Random Energy Research Articles

Effects of an anode sheath on energy and momentum transfer in vacuum arcs

Anode phenomena under high-current vacuum arcs have a significant impact on the interrupting capacity of vacuum interrupters. However, the vacuum arc energy flux and momentum flux on the anode—which are necessary boundary conditions for simulations—are either set to an imaginary distribution or calculated using simple formulas without considering anode sheath regulatory effects. The objective of this paper is to reveal the anode sheath effects on regulating the energy and momentum transfer from the arc column to the anode surface in vacuum arcs. A particle-in-cell model for the anode sheath is developed. The required input parameters are obtained from a magnetohydrodynamic model for the arc column. From the results, there exists a sheath near the anode with a negative voltage drop. Both the electron density and the ion density significantly decline in the anode sheath region. The kinetic energy of the ions absorbed by the anode consists of directed kinetic energy, random kinetic energy, and sheath acceleration energy. The sheath acceleration energy contribution is the largest, and the random kinetic energy also accounts for a large part that cannot be ignored. The arc pressure on the anode surface is mainly caused by ion impact, and the accelerating effect of the anode sheath on the ions cannot be neglected in pressure calculations. In addition, in the case of an arc current at 15 kA, the input energy and momentum upon the anode surface is not obviously affected by the evaporated atoms at surface temperatures of 1600 K and 2000 K.

Limit theorems associated with the Pitman–Yor process

Abstract The Pitman–Yor process is a random discrete measure. The random weights or masses follow the two-parameter Poisson–Dirichlet distribution with parameters 0 < α < 1, θ > -α. The parameters α and θ correspond to the stable and gamma components, respectively. The distribution of atoms is given by a probability η. In this paper we consider the limit theorems for the Pitman–Yor process and the two-parameter Poisson–Dirichlet distribution. These include the law of large numbers, fluctuations, and moderate or large deviation principles. The limiting procedures involve either α tending to 0 or 1. They arise naturally in genetics and physics such as the asymptotic coalescence time for explosive branching process and the approximation to the generalized random energy model for disordered systems.

Nonequilibrium transport through a disordered molecular nanowire

We investigate the non-equilibrium transport properties of a disordered molecular nanowire. The nanowire is regarded as a quasi-one-dimensional organic crystal composed of self-assembled molecules. One orbital and a single random energy are assigned to each molecule while the intermolecular coupling does not fluctuate. Consequently, electronic states are expected to be spatially localized. We consider the regime of strong localization, namely, the localization length is smaller than the length of the molecular wire. Electron-vibron interaction, taking place in each single molecule, is also taken into account. We investigate the interplay between disorder and electron-vibron interaction in response to either an applied electric bias or a temperature gradient. To this end, we calculate the electric and heat currents when the nanowire is connected to leads, using the Keldysh non-equilibrium Green's function formalism. At intermediate temperature, scattering by disorder dominates both charge and heat transport. We find that the electron-vibron interaction enhances the effect of the disorder on the transport properties due to the exponential suppression of tunneling.

Critical behavior of the two-dimensional Coulomb glass at zero temperature

The lattice model of Coulomb Glass in two dimensions with box-type random field distribution is studied at zero temperature for system size upto $96^{2}$. To obtain the minimum energy state we annealed the system using Monte Carlo simulation followed by further minimization using cluster-flipping. The values of the critical exponents are determined using the standard finite size scaling. We found that the correlation length $\xi$ diverges with an exponent $\nu=1.0$ at the critical disorder $W_{c} = 0.2253$ and that $\chi_{dis} \approx \xi^{4-\bar{\eta}}$ with $\bar{\eta}=2$ for the disconnected susceptibility. The staggered magnetization behaves discontinuously around the transition and the critical exponent of magnetization $\beta=0$. The probability distribution of the staggered magnetization shows a three peak structure which is a characteristic feature for the phase coexistence at first-order phase transition. In addition to this, at the critical disorder we have also studied the properties of the domain for different system sizes. In contradiction with the Imry-Ma arguments, we found pinned and non-compact domains where most of the random field energy was contained in the domain wall. Our results are also inconsistent with Binder's roughening picture.

