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The authors of the paper (Vitali et al 2022 J. Phys. A: Math. Theor. 55 224012) analyzed a simple CTRW model with a waiting time distribution defined as the weighted sum of two exponential distributions. They showed that their model meets many paradigmatic features that belong to the anomalous diffusion as it is observed in living systems. This comment point out the previous paper that considers a similar model and improves on the authors' result regarding the time dependence of the mean-square displacement. [ABSTRACT FROM AUTHOR]

Light-front formulations of quantum field theories have many advantages for computing electroweak matrix elements of strongly interacting systems and other quantities that are used to study hadronic structure. The theory can be formulated in Hamiltonian form so non-perturbative calculations of the strongly interacting initial and final states are in principle reduced to linear algebra. These states are needed for calculating parton distribution functions and other types of distribution amplitudes that are used to understand the structure of hadrons. Light-front boosts are kinematic transformations so the strongly interacting states can be computed in any frame. This is useful for computing current matrix elements involving electroweak probes where the initial and final hadronic states are in different frames related by the momentum transferred by the probe. Finally in many calculations the vacuum is trivial so the calculations can be formulated in Fock space. The advantages of light front-field theory would not be interesting if the light-front formulation was not equivalent to the covariant or canonical formulations of quantum field theory. Many of the distinguishing properties of light-front quantum field theory are difficult to reconcile with canonical or covariant formulations of quantum field theory. This paper discusses the resolution of some of the apparent inconsistencies in canonical, covariant and light-front formulations of quantum field theory. The puzzles that will be discussed are (1) the problem of inequivalent representations (2) the problem of the trivial vacuum (3) the problem of ill-posed initial value problems (4) the problem of rotational covariance (5) the problem of zero modes and (6) the problem of spontaneously broken symmetries. [ABSTRACT FROM AUTHOR]

Many domain adaptation (DA) approaches have been developed to address the challenge of domain divergence in cross-domain fault diagnosis. However, most of them only attempt to align statistical distribution while neglecting geometric alignment between source and target data. Furthermore, the use of some unreliable pseudo-labels may cause geometrical and statistical distributions mismatching and interfere with the DA model generating correct pseudo-labels during the iterative learning. In this paper, we propose a new model called discriminative subspace embedded dynamic geometrical and statistical alignment based on pseudo-label correction (DSDGSA-PC) for bearing fault diagnosis. Firstly, discriminative subspace alignment is proposed to mitigate feature redundancy and divergence by generating aligned subspaces for two domains, while preserving class discriminative information and global structures of data. Then, DSDGSA-PC leverages the representer theorem and the principle of structural risk minimization to learn a domain-invariant classifier in the subspace, while minimizing statistical and geometrical shift by jointly optimizing dynamic graph embedding and dynamic weighted distribution alignment strategies. Finally, a novel pseudo-label correction mechanism is integrated into DSDGSA-PC to evaluate the credibility of pseudo-labels and rectify the unreliable ones during the iterations. The experimental results illustrate that DSDGSA-PC has higher transfer performance compared to several advanced methods on 24 transfer tasks. [ABSTRACT FROM AUTHOR]

The two-particle rapidity correlation among the pions produced in p–p collisions at recent LHC energies s = 2.76, 5.02, 7 and 13 TeV are studied in this paper by using the analysis of events generated by UrQMD-3.4, AMPT-2.26 and PYTHIA-8.3. Our investigation for bin-to-bin fluctuation using the variance of forward–backward asymmetry parameter σ C 2 in the forward–backward pseudo-rapidity windows is done through the simulated data. In addition to that, energy-wise variation of correlation strength (β), the probability distribution of roughness parameter ( γ k 2 ) and number density fluctuation parameter (d ik ) are also incorporated in this investigation. Also, we have tried to study the same for the data of different impact parameters generated using the UrQMD model, and the comparison is made with its minimum biased events data-set. The analysis signifies, that the signature of dynamical fluctuation is not so prominent but increases a bit with the increase in energy. An increase in the correlation strength with the increase in energy signifies the contribution of long-range correlation is more in comparison to the short-range one. However, there is no such accountable effect of various impact parameters seen in the present study. [ABSTRACT FROM AUTHOR]

We explain and fix a mistake of the original paper related to derivation of the Fokker–Planck kinetic equation for the distribution function in the non-canonical (not Hamiltonian) phase space. [ABSTRACT FROM AUTHOR]

When applied to a stochastic process of interest, a restart protocol alters the overall statistical distribution of the process' completion time; thus, the completion-time's mean and randomness change. The explicit effect of restart on the mean is well understood, and it is known that: from a mean perspective, deterministic restart protocols—termed sharp restart —can out-perform any other restart protocol. However, little is known on the explicit effect of restart on randomness. This paper is the second in a duo exploring the effect of sharp restart on randomness: via a Shannon-entropy analysis in the first part, and via a diversity analysis in this part. Specifically, gauging randomness via diversity—a measure that is intimately related to the Renyi entropy—this paper establishes a set of universal criteria that determine: (A) precisely when a sharp-restart protocol decreases/increases the diversity of completion times; (B) the very existence of sharp-restart protocols that decrease/increase the diversity of completion times. Moreover, addressing jointly mean-behavior and randomness, this paper asserts and demonstrates when sharp restart has an aligned effect on the two (decreasing/increasing both), and when the effect is antithetical (decreasing one while increasing the other). The joint mean-diversity results require remarkably little information regarding the (original) statistical distributions of completion times, and are remarkably practical and easy to implement. [ABSTRACT FROM AUTHOR]

Line-intensity mapping (IM) experiments seek to perform statistical measurements of large-scale structure with spectral lines such as 21 cm, CO, and Ly α. A challenge in these observations is to ensure that astrophysical foregrounds, such as galactic synchrotron emission in 21 cm measurements, are properly removed. One method that has the potential to reduce foreground contamination is to cross correlate with a galaxy survey that overlaps with the IM volume. However, telescopes sensitive to high-redshift galaxies typically have small field of views compared to IM surveys. Thus, a galaxy survey for cross correlation would necessarily consist of pencil beams that sparsely fill the IM volume. In this paper, we develop the formalism to forecast the sensitivity of cross correlations between IM experiments and pencil-beam galaxy surveys. We find that a random distribution of pencil beams leads to very similar overall sensitivity as a lattice spaced across the IM survey and derive a simple formula for random configurations that agrees with the Fisher matrix formalism. We explore examples of combining high-redshift James Webb Space Telescope (JWST) observations with both an SPHEREx-like Ly α IM survey and a 21 cm experiment based on the Hydrogen Epoch of Reionization Array (HERA). We find that the JWST-SPHEREx case is promising, leading to a total signal-to-noise ratio of ∼5 after 100 total hours of JWST (at z = 7). We find that HERA is not well-suited for this approach owing to its drift-scan strategy, but that a similar experiment that can integrate down on one field could be. [ABSTRACT FROM AUTHOR]

