We derive the momentum and pseudomomentum conservation laws from a very general nonrelativistic Lagrangian theory of the interaction of the electromagnetic field with a deforming, dispersive dielectric. From the former of these laws, we obtain the momentum density of an electromagnetic wave in matter to be ${\mathrm{\epsilon }}_0$E×B, not the Abraham form of ${\mathrm{\epsilon }}_0$E×${\mathrm{\mu }}_0$H. From the latter of these laws, we obtain the electromagnetic pseudomomentum density in the absence of deformation of the matter to be P×B plus a dispersive term, not the Minkowski form of D×B as proposed by Blount (unpublished). We show by quantizing the energy of the wave that the sum of momentum and pseudomomentum, which we name wave momentum, corresponds to Nħk (N an integer), the quantity that enters wave-vector conservation or phase-matching relations in wave interactions and that is consistent with the Jones-Richards experiment.

The Green-function technique is used to study the interbase H-bond stretch poly(dT-dA)⋅poly(dT-dA) (where dT is deoxythymine and dA is deoxyadenine) when an effective enzyme is attached to the helix. Four different one-hydrogen-bond attachment points are studied, and two different two-atom attachment points are studied. The enzyme attachments are allowed to oscillate at an unassumed resonant frequency associated with a thermally activated enzyme. This is equivalent in the Green-function formalism to a physical simulation of a simple enzyme attachment to a large DNA helix. The frequency dependence of hydrogen-bond thermal mean motion seems to be a key to the distinction between a dynamic repressor and enhancer action. The response is enhanced interbase hydrogen-bond-stretch amplitude when the effective enzyme attachment to the helix in poly(dT-dA)⋅poly(dT-dA) is oscillating at frequencies that are near the interbase breathing mode of the helix. When the effective enzyme attachment is oscillating at frequencies far removed from the breathing mode of the helix, the response is usually repressed interbase hydrogen-bond stretch. Spectral density therefore may be a signature of protein enhancer or repressor action. A two-attachment effective enzyme is simulated, and it is shown that it can be approximated by the two individual one-point attachments if the force constant attaching them is small.

An analysis is given of the stochastic dynamics of time-summating binary neural networks. Such networks have a memory or trace of their previous output activity reaching back to some initial time. Particular attention is given to a class of networks based on a discrete time version of leaky-integrator shunting networks. The stochastic dynamics is formulated as a linear Markov process describing the evolution of densities on the infinite-dimensional space of neuronal activation states. Using certain results from the theory of linear Markov operators, due to Lasota and Mackey [Probabilistic Properties of Deterministic Systems (Oxford University, Oxford, 1986); Physica D 28, 143 (1987)], conditions are derived for asymptotic stability in which the network converges to a unique limiting density. Moreover, the limiting density is shown to be a differentiable function of the parameters of the network such as the weights and decay factors. Finally, dynamical mean-field equations are derived that have periodic and chaotic solutions, implying a breaking of asymptotic stability in the thermodynamic limit.

A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electrical-chemical properties of synaptic interactions. While not useful to yield insights at the single-neuron level, SMNI has demonstrated its capability in describing large-scale properties of short-term memory and electroencephalographic (EEG) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. In this paper, a more stringent test is placed on SMNI: The algebraic and numerical algorithms previously developed in this and similar systems are brought to bear to fit large sets of EEG and evoked-potential data being collected to investigate genetic predispositions to alcoholism and to extract brain ‘‘signatures’’ of short-term memory. Using the numerical algorithm of very fast simulated reannealing, it is demonstrated that SMNI can indeed fit these data within experimentally observed ranges of its underlying neuronal-synaptic parameters, and the quantitative modeling results are used to examine physical neocortical mechanisms to discriminate high-risk and low-risk populations genetically predisposed to alcoholism. Since this study is a control to span relatively long time epochs, similar to earlier attempts to establish such correlations, this discrimination is inconclusive because of other neuronal activity which can mask such effects. However, the SMNI model is shown to be consistent with EEG data during selective attention tasks and with neocortical mechanisms describing short-term memory previously published using this approach. This paper explicitly identifies similar nonlinear stochastic mechanisms of interaction at the microscopic-neuronal, mesoscopic-columnar, and macroscopic-regional scales of neocortical interactions. These results give strong quantitative support for an accurate intuitive picture, portraying neocortical interactions as having common algebraic or physics mechanisms that scale across quite disparate spatial scales and functional or behavioral phenomena, i.e., describing interactions among neurons, columns of neurons, and regional masses of neurons.

A method for carrying out Monte Carlo calculations for condensed-matter systems in the microcanonical ensemble is formulated and illustrated with example calculations. A complete statistical mechanics associated with the Monte Carlo procedure is presented. The same method applies to any of the microcanonical-like shell ensembles.

Chaotic transients resulting after a boundary crisis are examined in the presence of external, additive noise. Depending on its amplitude, the mean duration of chaotic evolution may be elongated or shortened.

The freezing of supercooled water is measured at the small-angle x-ray facilities at the Synchrotron Radiation Source in Daresbury, United Kingdom, for 0.1 ${\mathrm{nm}}^{\mathrm{-}1}$<k<2 ${\mathrm{nm}}^{\mathrm{-}1}$ in the temperature range from 250 to 273 K. A sharp peak in the spectra of ice is observed at a scattering wave-vector value given by 1/8(1-δ) times a reciprocal-lattice vector of the hexagonal or cubic ice. The mismatch δ decreases in time after the onset of freezing and vanishes after about two hours just as the intensity does. A possible explanation in terms of a growth mechanism is discussed.

