743 research outputs found
A statistical physics perspective on criticality in financial markets
Stock markets are complex systems exhibiting collective phenomena and
particular features such as synchronization, fluctuations distributed as
power-laws, non-random structures and similarity to neural networks. Such
specific properties suggest that markets operate at a very special point.
Financial markets are believed to be critical by analogy to physical systems
but few statistically founded evidence have been given. Through a data-based
methodology and comparison to simulations inspired by statistical physics of
complex systems, we show that the Dow Jones and indices sets are not rigorously
critical. However, financial systems are closer to the criticality in the crash
neighborhood.Comment: 23 pages, 19 figure
Modeling and control of complex dynamic systems: Applied mathematical aspects
The concept of complex dynamic systems arises in many varieties, including the areas of energy generation, storage and distribution, ecosystems, gene regulation and health delivery, safety and security systems, telecommunications, transportation networks, and the rapidly emerging research topics seeking to understand and analyse. Such systems are often concurrent and distributed, because they have to react to various kinds of events, signals, and conditions. They may be characterized by a system with uncertainties, time delays, stochastic perturbations, hybrid dynamics, distributed dynamics, chaotic dynamics, and a large number of algebraic loops. This special issue provides a platform for researchers to report their recent results on various mathematical methods and techniques for modelling and control of complex dynamic systems and identifying critical issues and challenges for future investigation in this field. This special issue amazingly attracted one-hundred-and eighteen submissions, and twenty-eight of them are selected through a rigorous review procedure
Asymptotic Representations for Root Vectors of Nonselfadjoint Operators and Pencils Generated by an Aircraft Wing Model in Subsonic Air Flow
AbstractThis paper is the second in a series of several works devoted to the asymptotic and spectral analysis of an aircraft wing in a subsonic air flow. This model has been developed in the Flight Systems Research Center of UCLA and is presented in the works by A. V. Balakrishnan. The model is governed by a system of two coupled integrodifferential equations and a two parameter family of boundary conditions modeling the action of the self-straining actuators. The differential parts of the above equations form a coupled linear hyperbolic system; the integral parts are of the convolution type. The system of equations of motion is equivalent to a single operator evolution-convolution equation in the energy space. The Laplace transform of the solution of this equation can be represented in terms of the so-called generalized resolvent operator, which is an operator-valued function of the spectral parameter. This generalized resolvent operator is a finite-meromorphic function on the complex plane having the branch cut along the negative real semi-axis. Its poles are precisely the aeroelastic modes and the residues at these poles are the projectors on the generalized eigenspaces. In the first paper and in the present one, our main object of interest is the dynamics generator of the differential parts of the system. It is a nonselfadjoint operator in the energy space with a purely discrete spectrum. In the first paper, we have shown that the spectrum consists of two branches and have derived their precise spectral asymptotics. In the present paper, we derive the asymptotical approximations for the mode shapes. Based on the asymptotical results of these first two papers, in the next paper, we will discuss the geometric properties of the mode shapes such as minimality, completeness, and the Riesz basis property in the energy space
Robust Stability Analysis for Uncertain Switched Discrete-Time Systems
This paper is concerned with the robust stability for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes
Surface properties of fluids of charged platelike colloids
Surface properties of mixtures of charged platelike colloids and salt in
contact with a charged planar wall are studied within density functional
theory. The particles are modeled by hard cuboids with their edges constrained
to be parallel to the Cartesian axes corresponding to the Zwanzig model and the
charges of the particles are concentrated in their centers. The density
functional applied is an extension of a recently introduced functional for
charged platelike colloids. Analytically and numerically calculated bulk and
surface phase diagrams exhibit first-order wetting for sufficiently small
macroion charges and isotropic bulk order as well as first-order drying for
sufficiently large macroion charges and nematic bulk order. The asymptotic
wetting and drying behavior is investigated by means of effective interface
potentials which turn out to be asymptotically the same as for a suitable
neutral system governed by isotropic nonretarded dispersion forces. Wetting and
drying points as well as predrying lines and the corresponding critical points
have been located numerically. A crossover from monotonic to non-monotonic
electrostatic potential profiles upon varying the surface charge density has
been observed. Due to the presence of both the Coulomb interactions and the
hard-core repulsions, the surface potential and the surface charge do not
vanish simultaneously, i.e., the point of zero charge and the isoelectric point
of the surface do not coincide.Comment: 14 pages, submitte
Stability and stabilization of fractional order time delay systems
U ovom radu predstavljeni su neki osnovni rezultati koji se odnose na kriterijume stabilnosti sistema necelobrojnog reda sa kaÅ”njenjem kao i za sisteme necelobrojnog reda bez kaÅ”njenja.TakoÄe, dobijeni su i predstavljeni dovoljni uslovi za konaÄnom vremenskom stabilnost i stabilizacija za (ne)linearne (ne)homogene kao i za perturbovane sisteme necelobrojnog reda sa vremenskim kaÅ”njenjem. Nekoliko kriterijuma stabilnosti za ovu klasu sistema necelobrojnog reda je predloženo koriÅ”Äenjem nedavno dobijene generalizovane Gronval nejednakosti, kao i 'klasiÄne' Belman-Gronval nejednakosti. Neki zakljuÄci koji se odnose na stabilnost sistema necelobrojnog reda su sliÄni onima koji se odnose na klasiÄne sisteme celobrojnog reda. Na kraju, numeriÄki primer je dat u cilju ilustracije znaÄaja predloženog postupka.In this paper, some basic results of the stability criteria of fractional order system with time delay as well as free delay are presented. Also, we obtained and presented sufficient conditions for finite time stability and stabilization for (non)linear (non)homogeneous as well as perturbed fractional order time delay systems. Several stability criteria for this class of fractional order systems are proposed using a recently suggested generalized Gronwall inequality as well as 'classical' Bellman-Gronwall inequality. Some conclusions for stability are similar to those of classical integerorder differential equations. Finally, a numerical example is given to illustrate the validity of the proposed procedure
- ā¦