Digital fringe projection (DFP) is widely applied in three-dimensional (3D) shape measurements. However, its performance is severely disturbed while measuring complex surfaces with an extensive range of reflectivity. In this paper, to enhance the underexposed regions and reduce the saturated regions, an automatic and effective method is proposed for the multi-exposure determination of the DFP system. During the whole process, only one unsaturated image must be captured preliminarily, which could establish an adaptive strategy based on the intensity value distribution function. Raw absolute phase maps captured with different exposure times are synthesized at the pixel level for phase retrieval and 3D reconstruction. To evaluate the effectiveness of our method, a high dynamic range method and a global optimal exposure method are introduced for comparison. Verification experiments demonstrate that our method performs better for the 3D reconstruction results of complex surfaces with a large reflectivity range. [ABSTRACT FROM AUTHOR]

The secular evolution of disk galaxies is largely driven by resonances between the orbits of "particles" (stars or dark matter) and the rotation of non-axisymmetric features (spiral arms or a bar). Such resonances may also explain kinematic and photometric features observed in the Milky Way and external galaxies. In simplified cases, these resonant interactions are well understood: for instance, the dynamics of a test particle trapped near a resonance of a steadily rotating bar is easily analyzed using the angle-action tools pioneered by Binney, Monari, and others. However, such treatments do not address the stochasticity and messiness inherent to real galaxies—effects that have, with few exceptions, been previously explored only with complex N -body simulations. In this paper, we propose a simple kinetic equation describing the distribution function of particles near an orbital resonance with a rigidly rotating bar, allowing for diffusion of the particles' slow actions. We solve this equation for various values of the dimensionless diffusion strength Δ, and then apply our theory to the calculation of bar–halo dynamical friction. For Δ = 0, we recover the classic result of Tremaine and Weinberg that friction ultimately vanishes, owing to the phase mixing of resonant orbits. However, for Δ > 0, we find that diffusion suppresses phase mixing, leading to a finite torque. Our results suggest that stochasticity—be it physical or numerical—tends to increase bar–halo friction, and that bars in cosmological simulations might experience significant artificial slowdown, even if the numerical two-body relaxation time is much longer than a Hubble time. [ABSTRACT FROM AUTHOR]

This paper studies the influence of the thermal disturbance process on the electro-thermo-mechanical properties of quasi-isotropic strand (Q-IS) in self-field. We first measured the heat transfer time as well as the longitudinal temperature distribution through experiments and compared them with simulated results. Subsequently, through the finite element analysis, the transversal distribution of the temperature in the center of the strand and the attenuation of the critical current during the thermal disturbance are obtained. Finally, with considering the uniformity of the temperature distribution, the internal stress of the strand under different operating currents was studied. The results show that compared to the strand formed by directly stacked tapes, the Q-IS has advantages of uniform temperature distribution, less attenuation of critical current, and lower amplitude of internal stress in the case of higher current. [ABSTRACT FROM AUTHOR]

In preparation for the tomography study of the intergalactic medium (IGM) by Subaru Prime Focus Spectrograph (PFS) survey and other large future telescopes such as TMT/ELT/GMT, we present the results of our pilot study on Lyα forest and IGM tomography statistics using the GADGET3-Osaka cosmological smoothed particle hydrodynamical simulation. Our simulation includes models for star formation and supernova feedback, which enables more realistic cross-correlation studies between galaxies, neutral hydrogen (H i), and metals in circumgalactic and intergalactic medium. We create a light-cone data set at z = 2–3 from our simulations and generate mock Lyα forest data. As a first step, in this paper, we focus on the distribution of H i and galaxies, and present statistical results on 1D flux probability distribution function, 1D power spectrum, flux contrast versus impact parameter, and H i –galaxy cross-correlations. Our results show overall agreement with current observational data, with some interesting discrepancies on small scales that are due to either feedback effects or varying observational conditions. Our simulation shows stronger H i absorption with decreasing transverse distance from galaxies. We find that massive galaxies with M⋆ ≥ 1010M⊙ contribute strongly to the flux contrast signal, and that lower-mass galaxies with M⋆ ∼ 108–1010M⊙ tend to dilute the flux contrast signal from massive galaxies. On large scales, the average flux contrast smoothly connects to the IGM level, supporting the concordance Λ cold dark matter model. We also find an increase in the H i absorption toward the center of a protocluster. [ABSTRACT FROM AUTHOR]

The cloaking methods of infinite length coaxial cylindrical and concentric spherical invisibility cloaks in the non-uniform static field are investigated. First, the arbitrary potential function at the infinite boundary is expanded into a series of orthogonal potential functions. When there is only the nth order orthogonal potential function distribution at the infinite boundary, the analytical cloaking conditions of both the infinite length coaxial cylindrical and concentric spherical cloaks are derived. Furthermore, based on the analytical cloaking conditions, the approaching cloaking method is proposed in a complex non-uniform static field which composed of multiple orders potential functions. This method can acquire the optimal cloaking condition and avoid the iteration process by using numerical methods such as the finite element method etc. Finally, three examples are given to verify the correctness of the analytical cloaking conditions and the effectiveness of the approaching cloaking method proposed in this paper. [ABSTRACT FROM AUTHOR]

Cable-in-conduit conductors comprised of twisted stacks of high-temperature superconducting (HTS) tapes constitute a very promising technology by virtue of their easy manufacturing process, flexibility capabilities, and high current densities. In a cable, the current distribution among tapes is one of the key parameters affecting the cable performances. The distribution of current is affected mainly by the self-field configuration (ultimately related to the cable layout) and the termination resistances. In this paper we present a 2D finite element (FE) model, based on the T-A formulation, which computes the magnetic field and current distribution in stacked tapes. This model has been used to describe the experimental V–I results obtained in cables in which different current distributions among tapes are expected. The first case refers to V–I curves of stacks of HTS tapes inserted into ducts formed in the extruded aluminium cylindrical core for a straight cable. The excellent agreement between the experimental findings and the simulation results can be explained in terms of uniform current distribution within the tapes stack, up to the superconducting to normal transition. The second sample, an Al-slotted core Cable-In-Conduit-Conductor, has been bent down to a radius of 0.15 m, and from the measured V–I characteristic of each individual tape, a different tape degradation depending on the tape position within the stack was recorded. The model is able to reconstruct the V–I of the stacks from the characteristic curves of the individual tapes with a satisfactory agreement. The finite element analysis reveals non-uniform current distribution among the tapes, which could expose the cable to a potentially irreversible damage during operation. The proposed FE model constitutes a useful tool for the analysis and predictions of HTS CIC conductor performances and represents a suitable basis for the implementation of more complex models aimed at the design of specific and large applications of this conductor in the next future. [ABSTRACT FROM AUTHOR]

