Probability Distribution Of Energy Research Articles

Ferroelectric switching and scale invariant avalanches in BaTiO3

Ferroelectric-field switching in $\mathrm{BaTi}{\mathrm{O}}_{3}$ generates ``Barkhausen noise'' when domain walls are displaced. We show by acoustic emission spectroscopy that electric-field switching of ${90}^{\ensuremath{\circ}}$ boundaries generates large strain fields, which emit acoustic phonons during ferroelectric hysteresis measurements. We use highly sensitive receivers (microphones) to measure the time sequences of noise in close analogy to noise patterns in ferroelastic and magnetic materials. Domain-wall interactions and jamming generate the ``crackling noise'' that follows scale invariant avalanche dynamics: the avalanche energy and amplitude probability distribution functions follow power laws with exponents $\ensuremath{\varepsilon}=1.65$ (energy) and \ensuremath{\tau}\ensuremath{'} = 2.25 (amplitudes). Aftershocks are very common and follow Omori law with probability $\ensuremath{\sim}{t}^{\ensuremath{-}p}$ where $t$ is the time elapsed after the main shock and $p$ is the Omori exponent $p\ensuremath{\sim}1$. The interevent times follow a double power-law distribution with exponents 0.9 for small times and 2.2 for the larger times. The scaling behavior is consistent with predictions of mean field theory.

Effect of anode magnetic shield on inner magnetic pole etched in anode layer Hall thruster

For anode layer Hall plasma thruster, the etching of inner magnetic pole is one of the key factors affecting its service life. In order to solve the problem of inner magnetic pole etching in anode layer Hall plasma thruster, the effect of anode magnetic shield on inner magnetic pole etched in anode layer Hall thruster is studied by combining particle simulation PIC with sputtering simulation. The magnetic shielding of anode changes the distribution of magnetic field configuration on the surface of the anode, and improves the magnetic mirror ratio of the magnetic mirror field of the thruster to the magnetic field width of the positive gradient on the central axis. The ratio of the magnetic mirror is 1.4 times that of the original one, and two additional saddle magnetic fields are added on both sides of the original saddle magnetic field region. It not only is conducive to confining electrons and improving the ionization rate of working gas, but also keeps a certain distance between the anode and the high temperature electron region, which provides the reliable reference data for the design of high power Hall plasma thruster. When the discharge voltage is 900 V and the working pressure is 2 × 10<sup>–2</sup> Pa, the simulation results show that after the anode is shielded by the magnetic shield, the energy range of most of the incident ions on the inner magnetic pole is 40–260 eV, which is 100 eV lower than the energy range 40–360 eV in the case without shielding the anode. The probability distribution of particle energy without magnetically shielding the anode between 260 eV and 600 eV is obviously higher than that of ion energy with magnetically shielding the anode. The maximum probability distribution of cosine value of incident angle is extended from a small range near 0.1 (incident angle 84°) to a large range of 0.1–0.45 (incident angle 84°–63°). The magnetic shielding makes the incident ions disperse on the surface of the inner magnetic pole, which is helpful in reducing the etching of inner magnetic pole. The maximum etching rate of inner magnetic pole after the anode has been magnetically shielded is reduced from 16 × 10<sup>–10</sup> m/s to 6.1 × 10<sup>–10</sup> m/s, which is 2.62 times lower. The comparison of simulation results with experimental results in the case without magnetically shielding the anode shows that they are in good agreement.

Microdosimetric specific energy probability distribution in nanometric targets and its correlation with the efficiency of thermoluminescent detectors exposed to charged particles

Due to their common use for dose measurements in space and hadron therapy facilities, it is of fundamental importance to know the efficiency of luminescent detectors for measuring a wide range of particles and energies. However, due to experimental limitations it is often not possible to irradiate the detectors with very high energies, less common isotopes or exotic particles. Furthermore, the efficiency determination at low energies is biased with associated large uncertainties in range, linear energy transfer and dose. This paper presents the recently developed Microdosimetric d(z) Model able to assess the relative efficiency of thermoluminescent detectors for measuring different radiation qualities by relating the simulated dose probability distribution of the specific energy in nanometric targets with an experimentally determined response function. The model was tested in case of LiF:Mg, Ti (MTS) and LiF:Mg,Cu,P (MCP) thermoluminescent detectors exposed to charged particles from 1H to 132Xe in the energy range 3–1000 MeV/u. A comparison with experimentally determined efficiency results showed a very good agreement in case of calculations performed in a simulated target size of 40 nm. This validated model can be used to assess detector efficiency to exotic particles, unavailable radiation qualities and energies at ground level accelerators or complex mixed fields. The assumptions behind the model, its methodology and results are discussed in detail. Furthermore, a systematic investigation on the effect of simulation parameters on the calculated efficiency values is included in the manuscript.

