Collective phase synchronization in locally-coupled limit-cycle oscillators

We study collective behavior of locally-coupled limit-cycle oscillators with scattered intrinsic frequencies on $d$-dimensional lattices. A linear analysis shows that the system should be always desynchronized up to $d=4$. On the other hand, numerical investigation for $d= 5$ and 6 reveals the emergence of the synchronized (ordered) phase via a continuous transition from the fully random desynchronized phase. This demonstrates that the lower critical dimension for the phase synchronization in this system is $d_{l}=4

Some new efficient multipoint iterative methods for solving nonlinear systems of equations

It is attempted to put forward a new multipoint iterative method of sixth-order convergence for approximating solutions of nonlinear systems of equations. It requires the evaluation of two vector-function and two Jacobian matrices per iteration. Furthermore, we use it as a predictor to derive a general multipoint method. Convergence error analysis, estimating computational complexity, numerical implementation and comparisons are given to verify applicability and validity for the proposed methods.This research was supported by Islamic Azad University - Hamedan Branch, Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and Universitat Politecnica de Valencia SP20120474.Lotfi, T.; Bakhtiari, P.; Cordero Barbero, A.; Mahdiani, K.; Torregrosa Sánchez, JR. (2015). Some new efficient multipoint iterative methods for solving nonlinear systems of equations. International Journal of Computer Mathematics. 92(9):1921-1934. https://doi.org/10.1080/00207160.2014.946412S1921193492

Apparent-Strain Correction for Combined Thermal and Mechanical Testing

Combined thermal and mechanical testing requires that the total strain be corrected for the coefficient of thermal expansion mismatch between the strain gage and the specimen or apparent strain when the temperature varies while a mechanical load is being applied. Collecting data for an apparent strain test becomes problematic as the specimen size increases. If the test specimen cannot be placed in a variable temperature test chamber to generate apparent strain data with no mechanical loads, coupons can be used to generate the required data. The coupons, however, must have the same strain gage type, coefficient of thermal expansion, and constraints as the specimen to be useful. Obtaining apparent-strain data at temperatures lower than -320 F is challenging due to the difficulty to maintain steady-state and uniform temperatures on a given specimen. Equations to correct for apparent strain in a real-time fashion and data from apparent-strain tests for composite and metallic specimens over a temperature range from -450 F to +250 F are presented in this paper. Three approaches to extrapolate apparent-strain data from -320 F to -430 F are presented and compared to the measured apparent-strain data. The first two approaches use a subset of the apparent-strain curves between -320 F and 100 F to extrapolate to -430 F, while the third approach extrapolates the apparent-strain curve over the temperature range of -320 F to +250 F to -430 F. The first two approaches are superior to the third approach but the use of either of the first two approaches is contingent upon the degree of non-linearity of the apparent-strain curve

On the gravitational, dilatonic and axionic radiative damping of cosmic strings

We study the radiation reaction on cosmic strings due to the emission of dilatonic, gravitational and axionic waves. After verifying the (on average) conservative nature of the time-symmetric self-interactions, we concentrate on the finite radiation damping force associated with the half-retarded minus half-advanced ``reactive'' fields. We revisit a recent proposal of using a ``local back reaction approximation'' for the reactive fields. Using dimensional continuation as convenient technical tool, we find, contrary to previous claims, that this proposal leads to antidamping in the case of the axionic field, and to zero (integrated) damping in the case of the gravitational field. One gets normal positive damping only in the case of the dilatonic field. We propose to use a suitably modified version of the local dilatonic radiation reaction as a substitute for the exact (non-local) gravitational radiation reaction. The incorporation of such a local approximation to gravitational radiation reaction should allow one to complete, in a computationally non-intensive way, string network simulations and to give better estimates of the amount and spectrum of gravitational radiation emitted by a cosmologically evolving network of massive strings.Comment: 48 pages, RevTex, epsfig, 1 figure; clarification of the domain of validity of the perturbative derivation of the string equations of motion, and of their renormalizabilit

Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation

Nonperturbative aspects of the quark-photon vertex

The electromagnetic interaction with quarks is investigated through a relativistic, electromagnetic gauge-invariant treatment. Gluon dressing of the quark-photon vertex and the quark self-energy functions is described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger-Dyson equation in the rainbow approximation respectively. Results for the calculation of the quark-photon vertex are presented in both the time-like and space-like regions of photon momentum squared, however emphasis is placed on the space-like region relevant to electron scattering. The treatment presented here simultaneously addresses the role of dynamically generated $q\bar{q}$ vector bound states and the approach to asymptotic behavior. The resulting description is therefore applicable over the entire range of momentum transfers available in electron scattering experiments. Input parameters are limited to the model gluon two-point function, which is chosen to reflect confinement and asymptotic freedom, and are largely constrained by the obtained bound-state spectrum.Comment: 8 figures available on request by email, 25 pages, Revtex, DOE/ER/40561-131-INT94-00-5

Masses of light tetraquarks and scalar mesons in the relativistic quark model

Masses of the ground state light tetraquarks are dynamically calculated in the framework of the relativistic diquark-antidiquark picture. The internal structure of the diquark is taken into account by calculating the form factor of the diquark-gluon interaction in terms of the overlap integral of the diquark wave functions. It is found that scalar mesons with masses below 1 GeV: f_0(600) (\sigma), K^*_0(800) (\kappa), f_0(980) and a_0(980) agree well with the light tetraquark interpretation.Comment: 9 pages, Report-no adde

Axion Radiation from Strings

This paper revisits the problem of the string decay contribution to the axion cosmological energy density. We show that this contribution is proportional to the average relative increase when axion strings decay of a certain quantity $N_{\rm ax}$ which we define. We carry out numerical simulations of the evolution and decay of circular and non-circular string loops, of bent strings with ends held fixed, and of vortex-antivortex pairs in two dimensions. In the case of string loops and of vortex-antivortex pairs, $N_{\rm ax}$ decreases by approximately 20%. In the case of bent strings, $N_{\rm ax}$ remains constant or increases slightly. Our results imply that the string decay contribution to the axion energy density is of the same order of magnitude as the well-understood contribution from vacuum realignment.Comment: 29 pages, 10 figure

The velocity potential and the interacting force for two spheres moving perpendicularly to the line joining their centers

The velocity potential around two spheres moving perpendicularly to the line joining their centers is given by a series of spherical harmonics. The appropriateness of the truncation is evaluated by determining the residual normal surface velocity on the spheres. In evaluating the residual normal velocity, a recursive procedure is constructed to evaluate the spherical harmonics to reduce computational effort and truncation error as compared to direct transformation or numerical integration. We estimate the lift force coefficient for touching spheres to be 0.577771, compared to the most accurate earlier estimate of 0.51435 by Miloh (1977).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42701/1/10665_2004_Article_BF00127479.pd