In this paper, we study stellar light curves from the Transiting Exoplanet Survey Satellite (TESS) for the presence of stellar flares. The main aim is to detect stellar flares using 2 minute cadence data and to perform a statistical analysis. To find and analyze stellar flares, we prepared the automatic software WARPFINDER. We implemented three methods described in this paper: trend, difference, and profile fitting. Automated searches for flares was accompanied by visual inspection. Using our software we analyzed the 2 minute cadence light curves of 330,000 stars located in the first 39 sectors of TESS observations. As a result, we detected over 25,000 stars showing flare activity with the total number of more than 140,000 flares. This means that about 7.7% of all the analyzed objects are flaring stars. The estimated flare energies range between 1031 and 1036 erg. We prepared a preliminary preview of the statistical distribution of parameters such as the flare duration, amplitude, and energy, and compared it with previous results. The relationship between stellar activity and spectral type, temperature, and mass was also statistically analyzed. Based on the scaling laws, we estimated the average values of the magnetic field strength and length of the flare loops. In our work, we used both single (about 60%), and double (about 40%) flare profiles to fit the observational data. The components of the double profile are supposed to be related to the direct heating of the photosphere by nonthermal electrons and back-warming processes. [ABSTRACT FROM AUTHOR]

Although traditional deep learning improves the accuracy of intelligent fault diagnosis, it suffers from a problem, which is that a change in working conditions may reduce the diagnostic accuracy. The reason for this phenomenon is that a change of working conditions influences the probability distributions. To solve this problem, domain adaptation is adopted to perform intelligent fault diagnosis. However, the design of regularization methods, such as maximum mean discrepancy (MMD), neglects the phenomenon of fault extension. Considering the property of fault extension, the paper sums up a concept named short-time consistency which means that ‘during stable operation, a failure does not expand over a short time period.’ Moreover, short-time consistent regularization is proposed to ensure that the output of the model meets the requirement for short-time consistency, and closed-set regularization is proposed to further solve the problem of ‘types of label drop’ when short-time consistent regularization is used. When the problem occurs, the number of predicted label types in the target domain is smaller than that in the source domain in the closed-set domain adaptation. Two types of regularization, namely entropy-based regularization and regularization based on the L 2 norm, are easily adopted in the final loss function. The proposed method is verified by experiments. [ABSTRACT FROM AUTHOR]

LHC data have the potential to provide constraints on the gluon distribution, especially at high x, with both ATLAS and CMS performing differential measurements. Recently, CMS has measured double-differential distributions at 8 TeV. In this paper we examine the impact of this data set on the gluon distribution. To that end we develop novel, double-differential NNLO predictions for that data. No significant impact is found when the CMS data is added to the CT14HERA2 global PDF fit, due to the larger impact of the inclusive jet data from both the Tevatron and the LHC. If the jet data are removed from the fit, then an impact is observed. If the CMS data is scaled by a larger weight, representing the greater statistical power of the jet data, a roughly equal impact on the gluon distribution is observed for the as for the inclusive jet data. For data samples with higher integrated luminosity at 13 TeV, a more significant impact of the double-differential data may be observed. [ABSTRACT FROM AUTHOR]

A novel strategy to solve the Boltzmann equation with variable reduced electric field E / N by using an artificial neural network (ANN) is introduced, where E is the electric field and N is the gas number density. In this method, the ANN learns the electron velocity distribution function (EVDF) for arbitrary E / N in the Boltzmann equation. Thus, the ANN can calculate the EVDFs in the training range of E / N without additional training. For validation of the ANN, the EVDFs in each Ar and SF6 gas were calculated with the trained ANN. The electron energy distribution function and electron transport coefficients calculated from the EVDF quantitatively agree with those from another ANN for a single E / N and those from a Monte Carlo simulation, proving the validity of the present method. [ABSTRACT FROM AUTHOR]

In recent years, a linearization method has been extensively employed to investigate the electromechanical fields and carrier distribution in flexoelectric semiconductors, where the assumption of a small perturbation of carrier concentration is adopted. However, this method fails to accurately describe the realistic physical process in which a considerable variation of carrier concentration takes place. Based on fully coupled nonlinear equations, this paper presents a finite element approach to study the electromechanical couplings and nonlinear carrier transport in flexoelectric semiconductors. This method is applied to calculate the electrostatic potential in a bent piezoelectric semiconductive nanowire (NW) going beyond simple considerations and to simulate the nonlinear current–voltage (I – V) characteristics of a mechanically loaded flexoelectric p–n junction. The results indicate that the inherently nonlinear drift of carriers gives rise to the asymmetric distribution of the electric potential relative to the NW axis in the upper body. Flexoelectricity brings about a remarkable enhancement in output voltage and is responsible for the linear variation of electric potential along the length direction of the NW unless close to two ends. Furthermore, the barrier height and I – V relations of a flexoelectric p–n junction can be effectively tuned by mechanical forces due to the flexoelectric effect, the effect of which relies on the size of the p–n junction configuration. This work is a good starting point to comprehend the coupling of flexoelectricity and nonlinear carrier transport in static and dynamic cases, and offers an effective approach to numerically deal with the issues involved in flexoelectronics and piezoelectronics at the nanoscale. [ABSTRACT FROM AUTHOR]

In this article, on the basis of the Langevin equation applied to velocity fluctuations, we numerically model the partial variance of increments, which is a useful tool to measure time and spatial correlations in space plasmas. We consider a coupled map lattice model to relate the spatial scale of fluctuations, k, to some macro parameters of the systems, such as the Reynolds number, R λ , the κ parameter of Kappa distributions, and a skewness parameter, δ. To do so, we compute the velocity probability density function (pdf) for each spatial scale and different values of Reynolds number in the simulations. We fit the pdf with a Skew–Kappa distribution, and we obtain a numerical relationship between the level of turbulence of the plasma and the skewness of obtained distributions, namely, 〈 δ 〉 ∼ R λ − 1 / 2 . We expect the results exposed in this paper to be useful as a tool to characterize the turbulence in the context of space plasma and other environments. [ABSTRACT FROM AUTHOR]

