NVU dynamics. III. Simulating molecules at constant potential energy

This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers [Ingebrigtsen et al., J. Chem. Phys. 135, 104101 (2011); ibid, 104102 (2011)], a numerical algorithm for simulating geodesic motion of atomic systems was developed and tested against standard algorithms. The conclusion was that the NVU algorithm has the same desirable properties as the Verlet algorithm for Newtonian NVE dynamics, i.e., it is time-reversible and symplectic. Additionally, it was concluded that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit. In this paper, the NVU algorithm for atomic systems is extended to be able to simulate geodesic motion of molecules at constant potential energy. We derive an algorithm for simulating rigid bonds and test this algorithm on three different systems: an asymmetric dumbbell model, Lewis-Wahnstrom OTP, and rigid SPC/E water. The rigid bonds introduce additional constraints beyond that of constant potential energy for atomic systems. The rigid-bond NVU algorithm conserves potential energy, bond lengths, and step length for indefinitely long runs. The quantities probed in simulations give results identical to those of Nose-Hoover NVT dynamics. Since Nose-Hoover NVT dynamics is known to give results equivalent to those of NVE dynamics, the latter results show that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit also for molecular systems.Comment: 14 pages, 12 figure

Soliton-dynamical approach to a noisy Ginzburg-Landau model

We present a dynamical description and analysis of non-equilibrium transitions in the noisy Ginzburg-Landau equation based on a canonical phase space formulation. The transition pathways are characterized by nucleation and subsequent propagation of domain walls or solitons. We also evaluate the Arrhenius factor in terms of an associated action and find good agreement with recent numerical optimization studies.Comment: 4 pages (revtex4), 3 figures (eps

Noisy regression and classification with continuous multilayer networks

We investigate zero temperature Gibbs learning for two classes of unrealizable rules which play an important role in practical applications of multilayer neural networks with differentiable activation functions: classification problems and noisy regression problems. Considering one step of replica symmetry breaking, we surprisingly find that for sufficiently large training sets the stable state is replica symmetric even though the target rule is unrealizable. Further, the classification problem is shown to be formally equivalent to the noisy regression problem.Comment: 7 pages, including 2 figure

Microcanonical quantum fluctuation theorems

Previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate spectra. In the particular case of microcanonical initial states explicit expressions for the characteristic function and the corresponding probability density of work are formulated. Their classical limit as well as their relations to the respective canonical expressions are discussed. A fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final Hamiltonians.From this Crooks-type fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time reversed process. This entropy-from-work theorem provides an experimentally accessible way to measure entropies.Comment: revised and extended versio

Optimal Resource Allocation in Random Networks with Transportation Bandwidths

We apply statistical physics to study the task of resource allocation in random sparse networks with limited bandwidths for the transportation of resources along the links. Useful algorithms are obtained from recursive relations. Bottlenecks emerge when the bandwidths are small, causing an increase in the fraction of idle links. For a given total bandwidth per node, the efficiency of allocation increases with the network connectivity. In the high connectivity limit, we find a phase transition at a critical bandwidth, above which clusters of balanced nodes appear, characterised by a profile of homogenized resource allocation similar to the Maxwell's construction.Comment: 28 pages, 11 figure

Chronic arsenic exposure and risk of infant mortality in two areas of Chile.

Chronic arsenic exposure has been associated with a range of neurologic, vascular, dermatologic, and carcinogenic effects. However, limited research has been directed at the association of arsenic exposure and human reproductive health outcomes. The principal aim of this study was to investigate the trends in infant mortality between two geographic locations in Chile: Antofagasta, which has a well-documented history of arsenic exposure from naturally contaminated water, and Valparaíso, a comparable low-exposure city. The arsenic concentration in Antofagasta's public drinking water supply rose substantially in 1958 with the introduction of a new water source, and remained elevated until 1970. We used a retrospective study design to examine time and location patterns in infant mortality between 1950 and 1996, using univariate statistics, graphical techniques, and Poisson regression analysis. Results of the study document the general declines in late fetal and infant mortality over the study period in both locations. The data also indicate an elevation of the late fetal, neonatal, and postneonatal mortality rates for Antofagasta, relative to Valparaíso, for specific time periods, which generally coincide with the period of highest arsenic concentration in the drinking water of Antofagasta. Poisson regression analysis yielded an elevated and significant association between arsenic exposure and late fetal mortality [rate ratio (RR) = 1.7; 95% confidence interval (CI), 1.5-1.9], neonatal mortality (RR = 1.53; CI, 1.4-1.7), and postneonatal mortality (RR = 1.26; CI, 1.2-1.3) after adjustment for location and calendar time. The findings from this investigation may support a role for arsenic exposure in increasing the risk of late fetal and infant mortality

Phase Diagram and Storage Capacity of Sequence Processing Neural Networks

We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium statistical mechanical analysis. Using generating functional methods we derive exact closed equations for dynamical order parameters, viz. the sequence overlap and correlation- and response functions, in the thermodynamic limit. We calculate the time translation invariant solutions of these equations, describing stationary limit-cycles, which leads to a phase diagram. The effective retarded self-interaction usually appearing in symmetric models is here found to vanish, which causes a significantly enlarged storage capacity of $\alpha_c\sim 0.269$, compared to \alpha_\c\sim 0.139 for Hopfield networks storing static patterns. Our results are tested against extensive computer simulations and excellent agreement is found.Comment: 17 pages Latex2e, 2 postscript figure

Analysis of Bidirectional Associative Memory using SCSNA and Statistical Neurodynamics

Bidirectional associative memory (BAM) is a kind of an artificial neural network used to memorize and retrieve heterogeneous pattern pairs. Many efforts have been made to improve BAM from the the viewpoint of computer application, and few theoretical studies have been done. We investigated the theoretical characteristics of BAM using a framework of statistical-mechanical analysis. To investigate the equilibrium state of BAM, we applied self-consistent signal to noise analysis (SCSNA) and obtained a macroscopic parameter equations and relative capacity. Moreover, to investigate not only the equilibrium state but also the retrieval process of reaching the equilibrium state, we applied statistical neurodynamics to the update rule of BAM and obtained evolution equations for the macroscopic parameters. These evolution equations are consistent with the results of SCSNA in the equilibrium state.Comment: 13 pages, 4 figure

Power-Laws in Nonlinear Granular Chain under Gravity

The signal generated by a weak impulse propagates in an oscillatory way and dispersively in a gravitationally compacted granular chain. For the power-law type contact force, we show analytically that the type of dispersion follows power-laws in depth. The power-law for grain displacement signal is given by $h^{-1/4(1-1/p)}$ where $h$ and $p$ denote depth and the exponent of contact force, and the power-law for the grain velocity is $h^{-1/4({1/3}+1/p)}$. Other depth-dependent power-laws for oscillation frequency, wavelength, and period are given by combining above two and the phase velocity power-law $h^{1/2(1-1/p)}$. We verify above power-laws by comparing with the data obtained by numerical simulations.Comment: 12 pages, 3 figures; Changed conten

A Phenomenological Description of the Non-Fermi-Liquid Phase of MnSi

In order to understand the non-Fermi-liquid behavior of MnSi under pressure we propose a scenario on the basis of the multispiral state of the magnetic moment. This state can describe the recent critical experiment of the Bragg sphere in the neutron scattering which is the key ingredient of the non-Fermi-liquid behavior.Comment: 3 page