Open dynamic behaviour of financial markets

Open dynamic behaviour of financial markets with internal interactions between agents and with external “fields” from other systems are investigated using the approach of Grossman and Stiglitz for inefficient markets, and Keynes for interference of the market using physics of finance (referred to hereafter as phynance). The simulation results indicate that the NYSE data analyzed in Plerou, V. et al., Nature 421, 130 (2003) can be fitted by an equation of order parameter Φ and local deviation R of type: -(R+0.03) Φ+ 0.6 Φ³ + 0.02 = 0, which is shown to be in remarkable agreement with Plerou's data.     

Second-order numerical method for domain optimization problems

This paper is concerned with a second-order numerical method for shape optimization problems. The first variation and the second variation of the objective functional are derived. These variations are discretized by introducing a set of boundary-value problems in order to derive the second-order numerical method. The boundary-value problems are solved by the conventional finite-element method.The authors would like to express their thanks to Mr. T. Masanao, who was an undergraduate student, for his cooperation and comments. They also thank Professor Y. Sakawa of Osaka University for his encouragement.A part of this paper was presented at the IFIP Conference on Control of Boundaries and Stabilization, Clermont-Ferrand, France, 1988.     

Complexity of Body Movements during Sleep in Children with Autism Spectrum Disorder

Recently, measuring the complexity of body movements during sleep has been proven as an objective biomarker of various psychiatric disorders. Although sleep problems are common in children with autism spectrum disorder (ASD) and might exacerbate ASD symptoms, their objectivity as a biomarker remains to be established. Therefore, details of body movement complexity during sleep as estimated by actigraphy were investigated in typically developing (TD) children and in children with ASD. Several complexity analyses were applied to raw and thresholded data of actigraphy from 17 TD children and 17 children with ASD. Determinism, irregularity and unpredictability, and long-range temporal correlation were examined respectively using the false nearest neighbor (FNN) algorithm, information-theoretic analyses, and detrended fluctuation analysis (DFA). Although the FNN algorithm did not reveal determinism in body movements, surrogate analyses identified the influence of nonlinear processes on the irregularity and long-range temporal correlation of body movements. Additionally, the irregularity and unpredictability of body movements measured by expanded sample entropy were significantly lower in ASD than in TD children up to two hours after sleep onset and at approximately six hours after sleep onset. This difference was found especially for the high-irregularity period. Through this study, we characterized details of the complexity of body movements during sleep and demonstrated the group difference of body movement complexity across TD children and children with ASD. Complexity analyses of body movements during sleep have provided valuable insights into sleep profiles. Body movement complexity might be useful as a biomarker for ASD.     

DLPNO‐CCSD(T) scaled methods for the accurate treatment of large supramolecular complexes

In this work, we present scaled variants of the DLPNO‐CCSD(T) method, dubbed as (LS)DLPNO‐CCSD(T) and (NS)DLPNO‐CCSD(T), to obtain accurate interaction energies in supramolecular complexes governed by noncovalent interactions. The novel scaled schemes are based on the linear combination of the DLPNO‐CCSD(T) correlation energies calculated with the standard (LoosePNO and NormalPNO) and modified (Loose2PNO and Normal2PNO) DLPNO‐CCSD(T) accuracy levels. The scaled DLPNO‐CCSD(T) variants provide nearly TightPNO accuracy, which is essential for the quantification of weak noncovalent interactions, with a noticeable saving in computational cost. Importantly, the accuracy of the proposed schemes is preserved irrespective of the nature and strength of the supramolecular interaction. The (LS)DLPNO‐CCSD(T) and (NS)DLPNO‐CCSD(T) protocols have been used to study in depth the role of the CH–π versus π–π interactions in the supramolecular complex formed by the electron‐donor truxene‐tetrathiafulvalene (truxTTF) and the electron‐acceptor hemifullerene (C₃₀H₁₂). (NS)DLPNO‐CCSD(T)/CBS calculations clearly reveal the higher stability of staggered (dominated by CH–π interactions) versus bowl‐in‐bowl (dominated by π–π interactions) arrangements in the truxTTF•C₃₀H₁₂ heterodimer. Hemifullerene and similar carbon‐based buckybowls are therefore expected to self‐assemble with donor compounds in a richer way other than the typical concave–convex π–π arrangement found in fullerene‐based aggregates. © 2017 Wiley Periodicals, Inc.     

Unidimensional SPH simulations of reactive shock tubes in an astrophysical perspective

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method widely used for the modelling of a large variety of astrophysical fluid flows in more than one dimension. Simulations of thermonuclear explosions in stars require, besides the hydrodynamic equations, a realistic equation of state, an energy source term, and a set of nuclear kinetic equations to follow the composition changes of the gas during the explosion. The implementation of a realistic stellar equation of state, and the coupling of hydrodynamics and nuclear burning are investigated in the framework of the simple shock tube geometry. We present and discuss the results of a series of SPH simulations of a detonation in the presence of (1) a single exothermic nuclear reaction, and (2) a restricted network of nuclear reactions. Our results are compared to those of identical simulations performed by other authors using a different hydrodynamic method.     