In this paper, we aim to use the DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO), a future Japanese space gravitational-wave antenna sensitive to the frequency range between LISA and ground-based detectors, to provide gravitational-wave constraints on the cosmic curvature at z ∼ 5. In the framework of the well-known distance sum rule, the perfect redshift coverage of the standard sirens observed by DECIGO, compared with lensing observations including the source and lens from LSST, makes such cosmological-model-independent tests more natural and general. Focusing on three kinds of spherically symmetric mass distributions for the lensing galaxies, we find that the cosmic curvature is expected to be constrained with the precision of ΔΩK ∼ 10−2 in the early universe (z ∼ 5.0), improving the sensitivity of ET constraints by about a factor of 10. However, in order to investigate this further, the mass-density profiles of early-type galaxies should be properly taken into account. Specifically, our analysis demonstrates the strong degeneracy between the spatial curvature and the lens parameters, especially the redshift evolution of the power-law lens index parameter. When the extended power-law mass-density profile is assumed, the weakest constraint on the cosmic curvature can be obtained, whereas the addition of DECIGO to the combination of LSST+DECIGO does improve significantly the constraint on the luminosity–density slope and the anisotropy of the stellar velocity dispersion. Therefore, our paper highlights the benefits of synergies between DECIGO and LSST in constraining new physics beyond the standard model, which could manifest themselves through accurate determination of the cosmic curvature. [ABSTRACT FROM AUTHOR]

Pebble accretion is recognized as a significant accelerator of planet formation. Yet only formulae for single-sized (monodisperse) distribution have been derived in the literature. These can lead to significant underestimates for Bondi accretion, for which the best accreted pebble size may not be the one that dominates the mass distribution. We derive in this paper the polydisperse theory of pebble accretion. We consider a power-law distribution in pebble radius, and we find the resulting surface and volume number density distribution functions. We derive also the exact monodisperse analytical pebble accretion rate for which 3D accretion and 2D accretion are limits. In addition, we find analytical solutions to the polydisperse 2D Hill and 3D Bondi limits. We integrate the polydisperse pebble accretion numerically for the MRN distribution, finding a slight decrease (by an exact factor 3/7) in the Hill regime compared to the monodisperse case. In contrast, in the Bondi regime, we find accretion rates 1–2 orders of magnitude higher compared to monodisperse, also extending the onset of pebble accretion to 1–2 orders of magnitude lower in mass. We find megayear timescales, within the disk lifetime, for Bondi accretion on top of planetary seeds of masses 10−6 to 10−4 M ⊕, over a significant range of the parameter space. This mass range overlaps with the high-mass end of the planetesimal initial mass function, and thus pebble accretion is possible directly following formation by streaming instability. This alleviates the need for mutual planetesimal collisions as a major contribution to planetary growth. [ABSTRACT FROM AUTHOR]

In Tokamak á Configuration Variable (TCV), unstable modes excited by resonant interaction between the shear Alfvèn waves in continuum gaps and energetic particles have been observed in scenarios with neutral beam injection (NBI). TCV is a middle-size device ( R 0 / a = 0.88 / 0.25) equipped with a 1 MW , 25 keV tangential neutral beam injector. In this paper the phenomenology of modes excited with on-axis NBI is presented. The Alfvènic nature of the modes has been confirmed investigating their sensitivity against plasma parameters such as NBI energy, toroidal magnetic field, and cross-checking with the predictions from linear kinetic stability code. The mode radial profile is estimated using electron cyclotron emission measurement and agrees well with modelling results. In addition, the fast particle distribution function has been modelled using TRANSP/NUBEAM code. Even with counter-current NBI (leading to higher losses), the drive from the resonant particles is sufficient for the mode excitation. An ad-hoc additional diffusion model allows to estimate the fast particle transport, modifying the fast particle gradient at the mode location and matching the neutron rates. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of the distribution of the total angular momentum in a relativistic configuration. Using cumulants and generating function formalism this analysis can be reduced to the study of individual subshells with N equivalent electrons of momentum j. An expression as a nth-derivative is provided for the generating function of the J distribution and efficient recurrence relations are established. It is shown that this distribution may be represented by a Gram–Charlier-like series which is derived from the corresponding series for the magnetic quantum number distribution. The numerical efficiency of this expansion is fair when the configuration consists of several subshells, while the accuracy is less good when only one subshell is involved. An analytical expression is given for the odd-order momenta while the even-order ones are expressed as a series which provides an acceptable accuracy though being not convergent. Such expressions may be used to obtain approximate values for the number of transitions in a spin–orbit split array: it is shown that the approximation is often efficient when few terms are kept, while some complex cases require to include a large number of terms. [ABSTRACT FROM AUTHOR]

Restart has the potential of expediting or impeding the completion times of general random processes. Consequently, the issue of mean-performance takes center stage: quantifying how the application of restart on a process of interest impacts its completion-time's mean. Going beyond the mean, little is known on how restart affects stochasticity measures of the completion time. This paper is the first in a duo of studies that address this knowledge gap via: a comprehensive analysis that quantifies how sharp restart—a keystone restart protocol—impacts the Shannon entropy of the completion time. The analysis establishes closed-form results for sharp restart with general timers, with fast timers (high-frequency resetting), and with slow timers (low-frequency resetting). These results share a common structure: comparing the completion-time's hazard rate to a flat benchmark—the constant hazard rate of an exponential distribution whose entropy is equal to the completion-time's entropy. In addition, using an information-geometric approach based on Kullback–Leibler distances, the analysis establishes results that determine the very existence of timers with which the application of sharp restart decreases or increases the completion-time's entropy. Our work sheds first light on the intricate interplay between restart and randomness—as gauged by the Shannon entropy. [ABSTRACT FROM AUTHOR]

Diffusion in narrow curved channels with dead-ends as in extracellular space in the biological tissues, e.g., brain, tumors, muscles, etc. is a geometrically induced complex diffusion and is relevant to different kinds of biological, physical, and chemical systems. In this paper, we study the effects of geometry and confinement on the diffusion process in an elliptical comb-like structure and analyze its statistical properties. The ellipse domain whose boundary has the polar equation ρ (θ) = b 1 − e 2 cos 2 θ with 0 < e < 1, θ ∈ [0,2 π ], and b as a constant, can be obtained through stretched radius r such that Υ = r ρ (θ) with r ∈ [0,1]. We suppose that, for fixed radius r = R, an elliptical motion takes place and is interspersed with a radial motion inward and outward of the ellipse. The probability distribution function (PDF) in the structure and the marginal PDF and mean square displacement (MSD) along the backbone are obtained numerically. The results show that a transient sub-diffusion behavior dominates the process for a time followed by a saturating state. The sub-diffusion regime and saturation threshold are affected by the length of the elliptical channel lateral branch and its curvature. [ABSTRACT FROM AUTHOR]