Hybrid annealing: Coupling a quantum simulator to a classical computer

Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Simulated annealing is a computational technique which explores the configuration space by mimicking thermal noise. By slow cooling, it freezes the system in a low-energy configuration, but the algorithm often gets stuck in local minima. In quantum annealing, the thermal noise is replaced by controllable quantum fluctuations, and the technique can be implemented in modern quantum simulators. However, quantum-adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasi-degenerate ground states.

Twisting Motion Frequency Dependent I-V Characteristics of 102 Base Pairs Poly(dG)-Poly(dC) DNA Molecule

The I-V characteristic of 102 base pair Poly(dG)-Poly(dC) DNA molecule have been calculated for several base pairs twisting motion frequencies. The calculation is carried out on doubled-stranded DNA model sandwiched in between two metallic electrodes. The effect is studied by taking into account twisting angle dependent on-site energy and hopping constant in the tight binding Hamiltonian of double-strand DNA model. We use semi-empirical Slater-Koster theory in the twisting angle dependent intra- and inter-strand hopping constant. We consider the temperature dependent sugar-phosphate backbone on-site energy by employing random energy disorder using uniform distribution function. The standard deviation of twisting angle is obtained by assuming that the average kinetic energy of twisting motions is proportional to system temperature. The transfer and scattering matrix methods are used simultaneously in calculating the transmission probability of charge on the molecule. We choose the contacts between molecule and both electrodes such that the main features of transport properties of the molecule do not change much by the presence of metallic electrodes. By assuming the voltage drops symmetrically at the contacts, Landauer-Buttiker Formalism is used in calculating the I-V characteristic of the molecule from transmission probability. The results show that the magnitude of current increases by twisting motion frequency increment. Larger current magnitude increment is observed at higher voltage. The influence of twisting motion frequency on the I-V characteristic is stronger at higher temperature, in the range of considered temperature.

Long-time predictability in disordered spin systems following a deep quench.

We study the problem of predictability, or "nature vs nurture," in several disordered Ising spin systems evolving at zero temperature from a random initial state: How much does the final state depend on the information contained in the initial state, and how much depends on the detailed history of the system? Our numerical studies of the "dynamical order parameter" in Edwards-Anderson Ising spin glasses and random ferromagnets indicate that the influence of the initial state decays as dimension increases. Similarly, this same order parameter for the Sherrington-Kirkpatrick infinite-range spin glass indicates that this information decays as the number of spins increases. Based on these results, we conjecture that the influence of the initial state on the final state decays to zero in finite-dimensional random-bond spin systems as dimension goes to infinity, regardless of the presence of frustration. We also study the rate at which spins "freeze out" to a final state as a function of dimensionality and number of spins; here the results indicate that the number of "active" spins at long times increases with dimension (for short-range systems) or number of spins (for infinite-range systems). We provide theoretical arguments to support these conjectures, and also study analytically several mean-field models: the random energy model, the uniform Curie-Weiss ferromagnet, and the disordered Curie-Weiss ferromagnet. We find that for these models, the information contained in the initial state does not decay in the thermodynamic limit-in fact, it fully determines the final state. Unlike in short-range models, the presence of frustration in mean-field models dramatically alters the dynamical behavior with respect to the issue of predictability.

The electronic stopping powers and angular energy-loss dependence of helium and lithium ions in the silicon crystal

We have measured the electronic stopping powers of helium and lithium ions in the channelling direction of the Si〈100〉 crystal. The energy range used (2.0–8.0MeV) was changed by 200 and 400-keV steps. The ratio α between the channelling and random stopping powers was determined as a function of the angle for 2, 3 and 4MeV 4He+ ions and for 3 and 6MeV 7Li+,2+ ions. The measurements were carried out using the Rutherford backscattering spectrometry in the channelling mode (RBS-C) in a silicon-on-insulator material. The experimental channelling stopping-power values measured in the channelling direction were then discussed in the frame of the random energy stopping predictions calculated using SRIM-2013 code and the theoretical unitary convolution approximation (UCA) model. The experimental channelling stopping-power values decrease with increasing ion energy. The stopping-power difference between channelled and randomly moving ions increases with the enhanced initial ion energy. The ratio between the channelling and random ion stopping powers α as a function of the ion beam incoming angle for 2, 3 and 4MeV He+ ions and for 3 and 6MeV Li+,2+ ions was observed in the range 0.5–1.

