Nonlinear response from the perspective of energy landscapes and beyond

The paper discusses the nonlinear response of disordered systems. In particular we show how the nonlinear response can be interpreted in terms of properties of the potential energy landscape. It is shown why the use of relatively small systems is very helpful for this approach. For a standard model system we check which system sizes are particular suited. In case of the driving of a single particle via an external force the concept of an effective temperature helps to scale the force dependence for different temperature on a single master curve. In all cases the mobility increases with increasing external force. These results are compared with a stochastic process described by a 1d Langevin equation where a similar scaling is observed. Furthermore it is shown that for different classes of disordered systems the mobility can also decrease with increasing force. The results can be related to the properties of the chosen potential energy landscape. Finally, results for the crossover from the linear to the nonlinear conductivity of ionic liquids are presented, inspired by recent experimental results in the Roling group. Apart from a standard imidazolium-based ionic liquid we study a system which is characterized by a low conductivity as compared to other ionic liquids and very small nonlinear effects. We show via a real space structural analysis that for this system a particularly strong pair formation is observed and that the strength of the pair formation is insensitive to the application of strong electric fields. Consequences of this observation are discussed.     

An evolution theory in finite size systems

A new model of evolution is presented for finite size systems. Conditions under which a minority species can emerge, spread and stabilize to a macroscopic size are studied. It is found that space organization is instrumental in addition to a qualitative advantage. Some peculiar topologies ensure the overcome of the initial majority species. However the probability of such local clusters is very small and depend strongly on the system size. A probabilistic phase diagram is obtained for small sizes. It reduces to a trivial situation in the thermodynamic limit, thus indicating the importance of dealing with finite systems in evolution problems. Results are discussed with respect to both Darwin and punctuated equilibria theories. Received 25 June 2000     

Fundamental Limitations and Topological Considerations for Fast Discharge Homopolar Machines

Fusion research experiments require high energy short duration pulses. A homopolar machine, as an inertial energy storage system, offers an attractive source of energy meeting these requirements. The Energy Storage Group at The University of Texas at Austin has investigated the fundamental limitations to the discharge time of homopolar machines of various topological configurations. This paper presents a mathematical model for fast discharge homopolar machines. Based on this model, various machine configurations are analyzed. A new configuration - the spool type machine - is also discussed, criteria for the evaluation of different alternatives are presented, and it is concluded that highly efficient (? 95%), high energy (? gigajoules), fast-discharge (? 5 to 30 milliseconds) homopolar inertial energy storage systems are technically feasible. Brief reference is also made to some of the experimental results obtained from the existing laboratory models.     

Superradiance and energy transfer within a system of atoms

We investigate cooperative effects in energy relaxation and energy transfer for N atoms in a thermal radiation field with superradiance master equations as well as a closed set of coupled moment equations. Both spatially large and spatially small systems are considered. For small systems nonlinear rate equations for the energy are related to the moment equations. Symmetry of the small system to interchanging atoms is used to incorporate off-diagonal solutions of the superradiance master equation in expressions for the probability of the transfer of energy from one group of atoms to another. The long time excitation probability for initially unexcited atoms is large and strongly correlated. Cooperative processes in a large system which fall off with the distance between a cooperating pair of atoms include energy loss and transfer terms in the master equation. The energy transfer is oscillatory in time. Energy relaxation is shown by numerical solution to become cooperative in a very sudden manner as the scale of the atomic system is decreased through the resonant wavelength.     

Processes of energy exchange in systems of nonidentical particles with inhomogeneous sources of heat

Processes of energy exchange in dissipative systems of nonidentical interacting particles (having different sizes, charges, etc.) with an inhomogeneous distribution of sources of heat and/or any other sources of stochastic kinetic energy are considered. A theoretical model is proposed for analyzing the energy balance in such systems. Analytical relations describing the redistribution of the “kinetic temperature” between interacting particles of the system are obtained within this model. These relations are tested by the numerical simulation of the problem for Yukawa systems.     