We revisit the Haakeâ€"Lewensteinâ€"Wilkens approach to Edwardsâ€"Anderson (EA) model of Ising spin glass (SG) (Haake et al 1985 Phys. Rev. Lett. 55 2606). This approach consists in evaluation and analysis of the probability distribution of configurations of two replicas of the system, averaged over quenched disorder. This probability distribution generates squares of thermal copies of spin variables from the two copies of the systems, averaged over disorder, that is the terms that enter the standard definition of the original EA order parameter, q EA . We use saddle point/steepest descent (SPSD) method to calculate the average of the Gaussian disorder in higher dimensions. This approximate result suggest that q EA > 0 at 0 < T < T c in 3D and 4D. The case of 2D seems to be a little more subtle, since in the present approach energy increase for a domain wall competes with boundary/edge effects more strongly in 2D; still our approach predicts SG order at sufficiently low temperature. We speculate, how these predictions confirm/contradict widely spread opinions that: (i) There exist only one (up to the spin flip) ground state in EA model in 2D, 3D and 4D; (ii) there is (no) SG transition in 3D and 4D (2D). This paper is dedicated to the memories of Fritz Haake and Marek Cieplak. [ABSTRACT FROM AUTHOR]

In this paper, we study the pointwise equidistribution properties of measures μ p defined by digit restrictions on the b -adic expansion, where b ⩾ 2 is an integer. We prove that, if a sequence ( α n ) n ⩾ 1 satisfies a certain b -adic diversity condition, then the sequence ( α n x) n ⩾ 1 is uniformly distributed modulo one for μ p -a.e. x. We also find some sufficient conditions to ensure the b -adic diversity. Moreover, we apply these results to establish the b -adic diversity for the sequences that can be written as certain combination of polynomial and exponential functions. [ABSTRACT FROM AUTHOR]

The spatial parallel diffusion coefficient (SPDC) is one of the important quantities describing energetic charged particle transport. There are three different definitions for the SPDC: the displacement variance definition , the Fick's law definition with , and the Taylor–Green–Kubo (TGK) formula definition. For a constant mean magnetic field, the three different definitions of the SPDC give the same result. However, for a focusing field, it is demonstrated that the results of the different definitions are not the same. In this paper, from the Fokker–Planck equation, we find that different methods, e.g., the general Fourier expansion and iteration method, can give different equations of the isotropic distribution function (EIDFs). But it is shown that one EIDF can be transformed into another by some derivative iterative operations (DIOs). If one definition of the SPDC is invariant for the DIOs, it is clear that the definition is also invariant for different EIDFs; therefore, it is an invariant quantity for the different derivation methods of the EIDF. For the focusing field, we suggest that the TGK definition is only an approximate formula, and the Fick's law definition is not invariant to some DIOs. However, at least for the special condition, in this paper we show that the definition is an invariant quantity to the DIOs. Therefore, for a spatially varying field, the displacement variance definition , rather than the Fick's law definition and TGK formula definition , is the most appropriate definition of the SPDCs. [ABSTRACT FROM AUTHOR]

Assessing the performance of reverberation chambers (RCs) is a continuous problem which requires constant development and analysis. Several performance indicators exist, have been proposed and continue to be proposed in the literature. Each one of these indicators exhibits different levels of applicability, robustness or relevance towards a particular aspect of the field (statistical) behavior inside the RC. In this paper, we address this problem by introducing an alternative methodology able to estimate the distribution of the statistical parameters of interest. The methodology is based on Bayesian inference and it is applied to two different statistical models for RC measurement data and to two different loading conditions. The present paper is a significant expansion of a relevant abstract presented at the 'Mathematical and Statistical Methods for Metrology' Workshop, Torino, Italy, 30–31 May 2019. The corresponding abstract can be found at http://www.msmm2019.polito.it/programme. [ABSTRACT FROM AUTHOR]

The arrangement of atoms in the microstructures of alloys plays a key role in defining their physical and functional properties. These microstructures are studied to detect deviations from the expected homogeneous distribution using frequency distribution tests and cluster detection algorithms on reconstructions obtained from atom probe microscopy. However, it is challenging to evaluate and validate the performance of these algorithms using the reconstructed data because of the experimental limitations of the atom probe data itself. Low detector efficiency and reconstructional artifacts may lead to loss of existing clusters, or introduce heterogeneities that do not reflect the original arrangement. Additionally, retrieving atom probe data is a time and cost-prohibitive process. These challenges call for the use of simulated datasets with known concentrations and distributions to evaluate algorithms that analyze distributions or detect clusters. In this paper, we extend the existing methodology to simulate the creation of solute clusters in very dilute solutions for any solution. We propose methods to create denser and wider clusters in any solution irrespective of the concentration. Three novel solute cluster simulation techniques incremental, hierarchical and gravitational clustering are presented and compared in this paper. The simulated datasets can be used to validate and compare the performance of frequency distribution or cluster discovery algorithms. We compare the cluster analysis results obtained from the single linkage algorithm and DBSCAN to highlight the utility of these datasets. [ABSTRACT FROM AUTHOR]

In practical bearing fault diagnosis tasks, the available labeled data are often not from the equipment to be diagnosed and cannot cover all manner of working conditions. The adopted data-driven method is required to have a certain degree of cross-domain and cross-working condition transfer learning diagnosis ability. However, limited by the performance of existing transfer learning methods, the potential difference between the source domain and the target domain poses a challenge for the accuracy of transfer diagnosis. In this paper, a cross-working condition data supplement method based on the cycle generative adversarial network (CycleGAN) and a dynamics model is proposed, which can use limited available data to approximate the missing parts of existing data and be used for diagnosis of the target domain. First, we considered the limited experimental data as the target domain, the simulation data corresponding to the working condition as the source domain and used the working condition as the benchmark to constrain the data correspondence between the two datasets. We then used the CycleGAN model to learn the feature mapping from simulation to experiment. Second, based on the working condition of the data to be tested, the corresponding simulation data were input into the trained generator to obtain labeled data with experimental characteristics under the corresponding working conditions, and transferred the dataset as the source domain data to the data to be tested. In the test using self-made simulation and experimental datasets, combined with the transfer learning method based on the probability distribution adaptation, it was shown that the proposed method could effectively improve the diagnostic impact of the single transfer learning method in cross-domain and cross-working conditions when the working condition span was large. [ABSTRACT FROM AUTHOR]

The paper presents the evaluation of the calibration uncertainty of the British pendulum slip resistance tester using Monte Carlo simulation method. A mathematical model was produced which describes pendulum behavior based on its calibration parameters. The Monte Carlo simulation, programmed in Python, was used for simulating the effect of each of the calibration parameters adjustment within their tolerance intervals, with uniform and triangular probability distribution. Four different tolerance limits were compared: limits from a current international standard, a proposition with reduced limits from recent literature, and two novel propositions, one with reduced but easily achievable limits, and a second one for best practically achievable limits. The results of the simulation show a fundamental standard uncertainty contribution of about 2.8% for pendulum calibration according to current standard limits. Furthermore, they suggest a possible improvement to 0.5%â€"0.7% as its best practical direct calibration standard uncertainty for reduced limits. [ABSTRACT FROM AUTHOR]

