基于声吸收谱峰值点的天然气燃烧特性检测理论

天然气的成分构成会随产地来源变化而不同, 使其具有不同的燃烧特性和经济价值.本文利用声吸收谱峰值点随气体成分变化而改变的声分子弛豫现象, 提出一种天然气燃烧特性检测理论.它基于两频点上声测量值可合成声吸收谱峰值点, 且依赖于频率的声吸收谱可由峰值点重建的物理原理; 可利用峰值点对应的特征量——弛豫频率和弛豫吸收最大值与气体成分的关系, 从两个维度同时定量检测天然气成分.该理论避免了传统上测量声吸收谱峰值点方法需要不断改变气体腔体压强的问题, 还具有无需测量气体密度的优点.     

On the molecular sound absorption in fluid mixtures

Measurements of sound absorption in binary mixtures of gases in which two relaxation processes can occur due to the specific heats of the molecular vibrations, have hitherto been evaluated by using a theory based mainly on gaskinetic considerations. The theory presented here, uses the thermodynamics of irreversible processes as developed byMeixner for sound absorption in fluid systems due to interior reactions of arbitrary kind and number. This treatment permits a concise derivation of the final formulas which are also valid for mixtures of real gases and fluids. According to which set of independent thermodynamical variables for the derivation is used, the final formulas seem to differ considerably. It is pointed out that these differences arise from introducing two types of relaxation times and may be eliminated by means of the relationship between these relaxation times.     

An Ising model for the stress relaxation of solids

A kinetic theory of stress relaxation of solids as a cooperative process is proposed. The theory is based on a two-state model for the relaxation. It is shown that the conventional mean field approximation leads to an exponential dependence of the rate of stress relaxation on the stress while the multiplicative approximation of Vol'kenstein et al. leads to a power law. It is argued that the exponential law should be valid initially in the relaxation process while the power law is appropriate when the system is nearer equilibrium, which is in qualitative agreement with recent experimental findings.     

The effect of quadrupole relaxation on nuclear magnetic resonance multiplets

A theory of the broadening of multiplet components in magnetic resonance spectra of coupled nuclei due to electric quadrupole spin-lattice relaxation is presented. It is shown that the broadening of the components of the 1:1:1 triplet for nuclei of spin 1/2 coupled to a nucleus of spin 1, is 3/2 as great for the outer lines as for the central one, provided that the rate of quadrupole relaxation is not too large. This is in agreement with experimental observations on ¹⁴NH₃. A theory of the line shape of the partly collapsed multiplet at higher rates of quadrupole relaxation is also given.     

On the relationship between fluctuating irreversible thermodynamics and “extended” irreversible thermodynamics

The relationship between fluctuating irreversible thermodynamics and theories of irreversible processes which include the thermodynamic fluxes as independent variables is explored. It is shown that the usual fluctuating linear theory of irreversible thermodynamics is a contraction of the extended theory. This contraction contains non-Markovian effects dependent upon the relaxation times associated with the thermodynamic fluxes. In the limit that these relaxation times are small, the extended theory is shown to be equivalent to the usual fluctuating thermodynamic theory. A critique of the extended theories is given from the point of view of the mechanistic statistical theory of irreversible processes.     

Self-induced avalanches in relaxing media

A theory of boson avalanches (self-induced waves) has been constructed with allowance for longitudinal relaxation. It is shown that inclusion of longitudinal relaxation requires a completely different approach to the theory of superradiance than that taken previously. For the first time an equation is derived for an avalanche with allowance for longitudinal and transverse relaxation. Numerical solution of this equation makes It possible to establish all the distinctive features of a coherent self-induced wave under the conditions of the action of relaxation mechanisms. An inversion effect is found to occur in the action of longitudinal and transverse relaxation on the delay parameter of a self-induced wave, i.e., the superradiance delay time. Analytic expressions are found of the ensemble-averaged delay time of an avalanche and the relative fluctuations of the delay time as a function of irreversible phase relaxation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 81–86, September, 1986.     