Thermal cycling leads grains to more homogeneous force networks and energy repartition

With the help of molecular dynamics simulations of a realistic granular system, here it is first reported that thermal cycling is able to induce the total system energy to be reallocated to grains, and this makes grains gradually evolve to the energy equilibrium, especially under larger cyclic temperatures. At the same time, the stress in force chains (and on grains) will also get much relieved, and this does not need the decrease in applied pressure. Consequently, the statistical probability distribution of both internal particle forces and energy will become narrower around the most likely value, and their spatial distribution will also become more and more homogeneous. The primary cause behind the above phenomena is that grains within the initial granular system are not in sufficient energy equilibrium, and they were rearranged by thermal excitations to a new steadier packing where grains are closer to energy equilibrium. Besides, it was also observed that for the macroscopic-scale grains, the internal particle energy distribution within the granular system obeys a more general Maxwell-Boltzmann (M-B) distribution which has a more uniform distribution profile than the classical M-B distribution for gases, suggesting that the direct-contact collision may be a more effective channel for the energy interchange between particles than the indirect-contact collision. The results showed here demonstrate that more homogeneous energy reallocations may be a universal phenomenon for granular matter and may have important practical implications for the handling of granular materials.

Validity and failure of the Boltzmann weight

The dynamics and thermostatistics of a classical inertial XY model, characterized by long-range interactions, are investigated on d-dimensional lattices (d = 1, 2, and 3), through molecular dynamics. The interactions between rotators decay with the distance rij like , where α → ∞ and respectively correspond to the nearest-neighbor and infinite-range interactions. We verify that the momenta probability distributions are Maxwellians in the short-range regime, whereas q-Gaussians emerge in the long-range regime. Moreover, in this latter regime, the individual energy probability distributions are characterized by long tails, corresponding to q-exponential functions. The present investigation strongly indicates that, in the long-range regime, central properties fall out of the scope of Boltzmann-Gibbs statistical mechanics, depending on d and α through the ratio .

QFT Derivation of the Decay Law of an Unstable Particle with Nonzero Momentum

We present a quantum field theoretical derivation of the nondecay probability of an unstable particle with nonzero three-momentum p. To this end, we use the (fully resummed) propagator of the unstable particle, denoted as S, to obtain the energy probability distribution, called dSp(E), as the imaginary part of the propagator. The nondecay probability amplitude of the particle S with momentum p turns out to be, as usual, its Fourier transform: aSp(t)=∫mth2+p2∞dEdSp(E)e-iEt (mth is the lowest energy threshold in the rest frame of S and corresponds to the sum of masses of the decay products). Upon a variable transformation, one can rewrite it as aSp(t)=∫mth∞dmdS0(m)e-imth2+p2t [here, dS0(m)≡dS(m) is the usual spectral function (or mass distribution) in the rest frame]. Hence, the latter expression, previously obtained by different approaches, is here confirmed in an independent and, most importantly, covariant QFT-based approach. Its consequences are not yet fully explored but appear to be quite surprising (such as the fact that the usual time-dilatation formula does not apply); thus its firm understanding and investigation can be a fruitful subject of future research.

On the use of the energy probability distribution zeros in the study of phase transitions

This contribution is devoted to cover some technical aspects related to the use of the recently proposed energy probability distribution zeros in the study of phase transitions. This method is based on the partial knowledge of the partition function zeros and has been shown to be extremely efficient to precisely locate phase transition temperatures. It is based on an iterative method in such a way that the transition temperature can be approached at will. The iterative method will be detailed and some convergence issues that has been observed in its application to the 2D Ising model and to an artificial spin ice model will be shown, together with ways to circumvent them.

