Effect of quantization and positron concentration on shielding potentials in electron-positron-ion plasma

The kinetic theory of plasma has been employed to compute the test-charge potential distributions accounting for quantization effects in magnetized electron-positron-ion (EPI) plasmas. In this regard, the degenerate positrons and electrons are assumed to follow the Fermi-Dirac distribution, while inertial ions are modelled by Maxwellian velocity distribution. By solving the Fourier-transformed Vlasov–Poisson equations, a modified dielectric function and electrostatic potential is obtained. By imposing various constraints on the test-charge speed, the potential profile has been analysed in terms of Debye–Hückel (DH), far-field (FF), and wake-field (WF) potentials. It has been found that the amplitude of DH and FF potentials increases by the inclusion of quantization effects, and it becomes the opposite for the WF potential profile. Furthermore, the variation of positron concentration significantly affects the DH, FF, and WF potentials. The present findings are important to understand the shielding phenomenon in degenerate multi-species plasmas.     

Single Sample Path-Based Optimization of Markov Chains

Motivated by the needs of on-line optimization of real-world engineering systems, we studied single sample path-based algorithms for Markov decision problems (MDP). The sample path used in the algorithms can be obtained by observing the operation of a real system. We give a simple example to explain the advantages of the sample path-based approach over the traditional computation-based approach: matrix inversion is not required; some transition probabilities do not have to be known; it may save storage space; and it gives the flexibility of iterating the actions for a subset of the state space in each iteration. The effect of the estimation errors and the convergence property of the sample path-based approach are studied. Finally, we propose a fast algorithm, which updates the policy whenever the system reaches a particular set of states and prove that the algorithm converges to the true optimal policy with probability one under some conditions. The sample path-based approach may have important applications to the design and management of engineering systems, such as high speed communication networks.This work was supported in part by     

Predicting XAFS scattering path cumulants and XAFS spectra for metals (Cu,Ni, Fe,Ti, Au) using molecular dynamics simulations

The ability of molecular dynamics (MD) simulations to support the analysis of X‐ray absorption fine‐structure (XAFS) data for metals is evaluated. The low‐order cumulants (ΔR, σ², C₃) for XAFS scattering paths are calculated for the metals Cu, Ni, Fe, Ti and Au at 300 K using 28 interatomic potentials of the embedded‐atom method type. The MD cumulant predictions were evaluated within a cumulant expansion XAFS fitting model, using global (path‐independent) scaling factors. Direct simulations of the corresponding XAFS spectra, χ(R), are also performed using MD configurational data in combination with the FEFFab initio code. The cumulant scaling parameters compensate for differences between the real and effective scattering path distributions, and for any errors that might exist in the MD predictions and in the experimental data. The fitted value of ΔR is susceptible to experimental errors and inadvertent lattice thermal expansion in the simulation crystallites. The unadjusted predictions of σ² vary in accuracy, but do not show a consistent bias for any metal except Au, for which all potentials overestimate σ². The unadjusted C₃ predictions produced by different potentials display only order‐of‐magnitude consistency. The accuracy of direct simulations of χ(R) for a given metal varies among the different potentials. For each of the metals Cu, Ni, Fe and Ti, one or more of the tested potentials was found to provide a reasonable simulation of χ(R). However, none of the potentials tested for Au was sufficiently accurate for this purpose.     

Semiempirical fine-tuning for Hartree–Fock ionization potentials of atomic ions with non-integral atomic number

Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z)$I(Z)$ in He-like atomic ions for the range of (fractional) nuclear charges Z   lying between the known critical value _Zc=0.911$Z_{\mathrm{c}}=0.911$ at which I(Z)$I(Z)$ tends to zero and Z=2$Z=2$. They showed that it is possible to fit I(Z)$I(Z)$ to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of _Zc$Z_{\mathrm{c}}$ for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z)$I(Z)$ for these series.     

A potential approach for ordinal games

We introduce the class of ordinal games with a potential, which are characterized by the absence of weak improvement cycles, the same condition used by Voorneveld and Norde (1997) for ordinal potential games.     

One-range addition theorems for generalized integer and noninteger μ Coulomb,and exponential type correlated interaction potentials with hyperbolic cosine in position,momentum,and four-dimensional

The formulae are established in position,momentum,and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb,and exponential type correlated interaction potentials with hyperbolic cosine（GCTCP and GETCP HC）.These formulae are expressed in terms of one-range addition theorems of complete orthonormal sets of Ψα-exponential type orbitals（Ψ α-ETO）,α-momentum space orbitals（α-MSO）,and zα-hyperspherical harmonics（zα-HSH） introduced.The one-range addition theorems obtained can be useful in the electronic structure calculations of atoms and molecules when the GCTCP and GETCP HC in position,momentum,and four-dimensional spaces are employed.     

Quasilinear Schrödinger equations with unbounded or decaying potentials

We study the existence of nonnegative and nonzero solutions for the following class of quasilinear Schrödinger equations: where V and Q are potentials that can be singular at the origin, unbounded or vanishing at infinity. In order to prove our existence result we used minimax techniques in a suitable weighted Orlicz space together with regularity arguments and we need to obtain a symmetric criticality type result.     

Solution of the Dirac equation by separation of variables in spherical coordinates for a large class of non-central electromagnetic potentials

A systematic and intuitive approach for the separation of variables of the three-dimensional Dirac equation in spherical coordinates is presented. Using this approach, we consider coupling of the Dirac spinor to electromagnetic four-vector potential that satisfies the Lorentz gauge. The space components of the potential have angular (non-central) dependence such that the Dirac equation becomes separable in all coordinates. We obtain exact solutions for a class of three-parameter static electromagnetic potential whose time component is the Coulomb potential. The relativistic energy spectrum and corresponding spinor wave functions are obtained. The Aharonov–Bohm and magnetic monopole potentials are included in these solutions.     

Optimal Control of the Obstacle for an Elliptic Variational Inequality

An optimal control problem for an elliptic obstacle variational inequality is considered. The obstacle is taken to be the control and the solution to the obstacle problem is taken to be the state. The goal is to find the optimal obstacle from H ¹ ₀ (Ω) so that the state is close to the desired profile while the H ¹ (Ω) norm of the obstacle is not too large. Existence, uniqueness, and regularity as well as some characterizations of the optimal pairs are established. Accepted 11 September 1996     

Superfluidity and Anderson localisation for a weakly interacting Bose gas in a quasiperiodic potential

Using exact diagonalisation and Density Matrix Renormalisation group (DMRG) approach we analyse the transition to a localised state of a weakly interacting quasi-1D Bose gas subjected to a quasiperiodic potential. The analysis is performed by calculating the superfluid fraction, density profile, momentum distribution and visibility for different periodicities of the second lattice and in the presence (or not) of a weak repulsive interaction. It is shown that the transition is sharper towards the maximally incommensurate ratio between the two lattice periodicities, and shifted to higher values of the second lattice strength by weak repulsive interactions. We also relate our results to recent experiments.