Elastic stability of DNA configurations. II. Supercoiled plasmids with self-contact

Configurations of protein-free DNA miniplasmids are calculated with the effects of impenetrability and self-contact forces taken into account by using exact solutions of Kirchhoff's equations of equilibrium for elastic rods of circular cross section. Bifurcation diagrams are presented as graphs of excess link, DeltaL, versus writhe, W, and the stability criteria derived in paper I of this series are employed in a search for regions of such diagrams that correspond to configurations that are stable, in the sense that they give local minima to elastic energy. Primary bifurcation branches that originate at circular configurations are composed of configurations with D(m) symmetry (m=2,3,...). Among the results obtained are the following. (i) There are configurations with C2 symmetry forming secondary bifurcation branches which emerge from the primary branch with m=3, and bifurcation of such secondary branches gives rise to tertiary branches of configurations without symmetry. (ii) Whether or not self-contact occurs, a noncircular configuration in the primary branch with m=2, called branch alpha, is stable when for it the derivative dDeltaL/dW, computed along that branch, is strictly positive. (iii) For configurations not in alpha, the condition dDeltaL/dW>0 is not sufficient for stability; in fact, each nonplanar contact-free configuration that is in a branch other than alpha is unstable. A rule relating the number of points of self-contact and the occurrence of intervals of such contact to the magnitude of DeltaL, which in paper I was found to hold for segments of DNA subject to strong anchoring end conditions, is here observed to hold for computed configurations of protein-free miniplasmids.     

Kinetics of crystalline configurations: I. General theory; Kinetics of homogeneous short range order

A simple and exact way of coarse graining the master equation for a Markov process in configuration space is shown to exist. The coarse grained master equation is applied to the Ising model of a homogeneous binary interstitial alloy and to a “magnetic” Ising model. Using an approximation analogous to the quasi-chemical approximation, for both models the macroscopic rate equations for the establishment of short range order and the Fokker-Planck equation governing the fluctuations are derived.     

Quantum theory of light propagation I. General theory

We present a particular approach to quantum theory of light propagation in nonlinear medium using space and time dependent modal operators. Spatial and temporal evolutions of this space and time dependent modal operators are given by the Heisenberg-like equation involving the momentum operator and Heisenberg equation, respectively, which can be justified from point of view of quantum electrodynamics. This useful concept can be applied to an arbitrary nonlinear interaction.The author would like to express his sincere thanks to Professor J. Peina for advice, comments and stimulating discussions.This work was partially supported by the grant PV202/1994 of Czech Ministry of Education and by an internal grant of the Palacký University.     

DNA单分子弹性理论

随着单分子操纵技术的发明与发展，人们已经可以对单个生物大分子施以力或力矩，并测量它们的物理性质，DNA单分子的力学实验表明，在分子尺度上理解生物大分子的生化过程，力与能量是同等重要的结构与功能参数。一个梯子模型被用来描述双链DNA的外力拉伸曲线，在这个模型中，DNA是由许多碱基对(梯子的横杆，横杆之间存在吸引势)连接两条聚核苷酸虫链(梯子的两侧)形成的高分子，利用路径积分法得出的理论曲线与实验曲线吻合得很好，对于单链DNA，用分立的杂化高分子链统计理论的母函数方法来计算其弹性行为，得出与实验相符合的外力引起的解链相变结果。此外，对于抑瘤蛋白p53识别序列DNA微环弹性进行分析，发现其弹性模量只是通常随机序列的三分之一。     

Nonlinear neural networks. I. General theory

A neural network is called nonlinear if the introduction of new data into the synaptic efficacies has to be performed through anonlinear operation. The original Hopfield model is linear, whereas, for instance, clipped synapses constitute a nonlinear model. Here a general theory is presented to obtain the statistical mechanics of a neural network with finitely many patterns and arbitrary (symmetric) nonlinearity. The problem is reduced to minimizing a free energy functional over all solutions of a fixed-point equation with synaptic kernelQ. The case of clipped synapses with bimodal and Gaussian probability distribution is analyzed in detail. To this end, a simple theory is developed that gives the spectrum ofQ and thereby all the solutions that bifurcate from the high-temperature phase.     

Symmetry breaking boundaries I. General theory

We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developed for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group. We explicitly construct the boundary states and reflection coefficients as well as the annulus amplitudes. Integrality of the annulus coefficients is proven in full generality.     