Resolving Controversies in the Application of the Method of Multiple Scales and the Generalized Method of Averaging

I compare application of the method of multiple scales with reconstitution and the generalized method of averaging for determining higher-order approximations of three single-degree-of-freedom systems and a two-degree-of-freedom system. Three implementations of the method of multiple scales are considered, namely, application of the method to the system equations expressed as second-order equations, as first-order equations, and in complex-variable form. I show that all of these methods produce the same modulation equations.I address the problem of determining higher-order approximate solutions of the Duffing equation in the case of primary resonance. I show that the conclusions of Rahman and Burton that the method of multiple scales, the generalized method of averaging, and Lie series and transforms might lead to incorrect results, in that spurious solutions occur and the obtained frequency–response curves bear little resemblance to the actual response, is the result of their using parameter values for which the neglected terms are the same order as the retained terms. I show also that spurious solutions cannot be avoided, in general, in any consistent expansion and their presence does not constitute a limitation of the methods. In particular, I show that, for the Duffing equation, the second-order frequency–response equation does not possess spurious solutions for the case of hardening nonlinearity, but possesses spurious solutions for the case of softening nonlinearity. For sufficiently small nonlinearity, the spurious solutions are far removed from the actual response. But as the strength of the nonlinearity increases, these solutions move closer to the backbone and eventually distort it. This is not a drawback of the perturbation methods but an indication of an application of the analysis for parameter values outside the range of validity of the expansion.Also, I address the problem of obtaining non-Hamiltonian modulation equations in the application of the method of multiple scales to multi-degree-of-freedom Hamiltonian systems written as second-order equations in time and how this problem can be overcome by attacking the state-space form of the governing equations. Moreover, I show that application of a variation of the method of Rahman and Burton to multi-degree-of-freedom systems leads to results that do not agree with those obtained with the generalized method of averaging.Contributed by Prof. R.A. Ibrahim.     

Spectral methods for compressible reactive flows

High order simulations are necessary in order to capture fine details in resolving supersonic reactive flows. However, high Mach number compressible flows feature sharp gradients and discontinuities, which present a challenge to successful simulations using high order methods. Spectral methods have proven a powerful tool in simulation of incompressible turbulent flows, and recent advances allow the application of spectral methods to compressible reactive flows. We review the recent advances in the theory and application of spectral methods which allow stable computations of discontinuous phenomena, and the recovery of high order information via postprocessing, and present applications of high Mach number reactive flows. To cite this article: D. Gottlieb, S. Gottlieb, C. R. Mecanique 333 (2005).     

Linear Dynamical Identification: An Integral Transform seen as a Complex Wavelet Transform

This paper presents a technique that allows the direct linearidentification of frequency response functions from the computation ofa weighted integral transform. This transform allows toemphasize the influence of the poles and zeros of the frequencyresponse functions its formation is based on the Cauchy--Weierstrass theorem. It isthen shown that this transform is directly linked to a complex wavelettransform. This representation with a wavelet transform provides abetter understanding of the amplification effects of the weightedintegral transform and allows the singularities analysis.     

The mutual variational principle of free wave propagation in periodic structures

By taking infinite periodic beams as examples, the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propagation constant in the present paper, and the corresponding hierarchical finite element formulation is then derived. Thus, it provides the numerical analysis of that problem with a firm theoretical basis of variational principles, with which one may conveniently illustrate the mathematical and physical mechanisms of the wave propagation in periodic structures and the relationship with the natural vibration. The solution is discussed and examples are given. Supported by Doctorate Training Fund of National Education Commission of China     

Fundamental and subharmonic resonances in a system with a ‘1-1’ internal resonance

The fundamental and subharmonic resonances of a two degree-of-freedom oscillator with cubic stiffness nonlinearities and linear viscous damping are examined using a multiple-seales averaging analysis. The system is in a 1–1 internal resonance, i.e., it has two equal linearized eigenfrequencies, and it possesses nonlinear normal modes. For weak coupling stiffnesses the internal resonance gives rise to a Hamiltonian Pitchfork bifurcation of normal modes which in turn affects the topology of the fundamental and subharmonic resonance curves. It is shown that the number of resonance branches differs before and after the mode bifurcation, and that jump phenomena are possible between forced modes. Some of the steady state solutions were found to be very sensitive to damping: a whole branch of fundamental resonances was eliminated even for small amounts of viscous damping, and subharmonic steady state solutions were shifted by damping to higher frequencies. The analytical results are verified by a numerical integration of the equations of motion, and a discussion of the effects of the mode bifurcation on the dynamics of the system is given.