Numerical resolution of the modified Langevin equation using a differential expression: Application to the Jiles magnetostriction law of approach

The Langevin equation is classically used to model the anhysteretic magnetization curve. A modified version of this equation has been introduced by Jiles to take into account the effects of magnetostriction on the anhysteretic magnetization behavior when a ferromagnetic material undergoes mechanical stresses. The numerical resolution of the modified Langevin equation is usually performed with a root-finding algorithm. In this paper, a differential form of the modified Langevin equation is proposed, allowing a faster numerical resolution.     

Nonlinearity management and diffraction management for the stabilization of two-dimensional spatial solitons

The nonlinear Schrödinger equation which governs the dynamics of two-dimensional spatial solitons in Kerr media with periodically varying diffraction and nonlinearity has been analyzed in this paper using variational approach and numerical studies. Analytical expressions for soliton parameters have been derived using variational analysis. Variational equations and partial differential equation have been simulated numerically. Analytical and numerical studies have shown that nonlinearity management and diffraction management stabilize the pulse against decay or collapse providing undisturbed propagation even for larger energies of the incident beam.     

A nonextensive approach to the dynamics of financial observables

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy . More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices q in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation q_stat+q_sens=2 is numerically satisfied, q_stat and q_sens being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems.     

Clusters in weighted macroeconomic networks: the EU case. Introducing the overlapping index of GDP/capita fluctuation correlations

GDP/capita correlations are investigated in various time windows (TW), for the time interval 1990–2005. The target group of countries is the set of 25 EU members, 15 till 2004 plus the 10 countries which joined EU later on. The TW-means of the statistical correlation coefficients are taken as the weights (links) of a fully connected network having the countries as nodes. Thereafter we define and introduce the overlapping index of weighted network nodes. A cluster structure of EU countries is derived from the statistically relevant eigenvalues and eigenvectors of the adjacency matrix. This may be considered to yield some information about the structure, stability and evolution of the EU country clusters in a macroeconomic sense.     

Soliton switching and propagation in two-core nonlinear fiber coupler with high order coupling coefficient

We use the variational approach (VA) and the split-step Fourier transforms (SSFT) to study the transmission and switching characteristics inside the fiber nonlinear directional coupler (NDLC). The results, based on the VA, indicate that the second-order coupling coefficient dispersion and initiative chirp all reduce the coupling length, and the second-order coupling coefficient dispersion makes the switching characteristics become sharper and threshold power become bigger under the case of not having initiative chirp. The outcomes, based on the SSFT, indicate that the first order intermodal dispersion coefficient make optical pulses splitting in the propagation of fundamental solitons, and the second-order coupling coefficient dispersion reduces the coupling length, sharpens the switching characteristics and increases the switching threshold power, the results agrees well with those from the VA.     

一种基于不同风险偏好投资多目标决策模型及解法

建立了风险投资的多目标决策模型，分别采用线性加权法、TOPSIS法和密切值法，对不同风险偏好下备选方案进行排序，再用平均值法对上述排序进行综合排序，从而避免单一方法的片面性，较为全面科学地得出最优方案。最后，用一个算例说明了方法的可行性和有效性。     

Small scale behavior of financial data

A new approach is presented to describe the change in the statistics of the log return distribution of financial data as a function of the timescale. To this purpose a measure is introduced, which quantifies the distance of a considered distribution to a reference distribution. The existence of a small timescale regime is demonstrated, which exhibits different properties compared to the normal timescale regime for timescales larger than one minute. This regime seems to be universal for individual stocks. It is shown that the existence of this small timescale regime is not dependent on the special choice of the distance measure or the reference distribution. These findings have important implications for risk analysis, in particular for the probability of extreme events.     

Multiple mobility edges in a 1D Aubry chain with Hubbard interaction in presence of electric field: Controlled electron transport

Electronic behavior of a 1D Aubry chain with Hubbard interaction is critically analyzed in presence of electric field. Multiple energy bands are generated as a result of Hubbard correlation and Aubry potential, and, within these bands localized states are developed under the application of electric field. Within a tight-binding framework we compute electronic transmission probability and average density of states using Green's function approach where the interaction parameter is treated under Hartree–Fock mean field scheme. From our analysis we find that selective transmission can be obtained by tuning injecting electron energy, and thus, the present model can be utilized as a controlled switching device.     

Non-local separable solutions of two interacting particles in a harmonic trap

We calculate the energy levels of two particles trapped in a harmonic potential. The actual two-body potential, assumed to be spherically symmetric, is replaced by a projective operator (non-local separable potential) to determine the energy levels in a closed form. This approach overcomes the limitations of the regularized Fermi pseudopotential when the characteristic length of the two-body interaction potential is of the order of the size of the harmonic trap. In addition, we recover the results obtained with the Fermi pseudopotential when the length of the interaction is much smaller than the size of the trap.