Hopping charge transport in amorphous organic and inorganic materials with spatially correlated random energy landscape

The general properties of the hopping transport of charge carriers in amorphous organic and inorganic materials are discussed. The case where the random energy landscape in the material is strongly spatially correlated is considered. This situation is typical of organic materials with the Gaussian density of states (DOS) and may also be realized in some materials with the exponential DOS. It is demonstrated that the different DOS types can lead to very different functional forms of the mobility field dependence even for the identical correlation function of random energy. Important arguments are provided in favor of the significant contribution of the local orientational order to the total magnitude of energetic disorder in organic materials. A simple but promising model of charge transport in highly anisotropic composites materials is proposed.

Medium Access for Concurrent Traffic in Wireless Body Area Networks: Protocol Design and Analysis

Wireless body area networks have been deployed to monitor the health condition of patients. In these applications, multiple sensors are required to report real-time data to the sink such that a physician can diagnose accurately, particularly for intensive care patients, which boosts the convergecast traffic load and increases the collision probability. However, the existing protocols cannot effectively operate under such concurrent traffic load. To bridge this gap, we present a novel two-phase receiver-initiated medium access control (MAC) protocol for concurrent traffic based on asynchronous duty cycling, which is called C-MAC. Technically, C-MAC in the first phase employs carrier-sense multiple access with collision avoidance of the IEEE 802.15.6 standard and designs an ordering-based communication algorithm to effectively avoid collisions. Moreover, C-MAC enables sensor nodes to switch to standby mode to avoid idle listening and overhearing in the second phase. Furthermore, theoretically, we explicitly formulate the mathematical expressions of the random delay and energy consumption of C-MAC. Finally, we conduct extensive numerical analysis and simulation to demonstrate the correctness of theoretical results and the better effectiveness and efficiency of C-MAC than that of RI-MAC and A-MAC in terms of transmission delay and energy consumption.

Liouville Field Theory and Log-Correlated Random Energy Models.

An exact mapping is established between the c≥25 Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian free field plus a logarithmic confining potential. The probability distribution of the position of the minimum of the energy landscape is obtained exactly by combining the conformal bootstrap and one-step replica symmetry-breaking methods. Operator product expansions in the LFT allow us to unveil novel universal behaviors of the log-correlated random energy class. High-precision numerical tests are given.

Multifunctional TENG for Blue Energy Scavenging and Self‐Powered Wind‐Speed Sensor

Triboelectric nanogenerator (TENG) has been considered to be a more effective technology to harvest various types of mechanic vibration energies such as wind energy, water energy in the blue energy, and so on. Considering the vast energy from the blue oceans, harvesting of the water energy has attracted huge attention. There are two major types of “mechanical” water energy, water wave energy in random direction and water flow kinetic energy. However, although the most reported TENG can be used to efficiently harvest one type of water energy, to simultaneously collect two or more types of such energy still remains challenging. In this work, two different freestanding, multifunctional TENGs are successfully developed that can be used to harvest three types of energies including water waves, air flowing, and water flowing. These two new TENGs designed in accordance with the same freestanding model yield the output voltages of 490 and ≈100 V with short circuit currents of 24 and 2.7 µA, respectively, when operated at a rotation frequency of 200 rpm and the movement frequency of 3 Hz. Moreover, the developed multifunctional TENG can also be explored as a self‐powered speed sensor of wind by correlating the short‐circuit current with the wind speed.