Generation of attosecond electron beams in relativistic ionization by short laser pulses

Ionization by relativistically intense short laser pulses is studied in the framework of strong-field quantum electrodynamics. Distinctive patterns are found in the energy probability distributions of photoelectrons, which are sensitive to the properties of a driving laser field. It is demonstrated that these electrons are generated in the form of solitary attosecond wave packets. This is particularly important in light of various applications of attosecond electron beams such as in ultrafast electron diffraction and crystallography, or in time-resolved electron microscopy of physical, chemical, and biological processes. We also show that, for intense laser pulses, high-energy ionization takes place in narrow regions surrounding the momentum spiral, the exact form of which is determined by the shape of a driving pulse. The self-intersections of the spiral define the momenta for which the interference patterns in the energy distributions of photoelectrons are observed. Furthermore, these interference regions lead to the synthesis of single-electron wave packets characterized by coherent double-hump structures.

The zeros of the Energy Probability Distribution - A new way to study phase transitions -

We describe an iterative method to study the critical behavior of a system based on the partial knowledge of the complex Fisher zeros set of the partition function. The method is general with advantages over most conventional techniques since it does not need to identify any order parameter a priori. The critical temperature and exponents can be obtained with great precision. To test the method and to show how it works we applied it to the 2D Ising and 6–states Potts models. The strategy can easily be adapted to any model, classical or quantum, once we can build the corresponding energy probability distribution.

Lifespan Development of the Human Brain Revealed by Large-Scale Network Eigen-Entropy

Imaging connectomics based on graph theory has become an effective and unique methodological framework for studying functional connectivity patterns of the developing and aging brain. Normal brain development is characterized by continuous and significant network evolution through infancy, childhood, and adolescence, following specific maturational patterns. Normal aging is related to some resting state brain networks disruption, which are associated with certain cognitive decline. It is a big challenge to design an integral metric to track connectome evolution patterns across the lifespan, which is to understand the principles of network organization in the human brain. In this study, we first defined a brain network eigen-entropy (NEE) based on the energy probability (EP) of each brain node. Next, we used the NEE to characterize the lifespan orderness trajectory of the whole-brain functional connectivity of 173 healthy individuals ranging in age from 7 to 85 years. The results revealed that during the lifespan, the whole-brain NEE exhibited a significant non-linear decrease and that the EP distribution shifted from concentration to wide dispersion, implying orderness enhancement of functional connectome over age. Furthermore, brain regions with significant EP changes from the flourishing (7–20 years) to the youth period (23–38 years) were mainly located in the right prefrontal cortex and basal ganglia, and were involved in emotion regulation and executive function in coordination with the action of the sensory system, implying that self-awareness and voluntary control performance significantly changed during neurodevelopment. However, the changes from the youth period to middle age (40–59 years) were located in the mesial temporal lobe and caudate, which are associated with long-term memory, implying that the memory of the human brain begins to decline with age during this period. Overall, the findings suggested that the human connectome shifted from a relatively anatomical driven state to an orderly organized state with lower entropy.

Log-gamma directed polymer with one free end via coordinate Bethe Ansatz

The discrete polymer model with random Boltzmann weights with homogeneous inverse gamma distribution, introduced by Seppäläinen, is studied in the case of a polymer with one fixed and one free end. The model with two fixed ends has been integrated by Thiery and Le Doussal, using coordinate Bethe Ansatz techniques and an analytic-continuation prescription. The probability distribution of the free energy has been obtained through the replica method, even though the moments of the partition sum do not exist at all orders due to the fat tail in the distribution of Boltzmann weights. To extend this approach to the polymer with one free end, we argue that the contribution to the partition sums in the thermodynamic limit is localised on parity-invariant string states. This situation is analogous to the case of the continuum polymer with one free end, related to the Kardar–Parisi–Zhang equation with flat boundary conditions and solved by Le Doussal and Calabrese. The expansion of the generating function of the partition sum in terms of numbers of strings can also be transposed to the log-gamma polymer model, with the induced Fredholm determinant structure. We derive the large-time limit of the rescaled cumulative distribution function, and relate it to the GOE Tracy–Widom distribution. The derivation is conjectural in the sense that it assumes completeness of a family of string states, and expressions of their norms, already useful in the fixed-end problem, and extends heuristically the order of moments of the partition sum to the complex plane.

