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arXiv2010

The role of final state correlation in double ionization of helium: a master equation approach

The process of nonsequential two-photon double ionization of helium is studied by two complementary numerical approaches. First, the time-dependent Schr{ö}dinger equation is solved and the final wave function is analyzed in terms of projection onto eigenstates of the uncorrelated Hamiltonian, i.e., with no electron-electron interaction included in the final states. Then, the double ionization probability is found by means of a recently developed approach in which the concept of absorbing boundaries has been generalized to apply to systems consisting of more than one particle. This generalization is achieved through the Lindblad equation. A model of reduced dimensionality, which describes the process at a qualitative level, has been used. The agreement between the methods provides a strong indication that procedures using projections onto uncorrelated continuum states are adequate when extracting total cross sections for the direct double ionization process.

quant-ph↗
arXiv2014

Radiation Pattern Reconstruction Techniques for Antenna Measurement using Chebyshev Polynomials

A new method of antenna radiation pattern reconstruction using Chebyshev polynomials was presented in this paper. The analysis starts from the data measured in the frequency domain, and it corresponds to a direct propagating between two antennas and reflected propagating waves from the copper plate. The accuracy of this technique is evaluated at the frequency of 3.35GHz by the anechoic conditions. As a result, the Chebyshev method shows us a good performance in the E-plane in the range of -70° ~0°.

math-ph↗
arXiv2011

A note on measurement of network vulnerability under random and intentional attacks

In this paper we propose an alternative approach for the assessment of network vulnerability under random and intentional attacks as compared to the results obtained from the "vulnerability function" given by Criado et al. [Criado et al. (Int. J. Comput. Math., 86 (2) (2009), pp. 209-218)]. By using spectral and statistical measurements, we assess robustness as the antonym to vulnerability of complex networks and suggest a tentative ranking for vulnerability, based on the interpretation of quantified network characteristics. We conclude that vulnerability function, derived from the network's degree distribution and its variations only, is not general enough to reflect the lack of robustness due to the specific configurations in graphs with hierarchical or centralized structures. The spectral and statistical metrics, on the other hand, capture different aspects of network topology which provide a more thorough assessment of network vulnerability.

physics.comp-ph↗
arXiv2010

Two-Loop Fermionic Integrals in Perturbation Theory on a Lattice

A comprehensive number of one-loop integrals in a theory with Wilson fermions at $r=1$ is computed using the Burgio-Caracciolo-Pelissetto algorithm. With the use of these results, the fermionic propagator in the coordinate representation is evaluated, thus making it possible to extend the Luscher-Weisz procedure for two-loop integrals to the fermionic case. Computations are performed with FORM and REDUCE packages.

hep-lat↗
arXiv2011

Calculation of free energy landscapes: A Histogram Reweighted Metadynamics approach

We present an efficient method for the calculation of free energy landscapes. Our approach involves a history dependent bias potential which is evaluated on a grid. The corresponding free energy landscape is constructed via a histogram reweighting procedure a posteriori. Due to the presence of the bias potential, it can be also used to accelerate rare events. In addition, the calculated free energy landscape is not restricted to the actual choice of collective variables and can in principle be extended to auxiliary variables of interest without further numerical effort. The applicability is shown for several examples. We present numerical results for the alanine dipeptide and the Met-Enkephalin in explicit solution to illustrate our approach. Furthermore we derive an empirical formula that allows the prediction of the computational cost for the ordinary metadynamics variant in comparison to our approach which is validated by a dimensionless representation.

physics.comp-ph↗
arXiv2011

From efficient symplectic exponentiation of matrices to symplectic integration of high-dimensional Hamiltonian systems with slowly varying quadratic stiff potentials

We present a multiscale integrator for Hamiltonian systems with slowly varying quadratic stiff potentials that uses coarse timesteps (analogous to what the impulse method uses for constant quadratic stiff potentials). This method is based on the highly-non-trivial introduction of two efficient symplectic schemes for exponentiations of matrices that only require O(n) matrix multiplications operations at each coarse time step for a preset small number n. The proposed integrator is shown to be (i) uniformly convergent on positions; (ii) symplectic in both slow and fast variables; (iii) well adapted to high dimensional systems. Our framework also provides a general method for iteratively exponentiating a slowly varying sequence of (possibly high dimensional) matrices in an efficient way.

