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These lecture notes review exact analytical results for quantum transients concerning the time evolution of decay for potentials of finite range by using the formalism of resonant states.
Recently, Xu et al.[Phys. Plasmas 18, 052301 (2011)] have studied the effects of various plasma parameters on interaction of two ion-acoustic solitary waves in an unmagnetized three-dimensional electron-positron-ion quantum plasma. They have used the extended reductive perturbation technique, the so-called, extended Poincare-Lighthill-Kuo technique, to deduce from the model governing the quantum hydrodynamics differential equations leading to the soliton dynamical properties, namely, Korteweg-de Vries evolution equations (one for each wave) and coupled differential equations describing the phase-shift in trajectories of solitons due to the two dimensional collision. The variation of the calculated collision phase-shifts are then numerically inspected in terms of numerous plasma fractional parameters. In this comment, we give some notes specific to the validity of the results of above-mentioned article and refer to important misconceptions about the use of the Fermi-temperature in quantum plasmas, appearing in this article and many other recently published ones.
The integro-differential Berk-Breizman (BB) equation, describing the evolution of particle-driven wave mode is transformed into a simple delayed differential equation form {nu}{partial_derivative}a({tau})/{partial_derivative}{tau}=a({tau}) -a{sup 2}({tau}- 1) a({tau}- 2). This transformation is also applied to the two modes extension of the BB theory. The obtained solutions are presented together with the derived asymptotic analytical solutions and the numerical results.
This software contains an algorithm to model and predict the time evolution of chemical kinetics in reacting flow simulations using neural ordinary differential equations (NODEs). The approach works by using artificial neural networks to predict the chemical source terms. It achieves this by using forward-mode automatic differentiation and the Levenberg-Marquardt algorithm to adjust the neural network parameters, such that the discrepancies between the actual and predicted species profiles are minimized.
Electrons accelerated in solar flares are injected into the surrounding plasma, where they are subjected to the influence of collisional (Coulomb) energy losses. Their evolution is modeled by a partial differential equation describing continuity of electron number. In a recent paper, Dobranskis & Zharkova claim to have found an "updated exact analytical solution" to this continuity equation. Their solution contains an additional term that drives an exponential decrease in electron density with depth, leading them to assert that the well-known solution derived by Brown, Syrovatskii & Shmeleva, and many others is invalid. We show that the solution of Dobranskis & Zharkova results from a fundamental error in the application of the method of characteristics and is hence incorrect. Further, their comparison of the "new" analytical solution with numerical solutions of the Fokker-Planck equation fails to lend support to their result.We conclude that Dobranskis & Zharkova's solution of the universally accepted and well-established continuity equation is incorrect, and that their criticism of the correct solution is unfounded. We also demonstrate the formal equivalence of the approaches of Syrovatskii & Shmeleva and Brown, with particular reference to the evolution of the electron flux and number density (both differential in energy) in a collisional thick target. We strongly urge use of these long-established, correct solutions in future works.
Measurements of elliptic (v 2 ) and triangular (v 3 ) flow coefficients of π ± , K ± , $p+\bar{p}$, $K$$^{0}_{S}$, and $Λ+\bar{Λ}$ obtained with the scalar product method in Xe-Xe collisions at $\sqrt{s_{NN}}$ = 5.44 TeV are presented. The results are obtained in the rapidity range |y| < 0.5 and reported as a function of transverse momentum, p T , for several collision centrality classes. The flow coefficients exhibit a particle mass dependence for p T < 3 GeV/c, while a grouping according to particle type (i.e., meson and baryon) is found at intermediate transverse momenta (3 < p T < 8 GeV/c). The magnitude of the baryon v 2 is larger than that of mesons up to p T = 6 GeV/c. The centrality dependence of the shape evolution of the p T -differential v 2 is studied for the various hadron species. The v 2 coefficients of π ± , K ± , and $p+\bar{p}$ are reproduced by MUSIC hydrodynamic calculations coupled to a hadronic cascade model (UrQMD) for p T < 1 GeV/c. A comparison with v n measurements in the corresponding centrality intervals in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV yields an enhanced v 2 in central collisions and diminished value in semicentral collisions.
