heavy nuclei. With a nucleon-nucleon interaction as the basic perturbation in a density matrix approach with “linear response” approximations, the one- and two-body nuclear friction coefficients for the ⁴⁰Ca + ⁴⁰Ca system have been calculated and their dependence on relative kinetic energy and smearing of nuclear single-particle states was obtained. The results of our calculation show that: (a) the combined one- and two-body friction coefficients compare favourably with phenomenological values, (b) the one-body dissipation is more effective than two-body in kinetic energy damping, while both the mechanisms are comparable for the damping of relative angular momentum, (c) the importance of the two-body friction compared to one-body increases at higher relative kinetic energies and (d) the effect of introducing a smearing in nuclear levels appears as a lowering of nuclear friction.     

Influence of nuclear dissipation on fission dynamics of the excited nucleus <Superscript>248</Superscript>Cf within a stochastic approach

A stochastic approach to fission dynamics based on two-dimensional Langevin equations was applied to calculate the anisotropy of the fission fragments angular distribution and average pre-scission neutron multiplicities for the compound nucleus ²⁴⁸Cf formed in the ¹⁶O+²³²Th reactions. Postsaddle nuclear dissipation strength of (12–14) × 10²¹ s^?1 was extracted for Cf nucleus by fitting the results of calculations with the experimental data. Furthermore, it was found that the results of calculations for the anisotropy of the fission fragments angular distribution and pre-scission neutron multiplicities are very sensitive to the magnitude of post-saddle nuclear dissipation.