math.NA↗
arXiv2012

Stretch Processing Using MPM

This paper presents a new approach on stretch processing for a fine range estimation using MPM (Matrix Pencil Method). The conventional method utilizes FFT (Fast Fourier Transform) with limited range resolution with its fixed number of samples. Numerical simulation shows that the new method gives better performance in the accuracy of the range resolution.

physics.comp-ph↗
arXiv2010

Total transmission and total reflection by zero index materials

In this report, we achieved total transmission and reflection in a slab of zero index materials with defect(s). By controlling the defect's radius and dielectric constant, we can obtain total transmission and reflection of EM wave. The zero index materials, in this report, stand for materials with permittivity and permeability which are simultaneously equal to zero or so called matched impedance zero index materials. Along with theoretical calculations and simulation demonstrations, we also discuss about some possible applications for the proposed structure such as shielding or cloaking an object without restricting its view. We also suggest a way to control total transmission and reflection actively by using tunable refractive index materials such as liquid crystal and BST. The physics behind those phenomena is attributed to intrinsic properties of zero index materials: constant field inside zero index slab.

cond-mat.mtrl-sci↗
arXiv2010

Temperature and Friction Accelerated Sampling of Boltzmann-Gibbs Distribution

This paper is concerned with tuning friction and temperature in Langevin dynamics for fast sampling from the canonical ensemble. We show that near-optimal acceleration is achieved by choosing friction so that the local quadratic approximation of the Hamiltonian is a critical damped oscillator. The system is also over-heated and cooled down to its final temperature. The performances of different cooling schedules are analyzed as functions of total simulation time.

physics.comp-ph↗
arXiv2010

Smoothed Particle Hydrodynamics

I present a review of Smoothed Particle Hydrodynamics (SPH), with the aim of providing a mathematically rigorous, clear derivation of the algorithms from first principles. The method of discretising a continuous field into particles using a smoothing kernel is considered, and also the errors associated with this approach. A fully conservative form of SPH is then derived from the Lagrangian, demonstrating the explicit conservation of mass, linear and angular momenta and energy/entropy. The method is then extended to self-consistently include spatially varying smoothing lengths, (self) gravity and various forms of artificial viscosity, required for the correct treatment of shocks. Finally two common methods of time integration are discussed, the Runge-Kutta-Fehlberg and leapfrog integrators, along with an overview of time-stepping criteria.

astro-ph.IM↗
arXiv2010

Some aspects of the Hadamard's ill-posedness in the hydrodynamical problem

Navier-Stokes equations establish the hydrodynamical problem by definition. The importance of these equations is quite natural to understand if we focus on the role they assume in a large spectrum of dynamical problems which involve 'fluids'. Neverthless, they are an undeniable source of pure mathematical problems in PDE's theory. The essential core of their formulation was primarily well structured on the simple concept that the infinitesimal portions of a continuous medium, which flows locally in some manner, must obey in a 'bounded' domain to the same fundamental rules we use to describe the evolution of isolated lagrangian systems, basically momentum and mass conservation laws, so that the consequent architecture of the mathematical implant appears very clear and understandable. Looking to the framework of the numerical solvers, taking in care the richness of their differential structure and the correlated existence of complex dynamics which are mathematically coherent, I try to put in light in the most simple way the fundamental difficulty that arises when we have to impose a reasonable 'initial values problem' in order to simulate numerically well known fluid-dynamical scenarios, trying at the same time to offer a possible method to avoid such an obstacle in determining simulation parameters from which starting in respect of the essential Hadamard's point of view of the Cauchy problem.

math-ph↗
arXiv2010

An Examination of the Time-Centered Difference Scheme for Dissipative Mechanical Systems from a Hamiltonian Perspective

