Simulation of ion behavior in an open three-dimensional Paul trap using a power series method

Simulations of the dynamics of ions trapped in a Paul trap with terms in the potential up to the order 10 have been carried out. The power series method is used to solve numerically the equations of motion of the ions. The stability diagram has been studied and the buffer gas cooling has been implemented by a Monte Carlo method. The dipole excitation was also included. The method has been applied to an existing trap and it has shown good agreement with the experimental results and previous simulations using other methods

The foam drainage equation with time- and space-fractional derivatives solved by the Adomian method

In this paper, by introducing the fractional derivative in the sense of Caputo, we apply the Adomian decomposition method for the foam drainage equation with time- and space-fractional derivative. As a result, numerical solutions are obtained in a form of rapidly convergent series with easily computable components

The Einstein-Maxwell-Particle System in the York Canonical Basis of ADM Tetrad Gravity: III) The Post-Minkowskian N-Body Problem, its Post-Newtonian Limit in Non-Harmonic 3-Orthogonal Gauges and Dark Matter as an Inertial Effect

We conclude the study of the Post-Minkowskian linearization of ADM tetrad gravity in the York canonical basis for asymptotically Minkowskian space-times in the family of non-harmonic 3-orthogonal gauges parametrized by the York time ${}^3K(\tau, \vec \sigma)$ (the inertial gauge variable, not existing in Newton gravity, describing the general relativistic remnant of the freedom in clock synchronization in the definition of the instantaneous 3-spaces). As matter we consider only N scalar point particles with a Grassmann regularization of the self-energies and with a ultraviolet cutoff making possible the PM linearization and the evaluation of the PM solution for the gravitational field. We study in detail all the properties of these PM space-times emphasizing their dependence on the gauge variable ${}^3{\cal K}_{(1)} = {1\over {\triangle}}\, {}^3K_{(1)}$ (the non-local York time): Riemann and Weyl tensors, 3-spaces, time-like and null geodesics, red-shift and luminosity distance. Then we study the Post-Newtonian (PN) expansion of the PM equations of motion of the particles. We find that in the two-body case at the 0.5PN order there is a damping (or anti-damping) term depending only on ${}^3{\cal K}_{(1)}$. This open the possibility to explain dark matter in Einstein theory as a relativistic inertial effect: the determination of ${}^3{\cal K}_{(1)}$ from the masses and rotation curves of galaxies would give information on how to find a PM extension of the existing PN Celestial frame (ICRS) used as observational convention in the 4-dimensional description of stars and galaxies. Dark matter would describe the difference between the inertial and gravitational masses seen in the non-Euclidean 3-spaces, without a violation of their equality in the 4-dimensional space-time as required by the equivalence principle.Comment: 86 pages. Deep revision of the second part of the paper with the addition of the center-of-mass problem in GR, with a refined treatment of the PostNewtonian expansion and with the explaination of dark matter as a relativistic inertial effect not only in the rotation curves of galaxies but also in the mass of galaxy clusters determined with the virial theorem and gravitational lensin

A mechanistic model for hydraulic behaviour and nitrogen dynamics in a vertical flow constructed wetland treating septage

A mechanistic model has been developed to simulate the hydraulic behaviour and nitrogen dynamics of a vertical flow constructed wetland treating septage. The proposed model, VF_Sep, consists of a hydraulic module, transport module and a bio-kinetics module. VF_Sep successfully predicted the effluent flux and the associated concentration of ammonium and nitrate. The simulated results indicated that nitrification and adsorption were the major removal mechanisms of ammonium, which were greatly affected by the hydraulic behaviour

Radiative Backreaction on Global Strings

We consider radiative backreaction for global strings using the Kalb-Ramond formalism. In analogy to the point electron in classical electrodynamics, we show how local radiative corrections to the equations of motion allow one to remove the divergence in the self field and calculate a first order approximation to the radiation backreaction force. The effects of this backreaction force are studied numerically by resubstituting the equations of motion to suppress exponentially growing solutions. By direct comparison with numerical field theory simulations and analytic radiation calculations we establish that the `local backreaction approximation' provides a satisfactory quantitative description of radiative damping for a wide variety of string configurations. Finally, we discuss the relevance of this work to the evolution of a network of global strings and their possible cosmological consequences. These methods can also be applied to describe the effects of gravitational radiation backreaction on local strings, electromagnetic radiation backreaction on superconducting strings and other forms of string radiative backreaction.Comment: 38 Pages, Plain TEX, to appear Phys. Rev. D. Figures not included. Hard copy available by email to [email protected]