Review of MEMS Electromagnetic Vibration Energy Harvester

This paper mainly introduces the research progress of MEMS electromagnetic vibration energy harvester, hoping to provide valuable guidance and reference for researchers in related fields. In this paper, recent studies are divided into three groups according to their objectives and approaches: reducing the resonant frequency of the harvester to collect low frequency vibration energy from the environment; broadening the bandwidth of the harvester to increase the utilization of the random vibration energy; and developing new process compatible with MEMS for mass production. Besides, maintaining valuable output performances, such as power and power density, is also an important concern in these studies. Limited to the current technology, it is impossible to make a perfect harvester with low resonant frequency, wide frequency band, good compatibility with MEMS, and good output performances at the same time. However, we can focus on one or two characteristics according to the application, to which this paper provides valuable reference. More works on simulation, new process, and detailed design of the components are required in MEMS electromagnetic vibration energy harvesters.

Finding Protein Folding Funnels in Random Networks

Many attempts have been made for understanding protein folding dynamics using network representations of folding pathway. For example, the Markov state model has been widely used in analyzing the transitions between protein conformations of trajectories obtained by molecular dynamics simulations.In the present work, I also focus on the network structures of protein folding dynamics, but from a somewhat different perspective. Currently most widely accepted theoretical framework of the protein folding is so-called funnel picture, which states that the number of conformations decreases as the energy lowers from the denatured state towards the native state. In other words, the energy landscapes of proteins have been designed through Darwinian evolution so that proteins readily fold to their native states. A question I would like to ask here is “How rare are such folding-friendly funnel structures?”.As a first attempt to answer this question, I introduce a random network model with each nodes assigned a random energy. Nodes represent the metastable conformation ensembles. One of the nodes is considered as denatured state and another the folded state. Other nodes represent the intermediate conformation ensembles between them. Edge connecting the nodes are possible transitions between the nodes. The network structure is assumed to be determined by the native state conformation, and the energy assignment is considered to reflects the amino-acid sequence. We then define the ideal funnel structure for this model as follows: Starting from the denatured state, if all the paths connecting the nodes in energy-lowering direction reach the folded state, then such a network is in a ideal funnel structure. The task now is to compute the probability that the ideal funnel is realized for a given network by changing the assignment of energy.We generated 1000 random networks for number of nodes from 8 to 16. The probability is widely distributed from network to network, and close to the log-normal distribution . This fact means that there are a small number of networks that are robust against the mutation. The funnel structure becomes rarer exponentially as the protein becomes longer.

Capacity Analysis of Discrete Energy Harvesting Channels

We study the channel capacity of a general discrete energy harvesting channel with a finite battery. Contrary to traditional communication systems, the transmitter of such a channel is powered by a device that harvests energy from a random exogenous energy source and has a finite-sized battery. As a consequence, at each transmission opportunity, the system can only transmit a symbol whose energy is no more than the energy currently available. This new type of power supply introduces an unprecedented input constraint for the channel, which is simultaneously random, instantaneous, and influenced by the full history of the inputs and the energy harvesting process. Furthermore, naturally, in such a channel, the energy information is observed causally at the transmitter. Both of these characteristics pose great challenges for the analysis of the channel capacity. In this paper, we use techniques developed for channels with side information and finite-state channels, to obtain lower and upper bounds on the capacity of energy harvesting channels. In particular, in a general case with Markov energy harvesting processes, we use stationarity and ergodicity theory to compute and optimize the achievable rates for the channels, and derive a series of computable capacity upper and lower bounds.

Energy consumption pattern and scalability of routing protocols for heterogeneous MANETs

Routing proposals in MANETs have been implemented and tested considering homogeneous environment where nodes have equal capabilities and responsibilities to perform. These assumptions are not helpful to realise the actual performance of the routing protocols. Therefore, existing routing protocols should be tested and benchmarked for heterogeneous MANETs H-MANETs. In this paper, an analysis of AODV, DSR, AOMDV and CBRP protocols is done. The efficacy of these protocols has been judged for varying network size and varying traffic for H-MANETs. Heterogeneity has been introduced in terms of different random initial energy values given to each node. The performance analysis has been done using network simulator NS-2 for various important performance parameters. Results show that CBRP as compare to other protocols performs better and as a second choice, especially for large traffic, AOMDV is the best protocol. This work is useful for the judicious and sensible selection of the base routing protocol.