Electrohydrodynamic self-synchronization of self-oscillations on two diaphragm current concentrators in electrolyte

This work presents the result of experimental studying the mechanisms of self-synchronization of electrohydrodynamic self-oscillation processes in electrolyte for two current concentrators of different size performed in the form of holes in dielectric diaphragms.When an inductance coil is connected to a discharge circuit, a phase synchronization of self-oscillations occurs and is realized as a result of energy accumulation in the coil at the stage of current rise and energy release during the overlapping the current channel by a bubble. The difference in self-synchronization mechanisms is due to small and great spread in concentrator sizes. When having small spread in concentrator sizes, the energy released before the overlapping the concentrators by bubbles is sufficient to provide a synchronization, and when having great spread in concentrator sizes, the energy is required to be released after the overlapping the concentrators due to gas ionization in bubbles.     

Emittance-dominated long bunches in dual harmonic RF system

The storage of long bunches for long time intervals needs flattened stationary buckets with a large bucket height. The longitudinal motion of the initially mismatched beam has been studied for both the single and dual harmonic RF systems. The RF amplitude is determined to be r.m.s wise matched. The bucket height of the single harmonic system is too small even for shorter bunch with only 20% increased energy spread. The Halo formation and even debunching can be seen after a few synchrotron periods for single particles with large amplitude. In the case of small energy spread for a cooled beam, Coulomb interaction cannot be ignored. The external voltage has to be increased to keep the r.m.s bunch length unchanged. The new voltage ratio R(N) simplifies physics for the emittance-dominated bunches with modest particle number N. For the single harmonic system, substantial amount of debunching occurs without increasing the external voltage, but very little if the RF amplitude is doubled. Results from the ORBIT tracking code are presented for the 1 GeV bunch in the HESR synchrotron, part of the GSI FAIR project.     

双谐波高频系统的同步加速器中发射度主导的长束团研究

在质子储存环中,长束团的长期储存要求采用比较平的 bucket 以增加纵向接收度。对于经过相空间冷却的低能散的束流,束流内部的库仑散射作用不能被忽略。本文讨论了对于处在临界能量以下的发射度主导的长束团双谐波高频系统的特性。为了保持束团长度不变,高频电压应作适当的提高以补偿空间电荷效应的作用。初始失配的束流的纵向运动也分别对于单谐波或双谐波系统进行了研究,对于前者失配度为20%时,纵向接收度太小导致经过几个同步周期后就出现明显的束流纤维化和散束。本文还引入了一种空间电荷作用因子和纵向失配度的概念来研究和分析发射度主导的长束团的纵向运动。采用ORBIT程序对FAIR-HESR加速器中的束流纵向运动进行了模拟跟踪计算,并与理论分析进行了比较。     

Narrowband and broadband active control in an enclosure using the acoustic energy density

An active control system based on the acoustic energy density is investigated. The system is targeted for use in three-dimensional enclosures, such as aircraft cabins and rooms. The acoustic energy density control method senses both the potential and kinetic energy densities, while the most popular control systems of the past have relied on the potential energy density alone. Energy density fields are more uniform than squared pressure fields, and therefore, energy density measurements are less sensitive to sensor location. Experimental results are compared to computer-generated results for control systems based on energy density and squared pressure for a rectangular enclosure measuring 1.5 x 2.4 x 1.9 m. Broadband and narrowband frequency pressure fields in the room are controlled experimentally. Pressure-field and mode-amplitude data are presented for the narrowband experiments, while spectra and pressure-field data are presented for the broadband experiment. It is found that the energy density control system has superior performance to the squared pressure control system since the energy density measurement is more capable of observing the modes of a pressure field. Up to 14.4 and 3.8 dB of cancellation are achieved for the energy density control method for the narrowband and broadband experiments presented, respectively.     