This paper presents an algorithm for the identification of parameters for a stochastic hot water end-use process that drives a homogeneous population of thermostatically controlled electric water heaters (EWH). Usually, only metered interval consumption data (kWh) is collected and the hot water end-use process is unobservable to utility and aggregators. However, the availability of EWHs for demand response (DR) is closely coupled with the hot water end-use process. In this context, the hot water end-use process is modeled as a two-state Markov chain (Use / No use), which causes the thermostatic ON-OFF switching process to behave as a Markov renewal process (MRP). A set of first passage-time problems is developed to obtain the moments of the transition probability densities of the MRP. These problems are addressed by establishing a system of coupled partial differential equations characterizing the temperature evolution of the EWH population. A key quantity in the methodology for estimating the parameters is the total time an EWH is ON within a period of interest. It is referred to as the total busy time. Total busy time in this approach is a random variable for which analytical expressions of the moments are developed as a function of the metered window length. The latter expressions become the basis of a hot water demand model identification algorithm which is validated using agent-based simulations of EWHs.
This paper constructs a nonlinear filtering framework that admits appearances of new information processes at random times by introducing piecewise enlargements of filtrations and proposes a new energy-based Schrodinger evolution expressed as a stochastic differential equation on a complex Hilbert space. Each information process is modeled as the sum of a random variable taking the eigenvalues of a Hamiltonian and an independent Brownian bridge noise. It is shown that under a piecewise enlarged filtration, the wave function is a jump-diffusion process until it collapses at some terminal time. In between discontinuities, the dynamics of the state vector are governed by different Wiener processes and diffusion coefficients. This motivates the introduction of an inclusive chain of Kolmogorov probability spaces or a *-isomorphic chain of commutative von Neumann probability spaces, on which the quantum system evolves differently based on the number of active information processes. The expectation of the Hamiltonian at a given state is the solution of a second-order nonlinear differential equation determined by one of the possible regimes that the quantum system belongs to. It is shown that the collapse rate is a submartingale with positive jumps and the Shannon entropy process is a supermartingale with expected negative jumps when passing to higher-order probability spaces. The framework is extended to the case when the Hamiltonian is modeled as a function of a set of commutative operators, where each operator is associated with a different piecewise enlarged filtration.
The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB ® codes are also provided. Extension to include translation Brownian motion is straightforward.
The cores of luminous B- and A-type (BA) supergiant stars are the seeds of later core-collapse supernovae. Thus, constraining the near-core conditions in this class of stars can place tighter constraints on the size, mass, and chemical composition of supernova remnants. Asteroseismology of these massive stars is one possible approach into such investigations. Recently, Moravveji et al. in 2012 (hereafter Paper I) extracted 19 significant frequencies from a 6-year radial velocity monitoring of Rigel ({beta} Ori, B8 Ia). The periods they determined broadly range from 1.22 to 74.74 days. Based on our differentially rotating stellar structure and evolution model, Rigel, at its current evolutionary state, is undergoing core He burning and shell H burning. Linear fully non-adiabatic non-radial stability analyses result in the excitation of a dense spectrum of non-radial gravity-dominated mixed modes. The fundamental radial mode (l = 0) and its overtones are all stable. When the hydrogen-burning shell is located even partially in the radiative zone, a favorable condition for destabilization of g-modes through the so-called {epsilon}-mechanism becomes viable. Only those g-modes that have high relative amplitudes in the hydrogen-burning (radiative) zone can survive the strong radiative damping. From the entire observed range of variability periods of Rigel (found in Paper I), and based on our model, only those modes with periods ranging between 21 and 127 days can be theoretically explained by the {epsilon}-mechanism. The origin of the short-period variations (found in Paper I) still remains unexplained. Because Rigel is similar to other massive BA supergiants, we believe that the {epsilon}-mechanism may be able to explain the long-period variations in {alpha} Cygni class of pulsating stars.
The quasi-bound states of a superconducting quantum dot that is weakly coupled to a normal metal appear as resonances in the Andreev reflection probability, measured via the differential conductance. We study the evolution of these Andreev resonances when an external parameter (such as the magnetic field or gate voltage) is varied, using a random-matrix model for the N × N scattering matrix. We contrast the two ensembles with broken time-reversal symmetry, in the presence or absence of spin-rotation symmetry (class C or D). The poles of the scattering matrix in the complex plane, encoding the center and width of the resonance, are repelled from the imaginary axis in class C. In class D, in contrast, a number ∝ √N of the poles has zero real part. The corresponding Andreev resonances are pinned to the middle of the gap and produce a zero-bias conductance peak that does not split over a range of parameter values (Y-shaped profile), unlike the usual conductance peaks that merge and then immediately split (X-shaped profile)
This paper presents the measurements of π ± , K ± , p and $\bar{p}$ transverse momentum (p T ) spectra as a function of charged-particle multiplicity density in proton–proton (pp) collisions at $\sqrt{s}$ = 13TeV with the ALICE detector at the LHC. Such study allows us to isolate the center-of-mass energy dependence of light-flavour particle production. The measurements reported here cover a p T range from 0.1 to 20 GeV / c and are done in the rapidity interval | y| < 0.5. The p T -differential particle ratios exhibit an evolution with multiplicity, similar to that observed in pp collisions at $\sqrt{s}$ = 7 TeV, which is qualitatively described by some of the hydrodynamical and pQCD-inspired models discussed in this paper. Furthermore, the p T -integrated hadron-to-pion yield ratios measured in pp collisions at two different center-of-mass energies are consistent when compared at similar multiplicities. This also extends to strange and multi-strange hadrons, suggesting that, at LHC energies, particle hadrochemistry scales with particle multiplicity the same way under different collision energies and colliding systems.