Multipacting studies in elliptic SRF cavities

Multipacting is a resonant process, where the number of unwanted electrons resulting from a parasitic discharge rapidly grows to a larger value at some specific locations in a radio-frequency cavity. This results in a degradation of the cavity performance indicators (e.g. the quality factor Q and the maximum achievable accelerating gradient Eacc), and in the case of a superconducting radiofrequency (SRF) cavity, it leads to a quenching of superconductivity. Numerical simulations are essential to pre-empt the possibility of multipacting in SRF cavities, such that its design can be suitably refined to avoid this performance limiting phenomenon. Readily available computer codes (e.g.FishPact, MultiPac,CST-PICetc.) are widely used to simulate the phenomenon of multipacting in such cases. Most of the contemporary two dimensional (2D) codes such as FishPact, MultiPacetc. are unable to detect the multipacting in elliptic cavities because they use a simplistic secondary emission model, where it is assumed that all the secondary electrons are emitted with same energy. Some three-dimensional (3D) codes such as CST-PIC, which use a more realistic secondary emission model (Furman model) by following a probability distribution for the emission energy of secondary electrons, are able to correctly predict the occurrence of multipacting. These 3D codes however require large data handling and are slower than the 2D codes. In this paper, we report a detailed analysis of the multipacting phenomenon in elliptic SRF cavities and development of a 2D code to numerically simulate this phenomenon by employing the Furman model to simulate the secondary emission process. Since our code is 2D, it is faster than the 3D codes. It is however as accurate as the contemporary 3D codes since it uses the Furman model for secondary emission. We have also explored the possibility to further simplify the Furman model, which enables us to quickly estimate the growth rate of multipacting without performing any multi-particle simulation. This methodology has been employed along with computer code for the detailed analysis of multipacting in βg=0.61 and βg=0.9, 650 MHz elliptic SRF cavities that we have recently designed for the medium and high energy section of the proposed Indian Spallation Neutron Source (ISNS) project.

Subgrid-scale stresses and scalar fluxes constructed by the multi-scale turnover Lagrangian map

The multi-scale turnover Lagrangian map (MTLM) [C. Rosales and C. Meneveau, “Anomalous scaling and intermittency in three-dimensional synthetic turbulence,” Phys. Rev. E 78, 016313 (2008)] uses nested multi-scale Lagrangian advection of fluid particles to distort a Gaussian velocity field and, as a result, generate non-Gaussian synthetic velocity fields. Passive scalar fields can be generated with the procedure when the fluid particles carry a scalar property [C. Rosales, “Synthetic three-dimensional turbulent passive scalar fields via the minimal Lagrangian map,” Phys. Fluids 23, 075106 (2011)]. The synthetic fields have been shown to possess highly realistic statistics characterizing small scale intermittency, geometrical structures, and vortex dynamics. In this paper, we present a study of the synthetic fields using the filtering approach. This approach, which has not been pursued so far, provides insights on the potential applications of the synthetic fields in large eddy simulations and subgrid-scale (SGS) modelling. The MTLM method is first generalized to model scalar fields produced by an imposed linear mean profile. We then calculate the subgrid-scale stress, SGS scalar flux, SGS scalar variance, as well as related quantities from the synthetic fields. Comparison with direct numerical simulations (DNSs) shows that the synthetic fields reproduce the probability distributions of the SGS energy and scalar dissipation rather well. Related geometrical statistics also display close agreement with DNS results. The synthetic fields slightly under-estimate the mean SGS energy dissipation and slightly over-predict the mean SGS scalar variance dissipation. In general, the synthetic fields tend to slightly under-estimate the probability of large fluctuations for most quantities we have examined. Small scale anisotropy in the scalar field originated from the imposed mean gradient is captured. The sensitivity of the synthetic fields on the input spectra is assessed by using truncated spectra or model spectra as the input. Analyses show that most of the SGS statistics agree well with those from MTLM fields with DNS spectra as the input. For the mean SGS energy dissipation, some significant deviation is observed. However, it is shown that the deviation can be parametrized by the input energy spectrum, which demonstrates the robustness of the MTLM procedure.