A four-dimensional imaging spectrometer with a fiber optic dimension transform element has the ability to capture all four dimensions of data (2D spatial, spectral and temporal) with a single, radiometrically calibrated sensor at a single exposure, which satisfies the need to record transient events and fast changing phenomena of interest. In order to analyze the corresponding relation between the input light intensity and the output light intensity of a four-dimensional imaging spectrometer with a fiber optic dimension transform element, this paper utilizes the Fourier optics theory and complex Gaussian functions expansion method to derive and analyze the transmission characteristics of the imaging spectrometer optical system. This paper introduces the light intensity distribution formula when the detector is fixed on the negative first order spectral image plane and establishes and simulates the corresponding relation between the light intensity distribution of the detector and the spatial/spectral information on the target space. The research results show that the target information can be extracted and analyzed directly according to the corresponding relation. [ABSTRACT FROM AUTHOR]

Rolling bearings often run under variable speed condition, in addition to constant speed condition. How to achieve the bearing fault diagnosis under variable speed condition has been an important and hot issue. Nevertheless, there are few works on bearing fault diagnosis under variable speed condition especially for the feature extraction of unknown fault. Thus, this paper proposes a method based on fractional Fourier transform (FRFT) and stochastic resonance (SR) to extract bearing fault features. First, we use FRFT filtering algorithm to extract fault formation from the original signal. Next, we apply zero centering and high pass filtering to the signal which contains the fault information. Since the separated fault information is usually relatively weak and is not easy to identify, SR is used to enhance the weak fault feature information. Finally, bearing fault is diagnosed by observing the fault characteristic frequency in the time-frequency distribution plane. The method can achieve the extraction of the bearing fault characteristic frequency in the unknown situation and meanwhile remove a lot of noise interference. The method has been validated by numerical simulations and experimental analyses, where the scratches on both outer race and rolling element can be diagnosed successfully. By comparison with previous methods, fast kurtogram and variable mode decomposition, fault features extracted by the proposed method are much clearer and more accurate. The method may provide reference for the application of fault diagnosis in engineering occasions. [ABSTRACT FROM AUTHOR]

Wideband excitation signals are essential in bioimpedance spectroscopy for measurements in a time ensuring a quasi-stable measurement condition. In particular, for wearable biomedical systems, due to limited system resources, several aspects regarding measurement time, crest factor, slew rate requirements, frequency distribution, amplitude spectrum, and energy efficiency need to be thoroughly investigated. In this paper, we present an investigation of excitation signals, which includes not only the theoretical aspects but also aspects of real implementation on microcontroller-based systems. At a fixed number of samples and sampling rate, we investigate the implementability of signal frequencies and the resulting spectral efficiency. We focus on sources of signal distortion due to timer and amplitude deviations. The results show that for 4096 samples and a sampling frequency of 1 MHz, wideband signals are 2.76 times faster than a stepped frequency sweep. The multisine signal provides a better energy efficiency and has a lower slew rate requirement on hardware (around 0.3 V µs−1), but has a relatively high crest factor, even after optimization. An exemplary investigation of the distortion of the time/frequency and amplitudes following implementation on a standard industrial advanced RISC machines microcontroller has shown that a sampling rate compensation is required to overcome timer inaccuracies. Furthermore, non-return-to-zero binary signals are more sensitive to distortion due to hardware-related issues and have a lower signal-to-distortion-and-noise (SINAD) ratio than 24 dB, which is lower than the multisine signal, having a SINAD of 31 dB. [ABSTRACT FROM AUTHOR]

In this paper we address two questions about the synchronisation of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical results in convex geometry to prove bounds on the size of the frequency set supporting the existence of stable, phase locked solutions and show that the set of such frequencies can be expressed by a seminorm which we call the Kuramoto norm. In the second part we use some ideas from extreme order statistics to compute upper and lower bounds on the probability of synchronisation for very general frequency distributions. We do so by computing exactly the limiting extreme value distribution of a quantity that is equivalent to the Kuramoto norm. [ABSTRACT FROM AUTHOR]

In this paper we prove that, after an appropriate rescaling, the sum of moments of an N × N Hermitian matrix H sampled according to the generalized Cauchy (also known as Hua–Pickrell) ensemble with parameter s > 0 is a continuous-Hahn polynomial in the variable k. This completes the picture of the investigation that began in (Cunden et al 2019 Commun. Math. Phys. 369 1091–45) where analogous results were obtained for the other three classical ensembles of random matrices, the Gaussian, the Laguerre and Jacobi. Our strategy of proof is somewhat different from the one in (Cunden et al 2019 Commun. Math. Phys. 369 1091–45) due to the fact that the generalized Cauchy is the only classical ensemble which has a finite number of integer moments. Our arguments also apply, with straightforward modifications, to the other three cases studied in (Cunden et al 2019 Commun. Math. Phys. 369 1091–45) as well. We finally obtain a differential equation for the one-point density function of the eigenvalue distribution of this ensemble and establish the large N asymptotics of the moments. [ABSTRACT FROM AUTHOR]

Plasmoids—magnetized quasi-circular structures formed self-consistently in reconnecting current sheets—were previously considered to be the graveyards of energetic particles. In this paper, we demonstrate the important role of plasmoids in shaping the particle energy spectrum in relativistic reconnection (i.e., with upstream magnetization σup ≫ 1). Using 2D particle-in-cell simulations in pair plasmas with σup = 10 and 100, we study a secondary particle energization process that takes place inside compressing plasmoids. We demonstrate that plasmoids grow in time, while their interiors compress, amplifying the internal magnetic field. The magnetic field felt by particles injected in an isolated plasmoid increases linearly with time, which leads to particle energization as a result of magnetic moment conservation. For particles injected with a power-law distribution function, this energization process acts in such a way that the shape of the injected power law is conserved, while producing an additional nonthermal tail f(E) ∝ E−3 at higher energies, followed by an exponential cutoff. The cutoff energy, which increases with time as , can greatly exceed σupmec2. We analytically predict the secondary acceleration timescale and the shape of the emerging particle energy spectrum, which can be of major importance in certain astrophysical systems, such as blazar jets. [ABSTRACT FROM AUTHOR]

Compressional Alfvén eigenmodes (CAEs) driven by energetic ions have been observed in magnetic fusion experiments. In this paper, we show that the modes can also be driven by runaway electrons formed in post-disruption plasma, which may explain kinetic instabilities observed in DIII-D disruption experiments with massive gas injection. The spatial structure is calculated, as are the frequencies which are in agreement with experimental observations. Using a runaway electron distribution function obtained from a kinetic simulation, the mode growth rates are calculated and found to exceed the collisional damping rate when the runaway electron density exceeds a threshold value. The excitation of CAEs poses a new possible approach to mitigate seed runaway electrons during the current quench and surpassing the avalanche. [ABSTRACT FROM AUTHOR]