Semiclassical scattering theory with complex trajectories. I. Elastic waves

The WKB approximation to the one-particle Schrödinger equation is used to obtain the wave function at a given point as a sum of semiclassical terms, each of them corresponding to a different classical trajectory ending up at the same point. Besides the usual, real trajectories, also possible complex solutions of the classical equations of motion are considered. The simplicity of the method makes its use easy in practical cases and allows realistic calculations. The general solution of the one-dimensional WKB equations for an arbitrary number of complex turning points is given, and the solution is applied to calculate the position of the Regge poles of the scattering amplitude. The solution of the WKB equations in three dimensions for a central analytical potential is also obtained in a way that can be easily generalized to N-dimensions, provided the problem is separable. A multiple reflection series is derived, leading to a separation of the scattering amplitude into a smooth “background” term (single reflection approximation) that can be treated using classical but complex trajectories and a second resonating term that can be treated using the Sommerfeld-Watson transformation. The physical interpretation of the complex solutions of the classical equations of motion is given: they describe diffractive effects such as Fresnel, Fraunhofer diffraction, or the penetration of the quantal wave into shadow regions of caustics. They arise also in the scattering by a complex potential in an absorptive medium. The comparison with exact quantal calculations shows an astonishingly good agreement, and establishes the complex semiclassical approximation as a quantitative tool even in cases where the potential varies rapidly within a fraction of a wavelength. An approximate property of classical paths is discussed. The general pattern of the trajectories depends only on the product ? = EΘ, and not on energy and angle separately. This property is confirmed by experiments and besides the signature it gives for the semiclassical behavior, it simplifies considerably the search for all trajectories scattering through the same angle. Finally, a general classification of the different types of elastic heavy ion cross sections is given.     

Strength distributions and statistical spectroscopy. I. General theory

The strength distribution for an arbitrary excitation is given in terms of a double expansion, and its sum rules by single expansions, in polynomials defined by the initial and final energy spectra. In model spaces which are not too large, a rapid convergence, to within fluctuations, is assured by the action of a central limit theorem, as is shown in particular by considering the response of the system under infinitesimal deformations of the Hamiltonian. When larger spaces are decomposed into subspaces defined by a partitioning of the single-particle space a similar convergence results. At the same time, close contact is made with, and important corrections are found to, intuitive procedures which are often used for approximating strength distributions. The general features of the distribution are often easily understood in termsof a simple geometry made effective in the model space by the central limit theorem, and further features by exploiting the connection of this geometry to the unitary group of transformations in the single-particle space. Extensions are given for multipole strengths and sum rules, appropriate when the angular momenta (and isospins) are specified for the states involved in the transitions. Measures for the RMS fluctuations in the sum-rule quantities, and correlations between them, are given by combining the low-order-polynomial (statistically smoothed) strengths with an assumed Porter-Thomas distribution for the (high-order) strength fluctuations.     

Analytical thermodynamics. Part I. Thermostatics—General theory

A new axiomatic treatment of equilibrium thermodynamics—thermostatics—is presented. The equilibrium states of a thermal system are assumed to be represented by a differentiable manifold of dimensionn + 1 (n finite). The empirical temperature is defined by the notion of thermal equilibrium. Empirical entropy is shown to exist for all systems with the property that the total work delivered along closed adiabats is zero. Absolute entropy and temperature follow from the additivity of heat and energy for two separate systems in thermal equilibrium considered as a whole. The absolute temperature is defined up to a multiplicative constant. The exterior differentiable calculus of Cartan is introduced and in a subsequent paper its use for the derivation of standard results in thermostatics will be explained.     

A phenomenological theory of light scattering by surfaces: I. General theory

A phenomenological theory of light scattering by surfaces is presented. The differential intensity of the scattered light is found in terms of autocorrelation functions characteristic for the distribution of matter in the surface layer. Local field factors are found.     

Nonstationary nonlinear phenomena in optical slab-waveguides. I. General theory

Generalizing the stationary coupled-mode concept, nonstationary field equations for slowly varying field envelopes are derived. These field equations are combined with the equations of motion for the non-linear polarization and the inversion as well yielding a set of coupled differential equations applicable to a variety of nonstationary phenomena in waveguides. Pulse shaping and SIT of pulses interacting with a thin layer of two-level system are considered in detail.     

An impact theory for Doppler and pressure broadening—I. General theory

A quantum-mechanical impact theory for the combined effects of Doppler and pressure broadening is developed from quantum radiation theory. The results are compared with other semiclassical theories and certain simplifying approximations relevant to cases of experimental and theoretical interest are discussed.     