Energy probability distribution zeros: A route to study phase transitions

In the study of phase transitions a very few models are accessible to exact solution. In most cases analytical simplifications have to be done or some numerical techniques have to be used to get insight about their critical properties. Numerically, the most common approaches are those based on Monte Carlo simulations together with finite size scaling analysis. The use of Monte Carlo techniques requires the estimation of quantities like the specific heat or susceptibilities in a wide range of temperaturesor the construction of the density of states in large intervals of energy. Although many of these techniques are well developed they may be very time consuming when the system size becomes large enough. It should be suitable to have a method that could surpass those difficulties. In this work we present an iterative method to study the critical behavior of a system based on the partial knowledge of the complex Fisher zeros set of the partition function. The method is general with advantages over most conventional techniques since it does not need to identify any order parameter a priori. The critical temperature and exponents can be obtained with great precision even in the most unamenable cases like the two dimensional XY model. To test the method and to show how it works we applied it to some selected models where the transitions are well known: The 2D Ising, Potts and XY models and to a homopolymer system. Our choices cover systems with first order, continuous and Berezinskii–Kosterlitz–Thouless transitions as well as the homopolymer that has two pseudo-transitions. The strategy can easily be adapted to any model, classical or quantum, once we are able to build the corresponding energy probability distribution.

Distribution of apparent activation energy counterparts during thermo - And thermo-oxidative degradation of Aronia melanocarpa (black chokeberry).

Kinetics of degradation for Aronia melanocarpa fresh fruits in argon and air atmospheres were investigated. The investigation was based on probability distributions of apparent activation energy of counterparts (εa). Isoconversional analysis results indicated that the degradation process in an inert atmosphere was governed by decomposition reactions of esterified compounds. Also, based on same kinetics approach, it was assumed that in an air atmosphere, the primary compound in degradation pathways could be anthocyanins, which undergo rapid chemical reactions. A new model of reactivity demonstrated that, under inert atmospheres, expectation values for εa occured at levels of statistical probability. These values corresponded to decomposition processes in which polyphenolic compounds might be involved. εa values obeyed laws of binomial distribution. It was established that, for thermo-oxidative degradation, Poisson distribution represented a very successful approximation for εa values where there was additional mechanistic complexity and the binomial distribution was no longer valid.

Gaussian and non-Gaussian fluctuations in pure classical fluids

The particle number, energy, and volume probability distributions in the canonical, isothermal-isobaric, grand canonical, and isobaric-isenthalpic ensembles are investigated. In particular, we consider Gaussian and non-Gaussian behavior and formulate the results in terms of a single expression valid for all the ensembles employing common, experimentally accessible, thermodynamic derivatives. This is achieved using Fluctuation Solution Theory to help manipulate derivatives of the entropy. The properties of the distributions are then investigated using available equations of state for fluid water and argon. Purely Gaussian behavior is not observed for any of the state points considered here. A set of simple measures, involving thermodynamic derivatives, indicating non-Gaussian behavior is proposed. A general expression, valid in the high temperature limit, for small energy fluctuations in the canonical ensemble is provided.

Stability of quantum statistical ensembles with respect to local measurements.

We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the total energy of the system. We apply this criterion to lattices of spins-1/2, thereby showing that the canonical ensemble is nearly stable, whereas statistical ensembles with much broader energy distributions are not stable. In the context of the foundations of quantum statistical physics, this result justifies the use of statistical ensembles with narrow energy distributions such as canonical or microcanonical ensembles.

Fluctuations of the fission energy generated in a multiplying system

The purpose of this work is to elaborate a master equation formalism for the evolution of the probability distribution of the cumulative energy generated by fissions in a multiplying system with delayed neutrons. The formalism accounts for the fact that the fission energy χ is also a random variable, thus the fluctuations of the total energy generated are due to both the fluctuations of the number of fissions, as well as to the fluctuations of the energy per fission. By comparing to the case where the fission energy is taken as constant, the significance of the fluctuations of the fission energy can be assessed. The first two moments of the cumulative fission energy are determined explicitly, and the time dependence of the expectation and the variance is calculated for different reactivities. As expected, the variance of the energy per fission does not play a significant role in the variance of the cumulative fission energy.