The pulsed-Townsend (PT) experiment is a well known swarm technique used to measure transport properties from a current in an external circuit, the analysis of which is based on the governing equation of continuity. In this paper, the Brambring representation (1964 Z. Phys. 179 532) of the equation of continuity often used to analyse the PT experiment, is shown to be fundamentally flawed when non-conservative processes are operative. The Brambring representation of the continuity equation is not derivable from Boltzmann's equation and consequently transport properties defined within the framework are not clearly representable in terms of the phase-space distribution function. We present a re-analysis of the PT experiment in terms of the standard diffusion equation which has firm kinetic theory foundations, furnishing an expression for the current measured by the PT experiment in terms of the universal bulk transport coefficients (net ionisation rate, bulk drift velocity and bulk longitudinal diffusion coefficient). Furthermore, a relationship between the transport properties previously extracted from the PT experiment using the Brambring representation, and the universal bulk transport coefficients is presented. The validity of the relationship is tested for two gases Ar and SF6, highlighting also estimates of the differences. [ABSTRACT FROM AUTHOR]

Elliptical accretion disk models for tidal disruption events (TDEs) have been recently proposed and independently developed by two groups. Although these two models are characterized by a similar geometry, their physical properties differ considerably. In this paper, we further investigate the properties of the elliptical accretion disk of the nearly uniform distribution of eccentricity within the disk plane. Our results show that the elliptical accretion disks have distinctive hydrodynamic structures and spectral energy distributions, associated with TDEs. The soft X-ray photons generated at pericenter and nearby are trapped in the disk and advected around the ellipse because of large electron scattering opacity. They are absorbed and reprocessed into emission lines and low-frequency continuum via recombination and bremsstrahlung emission. Because of the rapid increase of bound–free and free–free opacities with radius, the low-frequency continuum photons become trapped in the disk at large radius and are advected through apocenter and back to the photon-trapping radius. Elliptical accretion disks predict sub-Eddington luminosities and emit mainly at the photon-trapping radius of thousands of Schwarzschild radii with a blackbody spectrum of nearly single temperature of typically about 3 × 104 K. Because of the self-regulation, the photon-trapping radius expands and contracts following the rise and fall of accretion rate. The radiation temperature is nearly independent of BH mass and accretion rate and varies weakly with the stellar mass and the viscosity parameter. Our results are well consistent with the observations of optical/UV TDEs. [ABSTRACT FROM AUTHOR]

In this paper, the electrical behavior of tungsten carbide (WC) Schottky barrier on 4H-SiC was investigated. First, a statistical current-voltage (I–V) analysis in forward bias, performed on a set of equivalent diodes, showed a symmetric Gaussian-like distribution of the barrier heights after annealing at 700 °C, where a low Schottky barrier height (ΦB = 1.05 eV) and an ideality factor n = 1.06 were measured. The low value of the barrier height makes such a WC contact an interesting candidate to reduce the conduction losses in 4H-SiC Schottky diodes. A deeper characterization has been carried out, by monitoring the temperature dependence of the I–V characteristics and the behavior of the relevant parameters ΦB and n. The increase of the barrier height and decrease of the ideality factor with increasing temperature indicated a lateral inhomogeneity of the WC/4H-SiC Schottky contact, which was described by invoking Tung's model. Interestingly, the temperature dependence of the leakage current under reverse bias could be described by considering in the thermionic field emission model the temperature dependent barrier height related to the inhomogeneity. These results can be useful to predict the behavior of WC/4H-SiC Schottky diodes under operative conditions. [ABSTRACT FROM AUTHOR]

Fast radio bursts (FRBs) are millisecond-duration radio transients and can be used as a cosmological probe. However, the dispersion measure (DM) contributed by the intergalactic medium (IGM) is hard to distinguish from other components. In this paper, we use the IllustrisTNG simulation to realistically estimate DMIGM up to z ∼ 9. We find pc cm−3 at z = 1. The probability distribution of DMIGM can be well fitted by a quasi-Gaussian function with a long tail. The tail is caused by structures along the line of sight in the IGM. Subtracting DM contributions from the Milky Way and host galaxy for localized FRBs, the DMIGM value is close to that given by the derived DMIGM–z relation. We also show the ability to constrain the cosmic reionization history with DMIGM of high-redshift FRBs in the IllustrisTNG universe. The derived DMIGM–z relation at high redshifts can be well fitted by a tanh reionization model with the reionization redshift z = 5.95, which is compatible with the reionization model used by the IllustrisTNG simulation. DMIGM of high-redshift FRBs also provides an independent way to measure the optical depth of the cosmic microwave background. Our result can be used to derive the pseudo-redshifts of nonlocalized FRBs for DMIGM < 4000 pc cm−3. [ABSTRACT FROM AUTHOR]

Using Magnetospheric Multiscale observations at the Earth's quasi-parallel bow shock we demonstrate that electrons are heated by two different mechanisms: a quasi-adiabatic heating process during magnetic field compression, characterized by the isotropic temperature relation with α = 2/3 when the electron heating function , and a stochastic heating process when. Both processes are controlled by the value of the stochastic heating function for particles with mass mj and charge qj in the electric and magnetic fields and. Test-particle simulations are used to show that the stochastic electron heating and acceleration in the studied shock are accomplished by waves at frequencies (0.4–5) fce (electron gyrofrequency) for bulk heating, and waves for acceleration of the tail of the distribution function. Stochastic heating can give rise to flat-top electron distribution functions, frequently observed near shocks. It is also shown that obliquely polarized electric fields of electron cyclotron drift and ion acoustic instabilities scatter the electrons into the parallel direction and keep the isotropy of the electron distribution. The results reported in this paper may be relevant to electron heating and acceleration at interplanetary shocks and other astrophysical shocks. [ABSTRACT FROM AUTHOR]

The thermal Sunyaev–Zel'dovich (tSZ) and the kinematic Sunyaev–Zel'dovich (kSZ) effects trace the distribution of electron pressure and momentum in the hot universe. These observables depend on rich multiscale physics, thus, simulated maps should ideally be based on calculations that capture baryonic feedback effects such as cooling, star formation, and other complex processes. In this paper, we train deep convolutional neural networks with a U-Net architecture to map from the three-dimensional distribution of dark matter to electron density, momentum, and pressure at ∼100 kpc resolution. These networks are trained on a combination of the TNG300 volume and a set of cluster zoom-in simulations from the IllustrisTNG project. The neural nets are able to reproduce the power spectrum, one-point probability distribution function, bispectrum, and cross-correlation coefficients of the simulations more accurately than the state-of-the-art semianalytical models. Our approach offers a route to capture the richness of a full cosmological hydrodynamical simulation of galaxy formation with the speed of an analytical calculation. [ABSTRACT FROM AUTHOR]