Chaotic versus nonchaotic stochastic dynamics in Monte Carlo simulations: a route for accurate energy differences in N-body systems

We present a method to efficiently evaluate small energy differences of two close N-body systems by employing stochastic processes having a stability versus chaos property. By using the same random noise, energy differences are computed from close trajectories without reweighting procedures. The approach is presented for quantum systems but can be applied to classical N-body systems as well. It is exemplified with diffusion Monte Carlo simulations for long chains of hydrogen atoms and molecules for which it is shown that the long-standing problem of computing energy derivatives is solved.     

Phase rotation scheme of laser-produced ions for reduction of the energy spread

In order to widely spread out particle beams utilized in cancer therapy, laser-produced ions are developed as the injection beam for an ion synchrotron dedicated for cancer therapy. Such a laser ion source is expected to contribute largely to the realization of compactness of the size and low cost of the cancer therapy accelerator. The energy spectrum of the laser-produced ions, however, has no peak, but their intensities decrease exponentially according to the increase of the energy. For the purpose of modifying such a situation, we have proposed a scheme to rotate the beam in the longitudinal phase space with the use of the RF electric field, which is phase-adjusted with the pulse laser. We aim for a reduction of the energy spread of ± 5% selected by an energy analyzer and slits to ±1% by such phase rotation. For this purpose, a quarter wavelength resonator with two gaps with the same resonant frequency as the source laser has already been fabricated, together with its RF power source. The above phase rotation system and its recent experimental realization are presented.     

Monte Carlo simulations in the isothermal—isobaric ensemble: the requirement of a ‘shell’ molecule and simulations of small systems

A modification of the widely used Monte Carlo method for determining thermophysical properties in the isothermal-isobaric ensemble is presented. The new Monte Carlo method, now consistent with recent derivations describing the proper statistical mechanical formulation of the constant pressure ensemble for small systems, requires a ‘shell’ molecule to uniquely identify the volume of the system, thereby avoiding the redundant counting of configurations. Ensemble averages obtained with the new algorithm differ from averages calculated with the old Monte Carlo method, particularly for small system sizes, although both sets of averages become equal in the thermodynamic limit. Monte Carlo simulations in the constant pressure ensemble applied to the Lennard-Jones fluid demonstrate these differences for small systems. Peculiarities of small systems are also discussed, revealing that ‘shape’ is an important thermodynamic variable. Finally, an extension of the Monte Carlo method to mixtures is presented.     

Demonstration of high-trapping efficiency and narrow energy spread in a laser-driven accelerator

Laser-driven electron accelerators (laser linacs) offer the potential for enabling much more economical and compact devices. However, the development of practical and efficient laser linacs requires accelerating a large ensemble of electrons together ("trapping") while keeping their energy spread small. This has never been realized before for any laser acceleration system. We present here the first demonstration of high-trapping efficiency and narrow energy spread via laser acceleration. Trapping efficiencies of up to 80% and energy spreads down to 0.36% (1 sigma) were demonstrated.     

Generation of beams of charged particles with transverse energy

The paper describes the operation and construction of an electron gun designed to form beams with variable transverse energy and a variable spread of magnetic moments. Transverse energy is acquired by the electrons as the beam passes through a weakly non-adiabatic magnetic step, and in an adiabatic motion through a growing magnetic field. The small spread of magnetic moments of the beam electrons is achieved by fulfilling the so-called focusing conditions which ensure that the spread of moments resulting from different initial radii of the particles is compensated by their initial radial velocities.     