Theory of intramolecular spin relaxation by translational diffusion in locally ordered fluids

In locally ordered fluids, such as macromolecular solutions, clays and lyotropic liquid crystals, nuclear spin relaxation can be induced by modulation, through translational diffusion of the fluid molecules, of the magnitude and orientation of the residual intramolecular spin-lattice coupling tensor, which is only partially averaged by local molecular motions near an interface. A theory of spin relaxation in locally ordered fluids bounded by planar interfaces is developed, with special emphasis on effects of translational diffusion. The theory is based on a continuous diffusion model (CDM) which, in contrast to the commonly adopted discrete exchange model (DEM), treats equilibrium and time-dependent distribution functions in a self-consistent way. A striking feature of translational diffusion in heterogeneous systems is the abundance of reencounters with previously visited interfacial regions. It is demonstrated that these diffusional reencounters, which are inherent in the CDM theory, may lead to a relaxation behaviour which is qualitatively different from that predicted by the DEM theory. Furthermore, it is seen that the widespread concept of intrinsic relaxation rate (associated with a spatial region) and the fast/slow exchange classification are not generally valid. The formal framework of the CDM theory allows molecular interactions of any complexity to be introduced. In this paper a mean-field model based on the nonlinear Poisson-Boltzmann equation is used to obtain analytic expressions for the spectral density functions that determine the relaxation behaviour in the presence and in the absence of spectral line splittings.     

A TWO-STATE MODEL FOR NON-EXPONENTIAL RELAXATION IN CONDENSED MATTER

A two-state model is presented for polarization relaxation in condensed matter. The dynamics of relaxation is treated with quantum transition theory. The physical meaning of the so-called time-dependent transition rate is clarified. The new model not only gives the fractional exponential and power-law relaxation functions naturally, but also indicates that the universality of the relaxation law results from the scaling behavior of low-frequency effective spectrum.     

A theory of quantum diffusion localization

The quantum localization of chaotically diffusive classical motion is reviewed, using the kicked rotator as a simple but instructive example. The specific quantum steady state, which results from statistical relaxation in the discrete spectrum, is described in some detail. A new phenomenological theory of quantum dynamical relaxation is presented and compared with the previously existing theory.     

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

Exponentially Long Stability Times for a Nonlinear Lattice in the Thermodynamic Limit

In this paper, we construct an adiabatic invariant for a large 1–d lattice of particles, which is the so called Klein Gordon lattice. The time evolution of such a quantity is bounded by a stretched exponential as the perturbation parameters tend to zero. At variance with the results available in the literature, our result holds uniformly in the thermodynamic limit. The proof consists of two steps: first, one uses techniques of Hamiltonian perturbation theory to construct a formal adiabatic invariant; second, one uses probabilistic methods to show that, with large probability, the adiabatic invariant is approximately constant. As a corollary, we can give a bound from below to the relaxation time for the considered system, through estimates on the autocorrelation of the adiabatic invariant.     

Spin relaxation in fluids

The effect of spin relaxation in fluids on perturbed angular distributions is discussed. The first example, deals with dynamical perturbations resulting from collision-induced charge-transfer process in gases. A brief discussion of relaxation effects caused by molecular motion in non-metallic liquids is followed by a presentation of a new approach to the theory of quadrupole relaxation in liquid metals.     

Relaxation at critical points: Deterministic and stochastic theory

A generalized critical point can be characterized by non-linear dynamics. We formulate the deterministic and stochastic theory of relaxation at such a point. Canonical problems are used to motivate the general solutions. In the deterministic theory, we show that at the critical point certain modes have polynomial (rather than exponential) growth or decay. The stochastic relaxation rates can be calculated in terms of various incomplete special functions. Three examples are considered. First, a substrate inhibited reaction (marginal type dynamical system) is treated. Second, the relaxation of a mean field ferromagnet is considered. We obtain a result that generalizes the work of Griffiths et al. Third, we study the relaxation of a critical harmonic oscillator.     

Formation and thickness evolution of periodic twin domains in manganite films grown on SrTiO3(001) substrates

We present an extended synchrotron x-ray scattering study of the structure of thin manganite films grown on SrTiO3(001) substrates and reveal a new kind of misfit strain relaxation process which exploits twinning to adjust lattice mismatch. We show that this relaxation mechanism emerges in thin films as one-dimensional twinning waves which freeze out into a twin domain pattern as the manganite film continues to grow. A quantitative microscopic model which uses a matrix formalism is able to reproduce all x-ray features and provides a detailed insight into this novel relaxation mechanism. We further demonstrate how this twin angle pattern affects the transport properties in these functional films.     