Radiative efficiencies of QSOs and their distribution encode rich information on the evolution of both masses and spins of massive black holes (MBHs) across cosmic time. In this paper, we develop a maximum likelihood method to statistically extract the intrinsic relation between radiative efficiency (ϵ) and mass (M•) of QSOs from their distribution on the luminosity–(empirically estimated virial) mass plane. By using mock samples, we find that strong constraint can be put on the ϵ–M• relation at redshift z ≲ 0.4 from uniform QSO samples similar to those in the Sloan Digital Sky Survey (SDSS) and from QSO samples at z ∼ 0.6 (or ≲1.0) if the magnitude limit of the survey can be ∼1–2 (or 2–3) magnitude deeper. Applying this method to the SDSS DR7 QSOs with z ≲ 0.7, we find (or) correlation for QSOs with the masses obtained according to the H β (or Mg ii) empirical mass estimator. These contradictory results may be due to the unknown systematic errors in the two mass estimators, preventing an accurate constraint on the ϵ–M• relation by using current available QSO samples. We find that both the estimates of MBH mass and Eddington ratio distribution functions can be affected by the ϵ– relation, suggesting that the determination of this relation is important for understanding the accretion and growth history of MBHs. In the future, the intrinsic ϵ–M• relation is expected to be strongly constrained by using QSO samples obtained from surveys deeper than the SDSS if the host galaxy contamination and systematic errors of the mass estimator(s) can be well modeled or removed. [ABSTRACT FROM AUTHOR]

In this paper, a temperature-humidity-pressure (THP) sensor based on surface acoustic wave (SAW) devices is proposed for the simultaneous monitoring of temperature, humidity and pressure. The developed THP sensor consists of three SAW one-port resonators fabricated onto Y-cut LiNbO3 with frequencies of 81, 85.2, and 89.92 MHz for temperature, humidity and pressure sensing respectively. Graphene oxide was used as a sensitive layer material for the SAW humidity sensor. A flexible cantilever beam was used as a sensitive structure for the pressure sensor. Prior to fabrication, both the temperature sensitivity of the substrate and the deformation of the cantilever beam were simulated using the COMSOL Multiphysics. The frequency drift of the humidity sensor is obtained through analysis. According to the simulation results and analysis, the resonant frequency and frequency distribution of each sensor were reasonably set to avoid mutual interference. Experimental tests demonstrate that the proposed THP sensor can operate in an ambient environment with a temperature range of 25 °C–200 °C, pressure range of 0–42 kPa, and humidity range of 10%–90% relative humidity (RH) with good repeatability and stability, which can be attributed to simulation optimization and the use of strongly hydrophilic nanomaterials. The humidity sensor exhibits relatively high sensitivity (absolute sensitivity of 5.1 kHz/%RH and relative sensitivity of 59.97 ppm/%RH) over a wide test range from 10% to 90% RH with very little hysteresis at 35 °C and 0 kPa. Additionally, the humidity sensor provides good reversibility, excellent short-term repeatability and stability with a fast response time of approximately 8.3 s and recovery time of approximately 4.8 s. [ABSTRACT FROM AUTHOR]

In this paper we continue our earlier studies (Diao et al 2011 J. Phys. A: Math. Theor. 44 405202, Diao et al J. Phys. A: Math. Theor. 45 275203) on the generation methods of random equilateral polygons confined in a sphere. The first half of this paper is concerned with the generation of confined equilateral random walks.We show that if the selection of a vertex is uniform subject to the position of its previous vertex and the confining condition, then the distributions of the vertices are not uniform, although there exists a distribution such that if the initial vertex is selected following this distribution, then all vertices of the random walk follow this same distribution. Thus in order to generate a confined equilateral random walk, the selection of a vertex cannot be uniform subject to the position of its previous vertex and the confining condition. We provide a simple algorithm capable of generating confined equilateral random walks whose vertex distribution is almost uniform in the confinement sphere. In the second half of this paper we show that any process generating confined equilateral random walks can be turned into a process generating confined equilateral random polygons with the property that the vertex distribution of the polygons approaches the vertex distribution of the walks as the polygons get longer and longer. In our earlier studies, the starting point of the confined polygon is fixed at the center of the sphere. The new approach here allows us to move the starting point of the confined polygon off the center of the sphere. [ABSTRACT FROM AUTHOR]

In this paper, we apply a simple walk mechanism to the study of the traffic of many indistinguishable particles in complex networks. The network with particles stands for a particle system, and every vertex in the network stands for a quantum state with the corresponding energy determined by the vertex degree. Although the particles are indistinguishable, the quantum states can be distinguished. When the many indistinguishable particles walk randomly in the system for a long enough time and the system reaches dynamic equilibrium, we find that under diffeerent restrictive conditions the particle distributions satisfy diffeerent forms, including the Bose-Einstein distribution, the Fermi-Dirac distribution and the non-Fermi distribution (as we temporarily call it). As for the Bose-Einstein distribution, we find that only if the particle density is larger than zero, with increasing particle density, do more and more particles condense in the lowest energy level. While the particle density is very low, the particle distribution transforms from the quantum statistical form to the classically statistical form, i.e., transforms from the Bose distribution or the Fermi distribution to the Boltzmann distribution. The numerical results fit well with the analytical predictions. [ABSTRACT FROM AUTHOR]

In this paper, a vertical gaussian-doped tunnel-FET on SOI (VG-SOI-TFET) employing electrostatically doped (ED) p-type source is proposed and investigated. A thin silicon film with n-type Gaussian doping in the vertical direction is used initially. By using the ED concept, a p+ source region is realized with Platinum having suitable work function (ϕm = 5.93 eV). Various dc and analog/RF parameters are studied as a function of peak donor density (Np) and doping gradient (g) of the gaussian distribution function. A 2D calibrated simulation study of the proposed VG-SOI-TFET has revealed that the ION is increased by ∼7 times while the ambipolar current (IAMB) is reduced by ∼5 orders of magnitude at an optimum Np of 5 × 1018 cm−3 and g value of 2 nm/decade, compared to the uniformly-doped SOI TFET (UD-SOI-TFET). Furthermore, a superior analog/RF figures of merit are achieved such as transconductance, capacitances, cutoff-frequency, and gain bandwidth product. An improvement of ∼5 times in peak gm and ∼5 times in peak fT are also observed at an optimum Np of 5 × 1018 cm−3 and g value of 2 nm/decade. [ABSTRACT FROM AUTHOR]