Diffusion dominated dynamics of avalanching systems

A surprisingly large number of systems in nature are thought to be governed by internal dynamics which causes avalanches of various sizes. In such systems energy, which is delivered from outside, is redistributed as a result of the occurrence of localized avalanches. Starting an avalanche requires that some threshold condition be satisfied. Random driving (energy input) brings the system into a strongly inhomogeneous state, so that the probability of triggering an avalanche in a large part of the system is small. In most physical systems energy redistribution may occur due to diffusive processes without avalanches. Diffusion also makes the system more uniform, making large avalanche triggering more probable. The observed behavior of a such system may crucially depend on the competition between diffusion and driving. In this paper, the effects of diffusive processes are investigated using a dissipative, isotropic one-dimensional model, in which avalanches can propagate in both directions. It is shown that the system behavior changes progressively as the diffusion rate increases. In the absence of diffusion, many small avalanches are triggered. Increasing the diffusion rate gradually suppresses these small avalanches and leads to the development of large, quasi-periodic bursts.     

Accumulation and transmission of the light energy in nonreciprocal multilayer systems

The specific features of light energy distribution within a multiplayer optical system are calculated by using the effective layer addition method. Various mechanisms of nonreciprocity are discussed, and Jones matrices of systems with different mechanisms of nonreciprocity are considered and compared. Accumulation of polarized light energy and resonance light diode transmission (due to the asymmetric character of interaction between the light and nonreciprocal anisotropic system) in multilayer systems with cholesteric liquid crystal layer(s) in presence of small absorption are predicted in certain range of the light spectrum and polarization. The accumulation of light in the multilayer optical systems with the defects, based on realistic solid materials with periodical structure, are also discussed, aiming at their applications in the liquid or gas-heaters and solar energy and fiber optics converters.     

Optimizing the rapidity limit for nuclear stopping in intermediate energy heavy-ion collisions

A systematic study regarding the role of participant matter and spectator matter in nuclear stopping using isospin-dependent quantum molecular dynamics model is presented. The simulations have been carried out with soft equation of state along with the reduced isospin-dependent cross section to study the effect of different types and sizes of rapidity distributions on nuclear stopping for the whole colliding geometry with density-dependent symmetry energy. In addition to that, we attempt to investigate the role of isospin in heavy-ion collisions by calculating the individual contribution of neutrons and protons in nuclear stopping for different systems having different isotopic content.     

Direct calculation of intermolecular potential energy surfaces

A variation perturbation method is presented for the direct calculation of intermolecular interaction energies. The theory is based on valence bond ideas but avoids the full evaluation of the matrix elements by expansion in powers of interchange, a procedure which is valid for small overlap between the systems. The participating excited states are regarded as polarized pseudo-states and are determined by optimizing the long-range multipole-multipole part of the interaction energy. The validity of these ideas is illustrated by a calculation of the He-He interaction. A remarkable simplification is pointed out, in which the interaction energy is given almost exactly by the sum of the repulsive term, calculated as zero + single interchange, plus the long-range interaction.     

Partial equivalence of statistical ensembles and kinetic energy

The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the microcanonical and the canonical ensemble. Furthermore, the configurational microcanonical entropy is a smooth function, whereas a nonanalytic point of the configurational free energy indicates the presence of a phase transition in the canonical ensemble. In the presence of a standard kinetic energy contribution, partial equivalence is removed and a nonanalyticity arises also microcanonically. Hence in contrast to the common belief, kinetic energy, even though a quadratic form in the momenta, has a nontrivial effect on the thermodynamic behaviour. As a by-product we present the microcanonical solution of the mean-field spherical model with kinetic energy for finite and infinite system sizes.     

Particle dynamics simulations of triboelectric charging in granular insulator systems

Particle dynamics simulations are carried out to study triboelectric charging in granular systems composed of a single insulating material. The simulations implement a model in which electrons trapped in localized high energy states can be transferred during collisions to low energy states in the other particle. It is shown that this effect alone can generate electrostatic charging in the system, and cause net electron transfer from larger particles to smaller particles. The magnitude of charging is small for systems of a single particle size but becomes much greater for a system with polydispersal particle sizes, due to the net electron transfer from larger to smaller particles. The negative charge of smaller particles, and positive charge of larger particles has been observed in field studies and laboratory experiments of granular systems.