Physical meaning of the stretched exponential Kohlrausch function

In this paper the physical meaning of the empirical Kohlrausch-Williams-Watts (KWW) function is explained in terms of the linear oscillator theory. It is shown that the KWW function is a solution of the non-autonomous linear first order equation for an overdamped linear oscillator. From the linear oscillator model it follows that the KWW-type relaxation is the linear relaxation with a time (coordinate, stress, voltage, etc.) dependent dissipation of energy. The theoretical results are validated by measurements. A method for modeling KWW-type relaxation using simple electrical circuits is proposed.     

Non-newtonian flow for concentrated polymer systems

The modified Graessley theory with the three-dimensional Maxwell model can well explain some of the nonlinear viscoelastic behavior of concentrated polymer systems at least qualitatively with the assumption of a box-type relaxation spectrum for the equilibrium state.

The relaxation spectrum of concentrated polymer systems in shear flow is obtained by means of Graessley's theory. It is assumed that the characteristic time for the entanglement formation is the same order as that for its breakage and that the spectral density of the relaxation spectrum in the flow system is proportional to the number of entanglements between two molecules. The spectral density decreases approximately proportionally to 1/γ for relaxation times larger than 1/γ The non-Newtonian viscosity and other viscoelastic properties, such as the so-called stress overshoot and the stress relaxation, are calculated by using the obtained relaxation spectrum. Our theory explains very well the experimental results in many cases. Good agreement with experimental results is found if we assume that the so-called box-type relaxation spectrum in the equilibrium state has a finite gradient of the order of ?0.5 in the edge region of larger relaxation time on log-log plots.     

油水饱和球管孔隙模型弛豫的理论计算与计算机模拟

根据Brownstein-Tarr理论,采用特征函数展开法,通过求解基于扩散效应的Bloch控制方程,给出了油水饱和球管孔隙模型弛豫的理论计算公式.理论计算结果表明,在水润湿条件下,油的弛豫过程只与含油饱和度有关,而与岩石的孔隙结构无关.根据理论计算结果对球管模型中水的弛豫进行了数值模拟,模拟结果显示,球和管的主弛豫过程是一个单指数函数,其余部分与之相比可以忽略,即球管模型中水的弛豫可近似为一个双指数衰减过程. 关键词： 核磁共振 弛豫 球管孔隙模型 Bloch控制方程     

油水饱和球管孔隙模型弛豫的理论计算与计算机模拟

根据Brownstein-Tarr理论，采用特征函数展开法，通过求解基于扩散效应的Bloch控制方程，给出了油水饱和球管孔隙模型弛豫的理论计算公式.理论计算结果表明，在水润湿条件下，油的弛豫过程只与含油饱和度有关，而与岩石的孔隙结构无关.根据理论计算结果对球管模型中水的弛豫进行了数值模拟，模拟结果显示，球和管的主弛豫过程是一个单指数函数，其余部分与之相比可以忽略，即球管模型中水的弛豫可近似为一个双指数衰减过程.     

A lionville space formulation of wangsness-bloch-redfield theory of nuclear spin relaxation. II. Scalar relaxation

The superoperator formalism of nuclear spin relaxation theory presented in part I of this series is extended to the case of scalar relaxation, where attention is focused on observables associated with only part of a spin system while the remainder, which may consist of a set of rapidly relaxing nuclei, is treated as a pseudobath whose indirect influence on the subsystem of interest is exerted through scalar spin coupling. The consequences of symmetry features present in the subsystem of interest and/or the pseudobath are analyzed. In particular, it is demonstrated that the situation which has entered the literature under the appellation of “non-fully dissipative case” is to be interpreted as a manifestation of microscopic symmetry invariance. A new, simpler version of a general theory of scalar relaxation of the first kind is presented.     

Relaxation dynamics of a broadband nanosecond acoustic pulse in a bubbly medium

The first experimental observation of the propagation dynamics of a short broadband acoustic pulse in a resonance medium with gas bubbles is carried out. The probing pulse is generated using the optoacoustic effect. It is shown that the theory of short pulse propagation in media with generalized resonance relaxation adequately and accurately describes the dynamics of short pulse dispersion. A possibility to determine the relaxation and resonance parameters of media by the pulsed testing technique is demonstrated.