Spin morphologies and heat dissipation in spherical assemblies of magnetic nanoparticles

Aggregates of magnetic nanoparticles (MNPs) exhibit unusual properties due to the interplay of small system size and long-range dipole-dipole interactions. Using the micromagnetic simulation software oommf, we study the spin morphologies and heat dissipation in micron-size spherical assemblies of MNPs. In particular, we examine the sensitivity of these properties to the dipolar strength, manipulated by the interparticle separation. As oommf is not designed for such a study, we have incorporated a novel scaling protocol for this purpose. We believe that it is essential for all studies where volume fractions are varied. Our main results are as follows: (i) Dense assemblies exhibit strong dipolar effects which yield local magnetic order in the core but not on the surface, where moments are randomly oriented. (ii) The probability distribution of ground-state energy exhibits a long high-energy tail for surface spins in contrast to small tails for the core spins. Consequently, there is a wide variation in the energy of surface spins but not the core spins. (iii) There is strong correlation between ground-state energy and heating properties on application of an oscillating magnetic field $h(t)={h}_{o}cos2\ensuremath{\pi}ft$: the particles in the core heat uniformly, while those on the surface exhibit a wide range from cold to intensely hot. (iv) Specific choices of ${h}_{o}$ and $f$ yield characteristic spatial heat distributions, e.g., hot surface and cold core, or vice versa. (iv) For all values of ${h}_{o}$ and $f$ that we consider, heating was maximum at a specific volume fraction. These results are especially relevant in the context of contemporary applications such as hyperthermia and chemotherapy, and also for novel materials such as smart polymer beads and superspin glasses.

Reflection Characteristics of Oxygen Molecule on Ionomer Surface

The widespread utilization of polymer electrolyte fuel cells for transportation applications such as fuel cell vehicles requires high power density operation. However, as the current density increases, the diffusion polarization, which is attributed to the insufficient mass transport, degrades the cell performance. In particular, the oxygen transport resistance in catalyst layers (CLs) and micro porous layers (MPLs) at the cathode side is one of the major factors of the performance degradation. Therefore, the reduction in the oxygen transport resistance is important for the high power density operation. In the previous research, Kinefuchi et al. have investigated the oxygen diffusion resistance in MPLs and CLs using the direct simulation Monte Carlo (DSMC) method. They reported that the simulation well reproduces the experimental result in MPLs. However, the DSMC results underestimate the oxygen diffusion resistance in CLs. This discrepancy is caused by the drawback to a scattering model of gas molecules on surfaces, which plays a crucial role in DSMC analysis. In these calculations, the same scattering model is used for the scattering of oxygen molecules on surfaces regardless of the presence or absence of ionomer on micro porous carbons. An advanced scattering model that can reproduce the scattering and surface diffusion phenomena on ionomer surface, is required for more accurate analysis of the oxygen transport in CLs. The construction of the model needs the detailed understanding of the gas‒surface interaction. In this study, we have investigated the mechanics of oxygen scattering and surface diffusion on ionomer surface using molecular dynamics simulation. We modeled the solid surface in CLs as an ionomer film covering the carbon layers. The simulation domain was 51.1 × 44.2 × 100 Å3 in size. The ionomer film was composed of water molecules hydronium ions, and perfluorosulfonic acid molecules as typified by Nafion, water molecules, and hydronium ions. Oxygen molecules were directed to the ionomer surface and the trajectory calculations were performed for 20 ps. The initial translational energy and incident angle were the same for all the incident molecules, but the initial position and orientation were given randomly in order to obtain the sufficient statistics. If an oxygen molecule desorbed from the surface and reached the initial height, it was defined to be scattered. Firstly, we have evaluated the energy transfer between oxygen molecules and the ionomer surface by calculating between translational energy before and after the scattering. Oxygen molecules with low incident energy tend to receive energy when they leave the surface after the collisions. Next, we have evaluated the scattering phenomena of oxygen molecules on ionomer surface by examining the energy and angular probability distributions of scattered molecules. The energy distribution depends on the incident energy, and deviates from the distribution given by diffusive scattering model, that the incident molecules are assumed to accommodate completely with the surface. On the other hand, the scattering angle distribution is independent of the incident energy, and well-reproduced by the diffusive scattering model. These results suggest that oxygen molecules do not accommodate completely with the ionomer surface when they are reflected, however they are reflected following the diffusive scattering model because of the corrugation of the ionomer surface.