This repository is used to release code generated for manuscripts on the Photosynthetic Energy Transduction core program. This code simulates the reduction of HoxEFU by NADH. The electro transfer rate constants for the simulation are specified in the .csv files. The two .csv files correspond tot he two models described in Dawson et al. Cell. Rep. Phys. Sci. 2026. The code utilizes a chemical master equation, a set of differential equations, defining the time evolution of the oxidation and reduction kinetics of NAD+, NADH, a FMN flavin, and a set of iron sulfur clusters. The kinetics of HoxEFU reduction by NADH are evaluated by numerical integration of the chemical master equation using a variable-time-step Runge-Kutta algorithm.
We derive the most up-to-date Swift-Burst Alert Telescope (BAT) blazar luminosity function in the 14–195 keV range, making use of a clean sample of 118 blazars detected in the BAT 105 month survey catalog, with newly obtained redshifts from the BAT Active Galatic Nucleus Spectroscopic Survey. We determine the best-fit X-ray luminosity function for the whole blazar population, as well as for flat-spectrum radio quasars (FSRQs) alone. The main results are: (1) at any redshift, BAT detects the most luminous blazars, above any possible break in their luminosity distribution, which means we cannot differentiate between density and luminosity evolution; (2) the whole blazar population, dominated by FSRQs, evolves positively up to redshift z ~ 4.3, confirming earlier results and implying lower number densities of blazars at higher redshifts than previously estimated. The contribution of this source class to the cosmic X-ray background at 14–195 keV can range from 5%–18%, while possibly accounting for 100% of the MeV background. We also derived the average 14 keV–10 GeV spectral energy distribution for BAT blazars, which allows us to predict the number counts of sources in the MeV range, as well as the expected number of high-energy (>100 TeV) neutrinos. A mission like COSI will detect 40 MeV blazars, of which two may have coincident neutrino detections. Finally, taking into account beaming selection effects, the distribution and properties of the parent population of these extragalactic jets are derived. We find that the distribution of viewing angles is quite narrow, with most sources aligned within <5° of the line of sight. Moreover, the average Lorentz factor, $\langle$Γ$\rangle$ = 8–12, is lower than previously suggested for these powerful sources.
An IR spectrum of asteroid Vesta, the first of any asteroid, has been recorded at a spectral resolution of 44/cm with a Fourier spectrometer. An electronic absorption band is observed that is assigned to an iron-rich pyroxene (pigeonite) spectroscopically similar to that found in certain eucrites. Other important rock-forming minerals such as olivine and plagioclase feldspar are not observed. There is no evidence for compositional variation with rotational phase angle. This spectroscopic picture of Vesta suggests considerable evolution including the melting and differentiation of silicates.
The behavior of phase speed for 'slow' and 'fast' magnetosonic waves is well documented in the literature. Not so well documented is the behavior of the ray direction and its relation to the phase direction - indeed the ray behavior recorded in most of the standard plasma physics texts has not been found. This situation is rectified, and some of the curiosities associated with the direction of the 'slow' ray relative to the direction of the 'slow' phase wave are indicated. These calculations have been performed as a necessary basis for discussion of phase and ray evolution of magnetosonic waves in differentially shearing plasmas.
A thermodynamic analysis of pyroxene-melt equilibria is performed through use of a literature survey of analyses of high-Ca pyroxene and coexisting silicate melt pairs and analyses of low-Ca pyroxene silicate melt pairs. Reference is made to a modified version of a model developed by Bottinga and Weill (1972) which more successfully accounts for variations in melt composition than does a model which considers the melt to be composed of simple oxides which mix ideally. By using a variety of pyroxene melt relations, several pyroxene-melt and low-Ca pyroxene-high-Ca pyroxene geothermometers are developed which have internally consistant precisions of approximately + or - 20 C. Finally, it is noted that these equations may have application in modeling the evolution of mineral compositions during differentiation of basaltic magmas.
Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.