Time dependent canonical perturbation theory I: General theory

In this communication, we reanalyze the causes of the singularities of canonical perturbation theory and show that some of these singularities can be removed by using time-dependent canonical perturbation theory. A study of the local and global properties (in terms of the perturbation parameter) is also undertaken.     

Information theory and statistical nuclear reactions. I. General theory and applications to few-channel problems

Ensembles of scattering S-matrices have been used in the past to describe the statistical fluctuations exhibited by many nuclear-reaction cross sections as a function of energy. In recent years, there have been attempts to construct these ensembles explicitly in terms of S, by directly proposing a statistical law for S. In the present paper, it is shown that, for an arbitrary number of channels, one can incorporate, in the ensemble of S-matrices, the conditions of flux conservation, time-reversal invariance, causality, ergodicity, and the requirement that the ensemble average 〈S〉 coincide with the optical scattering matrix. Since these conditions do not specify the ensemble uniquely, the ensemble that has maximum information-entropy is dealt with among those that satisfy the above requirements. Some applications to few-channel problems and comparisons to Monte-Carlo calculations are presented.     

Renormalized theory of the time-dependent pair distribution function. I. General formulation

A classical renormalized theory of a time-dependent pair-distribution function (TDPDF), previously introduced by Oppenheim and Bloom, is presented. An equation of motion for the TDPDF is derived in which the memory function of the system appears. This is then split into a part which contains only static correlation functions and a part which describes the dynamics. The mean field approximation is discussed in some detail and contact is made witn the theory of Oppenheim and Bloom.Work supported in part by a National Research Council of Canada operating grant.     

On the hydrodynamic theory of a magnetic liquid I. General description

Using Zubarev's method of nonequilibrium statistical operator, the generalized hydrodynamic equations are obtained for a model of magnetic liquid in an inhomogeneous external field. In this model the “liquid” subsystem is treated as a classical one and the “magnetic” subsystem is described by quantum mechanical methods. The properties of the transport equations are analysed in the case of a weak nonequilibrium. The equations for time correlation functions and collective mode spectrum are also found in the same manner. It is shown that the generalized hydrodynamic equations reduce to the well-known results in the limiting cases when the dynamic variables of one subsystem are formally neglected. As an illustration, a simple model of spin relaxation is considered, and the frequency matrix and the matrix of memory functions are calculated. A comparison with previous works is made.     

Escape statistics for systems driven by dichotomous noise. I. General theory

Previous results on first-passage-time statistics for systems driven by dichotomous noise are extended in order to cover the escape from regions including fixed points of the stochastic flow. For such regions a treatment splitting the escape through one or the other boundary is required. The obtained escape probabilities and mean exit times are relevant for the complete characterization of stochastic systems undergoing bifurcations.     

Decoherence effects in Bose–Einstein condensate interferometry I. General theory

The present paper outlines a basic theoretical treatment of decoherence and dephasing effects in interferometry based on single component Bose–Einstein condensates in double potential wells, where two condensate modes may be involved. Results for both two mode condensates and the simpler single mode condensate case are presented. The approach involves a hybrid phase space distribution functional method where the condensate modes are described via a truncated Wigner representation, whilst the basically unoccupied non-condensate modes are described via a positive P representation. The Hamiltonian for the system is described in terms of quantum field operators for the condensate and non-condensate modes. The functional Fokker–Planck equation for the double phase space distribution functional is derived. Equivalent Ito stochastic equations for the condensate and non-condensate fields that replace the field operators are obtained, and stochastic averages of products of these fields give the quantum correlation functions that can be used to interpret interferometry experiments. The stochastic field equations are the sum of a deterministic term obtained from the drift vector in the functional Fokker–Planck equation, and a noise field whose stochastic properties are determined from the diffusion matrix in the functional Fokker–Planck equation. The stochastic properties of the noise field terms are similar to those for Gaussian–Markov processes in that the stochastic averages of odd numbers of noise fields are zero and those for even numbers of noise field terms are the sums of products of stochastic averages associated with pairs of noise fields. However each pair is represented by an element of the diffusion matrix rather than products of the noise fields themselves, as in the case of Gaussian–Markov processes. The treatment starts from a generalised mean field theory for two condensate modes, where generalised coupled Gross–Pitaevskii equations are obtained for the modes and matrix mechanics equations are derived for the amplitudes describing possible fragmentations of the condensate between the two modes. These self-consistent sets of equations are derived via the Dirac–Frenkel variational principle. Numerical studies for interferometry experiments would involve using the solutions from the generalised mean field theory in calculations for the stochastic fields from the Ito stochastic field equations.