On this paper, we have proposed an approach to observe the time-centered difference scheme for dissipative mechanical systems from a Hamiltonian perspective and to introduce the idea of symplectic algorithm to dissipative systems. The dissipative mechanical systems discussed in this paper are finite dimensional.This approach is based upon a proposition: for any nonconservative classical mechanical system and any initial condition, there exists a conservative one; the two systems share one and only one common phase curve; the Hamiltonian of the conservative system is the sum of the total energy of the nonconservative system on the aforementioned phase curve and a constant depending on the initial condition. Hence, this approach entails substituting an infinite number of conservative systems for a dissipative mechanical system corresponding to varied initial conditions. Therefore, first we utilize the time-centered difference scheme directly to solve the original system, after which we substitute the numerical solution for the analytical solution to construct a conservative force equal to the dissipative force on the phase curve, such that we would obtain a substituting conservative system numerically. Finally, we use the time-centered scheme to integrate the substituting system numerically. We will find an interesting fact that the latter solution resulting from the substituting system is equivalent to that of the former. Indeed, there are two transition matrices within time grid points: the first one is unsymplectic and the second symplectic. In fact, the time-centered scheme for dissipative systems can be thought of as an algorithm that preserves the symplectic structure of the substituting conservative systems. In addition, via numerical examples we find that the time-centered scheme preserves the total energy of dissipative systems.

math-ph↗
arXiv2011

Efficient Dealiased Convolutions without Padding

Algorithms are developed for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, the memory requirements are identical with the zero-padding technique, with the important distinction that the additional work memory need not be contiguous with the input data. This decoupling of data and work arrays dramatically reduces the memory and computation time required to evaluate higher-dimensional in-place convolutions. The technique also allows one to dealias the higher-order convolutions that arise from Fourier transforming cubic and higher powers. Implicitly dealiased convolutions can be built on top of state-of-the-art fast Fourier transform libraries: vectorized multidimensional implementations for the complex and centered Hermitian (pseudospectral) cases have been implemented in the open-source software FFTW++.

cs.CE↗
arXiv2011

Comparing the efficiency of numerical techniques for the integration of variational equations

We present a comparison of different numerical techniques for the integration of variational equations. The methods presented can be applied to any autonomous Hamiltonian system whose kinetic energy is quadratic in the generalized momenta, and whose potential is a function of the generalized positions. We apply the various techniques to the well-known Hénon-Heiles system, and use the Smaller Alignment Index (SALI) method of chaos detection to evaluate the percentage of its chaotic orbits. The accuracy and the speed of the integration schemes in evaluating this percentage are used to investigate the numerical efficiency of the various techniques.

nlin.CD↗
arXiv2011

A method to compute absolute free energies or enthalpies of fluids

We propose a new method to compute the free energy or enthalpy of fluids or disordered solids by computer simulation . The main idea is to construct a reference system by freezing one representative configuration, and then carry out a thermodynamic integration. We present a strategy and an algorithm which allows to sample the thermodynamic integration path even in the case of liquids, despite the fact that the particles can diffuse freely through the system. The method is described in detail and illustrated with applications to hard sphere fluids and solids with mobile defects.

physics.comp-ph↗
arXiv2010

Simulation Factory: Taming Application Configuration and Workflow on High-End Resources

Computational Science on large high performance computing resources is hampered by the complexity of these systems. Much of this complexity is due to low-level details on these resources that are exposed to the application and the end user. This includes (but is not limited to) mechanisms for remote access, configuring and building applications from source code, and managing simulations and their output files via batch queue systems. These challenges multiply in a modern research environment, where a research collaboration spans multiple groups, often in loosely defined international collaborations, where there is a constant influx of new students into multi-year projects, and where simulations are performed on several different resources. The Simulation Factory addresses these challenges by significantly simplifying remote access, building executables, and managing simulations. By abstracting out the low-level differences between different resources, it offers a uniform interface to these resources. At the same time, it can enforce certain standards for performing simulations that encapsulate best practices from experienced users. Furthermore, SimFactory's automation avoids many possible user errors that can in the worst case render month-long simulations worthless.

cs.DC↗
arXiv2011

Complete calculation of evaluated Maxwellian-averaged cross sections and their uncertainties for s-process nucleosynthesis

Present contribution represents a significant improvement of our previous calculation of Maxwellian-averaged cross sections and astrophysical reaction rates. Addition of newly-evaluated neutron reaction libraries, such as ROSFOND and Low-Fidelity Covariance Project, and improvements in data processing techniques allowed us to extend it for entire range of s-process nuclei, calculate Maxwellian-averaged cross section uncertainties for the first time, and provide additional insights on all currently available neutron-induced reaction data. Nuclear reaction calculations using ENDF libraries and current Java technologies will be discussed and new results will be presented.

astro-ph.SR↗