Electromagnetic Wave Propagation Modeling for Finding Antenna Specifications and Positions in Tunnels of Arbitrary Cross-Section

This chapter is organized as follows : Section II introduces the modal approach for guiding structures. It is based on a full-wave method, namely the Transmission Line Matrix (TLM) method. These methods has been hampered by their large computational time when compared to asymptotic methods when large size environments are considered. Thus, a suitable 2.5 D TLM implementation to reduce the computational time and to include lossy dielectric walls of tunnels is briefly presented [2]. The computation cost is reduced compared to typical solutions by using the concept of Surface Impedance Boundary Condition (SIBC). Section III is devoted to the description of a methodology for the determination of antenna field specifications and positioning in operational scenarios at high frequencies. Section IV presents the validation of this methodology for a simple canonical case. Lastly, section V describes the analysis and results for a real scenario representative of tunnel environments. Finally, discussions and conclusions are developed

Electromagnetic model subdivision and iterative solvers for surface and volume double higher order numerical methods and applications

2019 Fall.Includes bibliographical references.Higher order methods have been established in the numerical analysis of electromagnetic structures decreasing the number of unknowns compared to the low order discretization. In order to decrease memory requirements even further, model subdivision in the computational analysis of electrically large structures has been used. The technique is based on clustering elements and solving/approximating subsystems separately, and it is often implemented in conjunction with iterative solvers. This thesis addresses unique theoretical and implementation details specific to model subdivision of the structures discretized by the Double Higher Order (DHO) elements analyzed by i) Finite Element Method - Mode Matching (FEM-MM) technique for closed-region (waveguide) structures and ii) Surface Integral Equation Method of Moments (SIE-MoM) in combination with (Multi-Level) Fast Multipole Method for open-region bodies. Besides standard application in decreasing the model size, DHO FEM-MM is applied to modeling communication system in tunnels by means of Standard Impedance Boundary Condition (SIBC), and excellent agreement is achieved with measurements performed in Massif Central tunnel. To increase accuracy of the SIE-MoM computation, novel method for numerical evaluation of the 2-D surface integrals in MoM matrix entries has been improved to achieve better accuracy than traditional method. To demonstrate its efficiency and practicality, SIE-MoM technique is applied to analysis of the rain event containing significant percentage of the oscillating drops recorded by 2D video disdrometer. An excellent agreement with previously-obtained radar measurements has been established providing the benefits of accurately modeling precipitation particles

On transformation to the singularly perturbed system

A rapid progress in hard- and software development of computational facilities as well as in numerical methods has increased the role of numerical simulations in the quantitative system analysis of many engineering problems. At the same time, the system complexity (in terms of dimensionality and non-linearity) has grown considerably increasing demand for automatic methods of analysis of qualitative system behavior. For instance, nowadays, definition of key system parameters controlling the system dynamics and finding critical regimes automatically have become crucial issue of numerical system analysis. In the present paper a transformation to the Singularly Perturbed System (SPS) as a main theoretical framework to cope with the complexity and high dimensionality will be discussed in detail. Both simple but famous and meaningful model example of Van der Pol oscillator and an example of application to numerical analysis of chemical kinetics mechanisms will be used to show the potential of the suggested framework

Legendre Wavelets Method for Solving Fractional Population Growth Model in a Closed System

A new operational matrix of fractional order integration for Legendre wavelets is derived. Block pulse functions and collocation method are employed to derive a general procedure for forming this matrix. Moreover, a computational method based on wavelet expansion together with this operational matrix is proposed to obtain approximate solution of the fractional population growth model of a species within a closed system. The main characteristic of the new approach is to convert the problem under study to a nonlinear algebraic equation