Mechanisms behind the generalized synchronization conditions

A universal mechanism underlying generalized synchronization conditions in unidirectionally coupled stochastic oscillators is considered. The consideration is carried out in the framework of a modified system with additional dissipation. The approach developed is illustrated with model examples. The conclusion is reached that two types of the behavior of nonlinear dynamic systems known as generalized synchronization and noise-induced synchronization, which are viewed as different phenomena, actually represent a unique type of the synchronous behavior of stochastic oscillators and are caused by the same mechanism.     

混沌同步的充分条件及应用

对两大类常用连续混沌系统，给出了同步的充分条件，以及状态变量的演化范围，对其作了证明，从理论上分析了这些充分条件一定可实现. 作为应用，证明了时变参数混沌同步的实现充分条件，并用Chua系统仿真实现. 时变参数混沌同步通信具有强抗破译性，也给出其抗破译的仿真. 关键词： 条件Lyapunov指数(CLE) Chua电路 参数同步     

Structural instability in fluid-structure systems under hydrodynamic shock conditions

The effects of non-linear fluid-structure interaction on the dynamic buckling of structures are investigated. In particular the structural buckling characteristics are studied for the case of a strong shock wave propagating through a fluid medium striking a structure. Non-linear terms are retained for both fluid and structural systems. A one-dimensional example consisting of a perfect gas-spring-mass system is solved for shock wave loading. Solutions are obtained by using the finite element method. The numerical methods utilized appear to be applicable to complex multi-dimensional systems. It is shown that in a non-linear fluid-structure interaction problem the incident pressure may be amplified significantly during reflection from a structure. Thus, an acoustic fluid model may be non-conservative for strong shock problems. Structures in a fluid will buckle at an incident pressure level which is much less than that which causes buckling in a vacuum.     

Penetration of long strikers under hydrodynamic conditions with allowance for the material compressibility

The influence of compressibility on the fast penetration of long metallic strikers into different barriers at interaction speeds of up to 10 km/s is investigated. The investigation is based on the hydrodynamic theory of penetration. Compressibility-related corrections to Lavrent’ev’s rate and depth of penetration, which were obtained in terms of the concept representing the penetration process as collisions of ideal incompressible liquid jets, are estimated. The variation of these corrections with the interaction speed under subsonic and supersonic conditions is analyzed. If the compressibilities of the striker and barrier materials differ radically, the penetration depth disagrees with that predicted by the hydrodynamic theory (assuming the incompressibility of the materials) by 10–15%.     

Femtoscopy within a hydrodynamic approach based on flux tube initial conditions

In pp scattering at LHC energies, large numbers of elementary scatterings will contribute significantly, and the corresponding high multiplicity events will be of particular interest. Elementary scatterings are parton ladders, identified with color flux tubes. In high multiplicity events, many of these flux tubes are produced in the same space region, creating high energy densities. We argue that there is good reason to employ the successful procedure used for heavy ion collisions: matter is assumed to thermalize quickly, so that the energy from the flux tubes can be taken as initial condition for a hydro-dynamic expansion. This scenario gets spectacular support from very recent results on Bose-Einstein correlations in pp scattering at 900 GeV at the LHC.     

Towards a generalization of hydrodynamic boundary conditions for flows of fluids with homogeneous internally rotating structures

A generalized boundary condition in the Stokes regime is developed for modeling wall bounded flows of fluids with homogeneous internally rotating structures. The governing equations are solved to obtain a universal scaling behavior of the micro-rotation boundary condition at the walls. These observations are supported by molecular dynamics simulation predictions.     

On Spin Distributions for Generic p-Spin Models

Journal of Statistical Physics - We provide an alternative formula for spin distributions of generic p-spin glass models. As a main application of this expression, we write spin statistics as...     

Kubo formulas for second-order hydrodynamic coefficients

At second order in gradients, conformal relativistic hydrodynamics depends on the viscosity η and on five additional "second-order" hydrodynamical coefficients τ(Π), κ, λ?, λ?, and λ?. We derive Kubo relations for these coefficients, relating them to equilibrium, fully retarded three-point correlation functions of the stress tensor. We show that the coefficient λ? can be evaluated directly by Euclidean means and does not in general vanish.     

Susceptibility Amplitude Ratio for Generic Competing Systems

We calculate the susceptibility amplitude ratio near a generic higher character Lifshitz point up to one-loop order. We employ a renormalization group treatment with L independent scaling transformations associated to the various inequivalent subspaces in the anisotropic case in order to compute the ratio above and below the critical temperature and demonstrate its universality. Furthermore, the isotropic results with only one type of competition axes have also been shown to be universal. We describe how the simpler situations of m-axial Lifshitz points as well as ordinary (noncompeting) systems can be retrieved from the present framework.     