Energy consumption pattern and scalability of routing protocols for heterogeneous MANETs

Routing proposals in MANETs have been implemented and tested considering homogeneous environment where nodes have equal capabilities and responsibilities to perform. These assumptions are not helpful to realise the actual performance of the routing protocols. Therefore, existing routing protocols should be tested and benchmarked for heterogeneous MANETs (H-MANETs). In this paper, an analysis of AODV, DSR, AOMDV and CBRP protocols is done. The efficacy of these protocols has been judged for varying network size and varying traffic for H-MANETs. Heterogeneity has been introduced in terms of different random initial energy values given to each node. The performance analysis has been done using network simulator (NS-2) for various important performance parameters. Results show that CBRP as compare to other protocols performs better and as a second choice, especially for large traffic, AOMDV is the best protocol. This work is useful for the judicious and sensible selection of the base routing protocol.

Geometry of the Gibbs measure for the discrete 2D Gaussian free field with scale-dependent variance

We continue our study of the scale-inhomogeneous Gaussian free field introduced in Arguin and Ouimet (2016). Firstly, we compute the limiting free energy on V_N and adapt a technique of Bovier and Kurkova (2004b) to determine the limiting two-overlap distribution. The adaptation was already successfully applied in the simpler case of Arguin and Zindy (2015), where the limiting free energy was computed for the field with two levels (in the center of V_N) and the limiting two-overlap distribution was determined in the homogeneous case. Our results agree with the analogous quantities for the Generalized Random Energy Model (GREM); see Capocaccia et al. (1987) and Bovier and Kurkova (2004a), respectively. Secondly, we show that the extended Ghirlanda-Guerra identities hold exactly in the limit. As a corollary, the limiting array of overlaps is ultrametric and the limiting Gibbs measure has the same law as a Ruelle probability cascade.

Optimal Save-Then-Transmit for Random Energy Harvesting Communications: An Optimal Stopping Approach

Energy harvesting (EH) from renewable energy sources is more environmental friendly and convenient than the conventional energy supplies. This paper considers a point-to-point channel with the transmitter powered by random energy harvester, for which the energy arrival process is stochastic, and the save-then-transmit scheme is adopted due to the battery half-duplex constraint: The transmitter first harvests energy for a certain time, and then stops EH to transmit information with all the accumulated energy at the battery. Obviously, it is crucial to determine a proper stopping time for EH, since larger EH duration provides more accumulated energy, while it may decrease the average throughput. In this paper, our goal is to compute the optimal stopping time to maximize the average throughput of the considered EH systems. First, considering the Gaussian channel scenario, this paper proves the existence of the optimal stopping rule and shows that this rule has a state-dependent"threshold-based" structure under the Markov energy arrival case. Then, for a special independent and identically distributed energy arrival case, this paper further proves that the corresponding stopping threshold is a constant, and can be efficiently computed by a proposed algorithm. Finally, this paper generalizes the above results to the fading channel scenario and obtains the corresponding optimal stopping rule, which can be computed by a recursive algorithm.

One step replica symmetry breaking and extreme order statistics of logarithmic REMs

Building upon the one-step replica symmetry breaking formalism, we show that the extreme values of a general class of Euclidean-space logarithmic correlated random energy models behave as a randomly shifted decorated exponential Poisson point process in the thermodynamic limit. The distribution of the random shift is determined solely by the large-distance ( “infra-red”, IR) limit of the model, and is equal to the free energy distribution at the critical temperature up to a translation. the decoration process is determined solely by the small-distance (“ultraviolet”, UV) limit, in terms of the biased minimal process. We discuss the relations of our approach with that based on the freezing/duality conjecture, and connections to results in the probability literature. Our approach allowed us to derive the general and explicit formulae for the joint probability density of depths of the first and second minima (as well its higher-order generalizations) in terms of model-specific contributions from UV as well as IR limits. In particular, we show that the distribution of the second minimum is independent of UV data, and depends on IR behaviour via a single parameter, the mean value of the gap. For a given log-correlated field this parameter can be evaluated numerically, and we provide several numerical tests of our theory using the circular model of 1/f-noise.