The purpose of this paper is to quantify the role of initial configurations that have an electron beyond the L shell in 1s-2p absorption of aluminum ions. The study is done in the context of a recent x-ray transmission experiment and is based on a theoretical model that is in good agreement with the measurements. In addition, the method of Epstein will be used to study the temperature-dependent effect of excited states on the cross section for the individual ions. Results indicate that about 50% of the absorption is due to initial configurations that have an excited electron beyond the L shell, and the overall opacity of the 1s-2p manifold of transitions can be enhanced by these configurations at elevated temperatures for some ion species.

This paper reports the first stage of a study intended to shed light on our understanding of the connection between chaotic classical trajectories and scattering resonance distributions. We have numerically examined scalar-wave-equation solutions for light scattering from an array of three dielectric cylinders. Similar systems using hard disks as well as continuous repulsive potentials, which support classical chaos, have been studied before. Our dielectric cylinders have the advantage of allowing us to study the effect of caustics on the scattering while being a system simple enough to be solved exactly. Using a Green’s-theorem approach, we have calculated differential and total cross sections in the relatively-long-wavelength regime (ka≲20) and compared them to previous results. We find interestingly large differences between the three-hard-disk case and our dielectric case: the dielectric scattering cross section displays considerably more structure. It may be possible to experimentally verify these results for our dielectric cylinders. Our paper includes an explanation of the major qualitative features exhibited by the cross sections.

The minimization of the relativistic total energy with respect to the linear and nonlinear parameters in the wave function is a notoriously cumbersome task due to the phenomenon usually referred to as ‘‘variational collapse.’’ This property of the Dirac matrix equation is generally attributed to the fact that the Dirac operator is not bounded from below. Several methods have been developed to avoid these unphysical solutions. Here we examine the possibility of finding the solutions to the Dirac equation by minimizing the variance of the energy. Monte Carlo integration techniques are used to evaluate the variance functional. The results are very encouraging. No spurious roots are found for any of the basis sets used in the calculations. However, the solutions are not strictly variational and hence are not upper bounds to the energy.

The multiconfiguration relativistic random-phase approximation theory is applied to magnetic dipole transitions in atoms. Excitation energies and oscillator strengths from the ground level ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$ to the excited level ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ of Pb-like ions are calculated as prototypal examples. The first ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ level for the neutral Pb atom, which is missing in the relativistic random-phase approximation, appears naturally in this theory, which accounts for two-particle–two-hole correlations.

Threshold-electron spectra have been measured in the vicinity of Kr 3d and Xe 4d shake-up regions using a threshold-electron analyzer. With the aid of multiconfigurational Dirac-Fock energy calculations, we have uncovered conjugate shake-up satellites in the spectra. The conjugate shake-up process has been found to be strongly enhanced at the Kr 3d and Xe 4d shake-up thresholds.

A continuous parameter introduced into the convolution transformation between P and Q functions leads to a measure of how nonclassical quantum states are with values ranging from 0 to 1: For photon-number states, the value is 1, the maximum possible. For squeezed vacuum states, it is a monotonically increasing function of the squeeze parameter with values varying from 0 to 1/2. This measure is identical to the minimum number of thermal photon necessary to destroy whatever nonclassical effects existing in the quantum states.

The transition between diffractive and diffusive regimes in the deflection of atoms by a standing-wave light field has recently been observed experimentally by Gould et al, [Phys. Rev. A 43, 585 (1991)]. We describe and present the results of a numerical simulation which allows these results to be understood in terms of the theory developed by Tanguy, Reynaud, and Cohen-Tannoudji [J. Phys. B 17, 4623 (1984)].

We investigate various statistics of energy levels of integrable quantum systems with Hamiltonians H=1/2(I-α${)}^2$ on the unit torus, with α a parameter. We find strong numerical evidence, by using up to ${10}^9$ levels, that for typical α, with respect to uniform distribution in the unit square, the local empirical statistics of the levels ${\mathit{E}}_{\mathbf{n}}$=1/2(n-α${)}^2$, n∈${\mathit{openZ}}^2$, converge for large energies to a Poisson limit. The fluctuation of the total number of levels, ${\mathit{E}}_{\mathit{n}}$<E, scales like ${\mathit{E}}^{1/4}$ and its distribution converges to a non-Gaussian limit. The variance and skewness of this distribution can be computed analytically.

We propose a quantitative measure of correlations between coevolving dynamical systems. This measure proves to be very useful in characterizing synchronization in chaotic systems. It can distinguish between chaotic signals that are perfectly synchronized, partially synchronized, and completely asynchronized. We further illustrate the utility of this measure by using it for the analysis of the degradation of synchronization due to the variation of the parameters of the synchronizing or response systems. We find that the degradation is a smooth function of the parameter difference between the response systems and is almost symmetric about the origin.

We consider the stability properties of spatial and temporal periodic orbits of one-dimensional coupled-map lattices. The stability matrices for them are of the block-circulant form. This helps us to reduce the problem of stability of spatially periodic orbits to the smaller orbits corresponding to the building blocks of spatial periodicity, enabling us to obtain the conditions for stability in terms of those for smaller orbits.

We study the interaction of two-dimensional (2D) solutions as they arise for the envelope equations for a subcritical bifurcation to traveling waves. We show that these 2D localized solutions can collide and reemerge unchanged in size and shape after the collision in contrast to what is found in 2D soliton systems. Various other types of behavior arise as the impact parameter and the cross coupling between the waves are varied. We point out that these phenomena should be observable experimentally for hydrodynamic instabilities in anisotropic liquids such as nematic liquid crystals.