Fractional hydrodynamic equations for fractal media

We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the “fractional” continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered.     

Generic Rigidity for Circle Diffeomorphisms with Breaks

We prove that \({C^r}\)-smooth (\({r > 2}\)) circle diffeomorphisms with a break, i.e., circle diffeomorphisms with a single singular point where the derivative has a jump discontinuity, are generically, i.e., for almost all irrational rotation numbers, not \({C^{1+\varepsilon}}\)-rigid, for any \({\varepsilon > 0}\). This result complements our recent proof, joint with Khanin (Geom Funct Anal 24:2002–2028, 2014), that such maps are generically \({C^1}\)-rigid. It stands in remarkable contrast to the result of Yoccoz (Ann Sci Ec Norm Sup 17:333–361, 1984) that \({C^r}\)-smooth circle diffeomorphisms are generically \({C^{r-1-\varkappa}}\)-rigid, for any \({\varkappa > 0}\).     

Two-pion interferometry for viscous hydrodynamic sources

The space-time evolution of the (1+1)-dimensional viscous hydrodynamics with an initial quark-gluon plasma (QGP) produced in ultrarelativistic heavy ion collisions is studied numerically. The particle-emitting sources undergo a crossover transition from the QGP to hadronic gas. We take into account a usual shear viscosity for the strongly coupled QGP as well as the bulk viscosity which increases significantly in the crossover region. The two-pion Hanbury-Brown-Twiss (HBT) interferometry for the viscous hydrodynamic sources is performed. The HBT analyses indicate that the viscosity effect on the two-pion HBT results is small if only the shear viscosity is taken into consideration in the calculations. The bulk viscosity leads to a larger transverse freeze-out configuration of the pion-emitting sources, and thus increases the transverse HBT radii. The results of the longitudinal HBT radius for the source with Bjorken longitudinal scaling are consistent with the experimental data.     

简并光学参量振荡器混沌相同步与反相同步

从广泛意义上研究了简并光学参量振荡器的混沌同步. 数值结果表明, 当最大条件李指数小于零时, 处于混沌态的两个简并光学参量振荡器通过单向耦合可以实现相同步或反相同步. 当两个简并光学参量振荡器同时实现正耦合或负耦合时为相同步, 当其中一个为正耦合而另一个为负耦合时实现反相同步.     

Generic eigenvalue multiplicities for two-parameter families of operators

A theorem about two-parameter families of Schrödinger operators in proved; the potential is parameter dependent.     

Generic Bell inequalities for multipartite arbitrary dimensional systems

We present generic Bell inequalities for multipartite arbitrary dimensional systems. The inequalities that any local realistic theory must obey are violated by quantum mechanics for even dimensional systems. A large set of variants are shown to naturally emerge from the generic Bell inequalities. We discuss particular variants of Bell inequalities that are violated for all the systems including odd dimensional systems.     

Scaling Limits and Generic Bounds for Exploration Processes

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.     

A hydrodynamic model for cooperating solidary countries

The goal of international trade theories is to explain the exchange of goods and services between different countries, aiming to benefit from it. Albeit the idea is very simple and known since ancient history, smart policy and business strategies need to be implemented by each subject, resulting in a complex as well as not obvious interplay. In order to understand such a complexity, different theories have been developed since the sixteenth century and today new ideas still continue to enter the game. Among them, the so called classical theories are country-based and range from Absolute and Comparative Advantage theories by A. Smith and D. Ricardo to Factor Proportions theory by E. Heckscher and B. Ohlin. In this work we build a simple hydrodynamic model, able to reproduce the main conclusions of Comparative Advantage theory in its simplest setup, i.e. a two-country world with country A and country B exchanging two goods within a genuine exchange-based economy and a trade flow ruled only by market forces. The model is further generalized by introducing money in order to discuss its role in shaping trade patterns. Advantages and drawbacks of the model are also discussed together with perspectives for its improvement.     

统一超混沌系统的投影同步

利用两种方法研究了统一超混沌系统的同步问题.首先以全状态混合投影自适应同步方法,基于Lyapunov稳定性理论,设计了自适应控制器,理论证明了该控制器可以实现参数已知的统一超混沌系统的全状态混合映射同步.其次使用主动控制同步方法,设计了同步控制器,实现了统一超混沌系统的完全同步,最后数值仿真实验进一步验证了所提出方案的有效性. 关键词： 统一超混沌系统 自适应控制器 全状态混合投影同步 主动控制同步