Effect of polarization on the trajectory of dissipative solitons

We show that the optical Magnus effect for dissipative solitons is determined not only by the helicity but also by the topological index, i.e., by the magnetic quantum number or by the projection of the soliton orbital moment on its trajectory. In the case of inhomogeneous media, we find a relation between the optical Magnus effect and the nonholonomy of the field of unit vectors tangent to the trajectory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 1, pp. 126–134, January, 2009.     

Computer Simulations on the Channel Membrane Formation by Nonsolvent Induced Phase Separation

The formation of channel membrane of polystyrene‐block‐poly(4‐vinyl pyridine) block copolymer is studied by computer simulations with the nonsolvent induced phase separation (SNIPS) method. Dissipative particle dynamics is employed to study the microphase separation process and the SNIPS mechanism. Simulation results indicate that polymer concentration has a significant effect on the membrane structure. Channel membranes form in the copolymer concentration range of 44–58%. Block ratio plays an important role in shaping the membrane structure. Solvent exchange rate also affects the degree of microphase separation at each evolution stage of simulation. The time evolution of morphologies shows that the microphase separation processes happen with the following sequences: the polymer self‐assembled and many small pores appear, then they form irregular cavities and cross‐link gradually, finally the channel membrane forms. These results throw light on the formation mechanism of polymer membranes and provide insightful guidance for future membrane design and preparation.     

Monolayer and multilayer compact film formations on different substrates by physical deposition

Dissipative particle dynamics simulations are applied to investigate the monolayer and multilayer film formations on different solid substrates by physical deposition. The influences of the polymer concentration, the polymer chain length, the solvent quality, and the interactions between the polymer solution and the solid substrate surface on the film formation dynamics and the mechanism are studied in detail. The results are analyzed in terms of the thickness and the shape of the deposited film, the kinetics of phase separation in the polymer solution, and the contact angle formed between the polymer aggregations and the substrate surface. Moreover, we suggest two strategies, designing a deposition process analogous to “chemical titration” and physically blocking interlayer diffusion by a simple crosslinked network barrier, to deposit the compact monolayer and multilayer films with better quality, respectively. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 353–365, 2009     

Functional Interdependence in Coupled Dissipative Structures: Physical Foundations of Biological Coordination

Coordination within and between organisms is one of the most complex abilities of living systems, requiring the concerted regulation of many physiological constituents, and this complexity can be particularly difficult to explain by appealing to physics. A valuable framework for understanding biological coordination is the coordinative structure, a self-organized assembly of physiological elements that collectively performs a specific function. Coordinative structures are characterized by three properties: (1) multiple coupled components, (2) soft-assembly, and (3) functional organization. Coordinative structures have been hypothesized to be specific instantiations of dissipative structures, non-equilibrium, self-organized, physical systems exhibiting complex pattern formation in structure and behaviors. We pursued this hypothesis by testing for these three properties of coordinative structures in an electrically-driven dissipative structure. Our system demonstrates dynamic reorganization in response to functional perturbation, a behavior of coordinative structures called reciprocal compensation. Reciprocal compensation is corroborated by a dynamical systems model of the underlying physics. This coordinated activity of the system appears to derive from the system’s intrinsic end-directed behavior to maximize the rate of entropy production. The paper includes three primary components: (1) empirical data on emergent coordinated phenomena in a physical system, (2) computational simulations of this physical system, and (3) theoretical evaluation of the empirical and simulated results in the context of physics and the life sciences. This study reveals similarities between an electrically-driven dissipative structure that exhibits end-directed behavior and the goal-oriented behaviors of more complex living systems.     

Dissipative Heating of a Viscoelastic Cylinder under a Load Steadily Moving over Its Surface

The Fourier method is used to find the analytical solutions to two-dimensional quasistatic problems of stationary polyharmonic vibrations and dissipative heating of a linearly viscoelastic cylinder. The influence of the cylinder thickness and the width of the loading area on the thermomechanical state of the cylinder is studied based on numerical data__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 23–32, February 2005.     

The chaotic response of a fluttering panel: The influence of maneuvering

The influence of maneuvering on the chaotic response of a fluttering buckled plate on an aircraft has been studied. The governing equations, derived using Lagrangian mechanics, include geometric non-linearities associated with the occurrence of tensile stresses, as well as coupling between the angular velocity of the maneuver and the elastic degrees of freedom. Numerical simulation for periodic and chaotic responses are conducted in order to analyze the influence of the pull-up maneuver on the dynamic behavior of the panel. Long-time histories phase-plane plots, and power spectra of the responses are presented. As the maneuver (load factor) increases, the system exhibits complicated dynamic behavior including a direct and inverse cascade of subharmonic bifurcations, intermittency, and chaos. Beside these classical routes of transition from a periodic state to chaos, our calculations suggest amplitude modulation as a possible new mode of transition to chaos. Consequently this research contributes to the understanding of the mechanisms through which the transition between periodic and strange attractors occurs in, dissipative mechanical systems. In the case of a prescribed time dependent maneuver, a remarkable transition between the different types of limit cycles is presented.Nomenclature a plate length - a _r u _r /h - D plate bending stiffness - E modulus of elasticity - g acceleration due to gravity - h plate thickness - j₁,j₂,j₃ base vectors of the body frame of reference - K spring constant - M Mach number - n 1 + ₀/g - N ₁ applied in-plane force - p–p aerodynamic pressure - P pa ⁴/Dh - q ₀/2 - Q _r generalized Lagrangian forces - R rotation matrix - R ₄ N, a ²/D - t time - kinetic energy - u plate deflection - u displacement of the structure - u _r modal amplitude - v₀ velocity - x coordinates in the inertial frame of reference - z coordinates in the body frame of reference - Ka/(Ka+Eh) - - elastic energy - 2qa ³/D - a/_mh - Poisson's ratio - material coordinates - air density - _m plate density - - _r prescribed functions - _r sin(r z/a) - angular velocity - a/v₀ - skew-symmetric matrix form of the angular velocity     

A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

This paper considers the one-dimensional dissipative cubic nonlinear Schrödinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.     

Dissipation of a two-mode squeezed vacuum state in the single-mode amplitude damping channel

We explore how a two-mode squeezed vacuum state sechθ e^{a+b+ tanh θ} |00> evolves when it undergoes a singlemode amplitude dissipative channel with rate of decay κ. We find that in this process not only the squeezing parameter decreases, tanh θ → e^-κt tanh θ, but also the second-mode vacuum state evolves into a chaotic state exp{b⁺bln[1 - e^-2κt tanh² θ]}. The outcome state is no more a pure state, but an entangled mixed state.     

Unitarily invariant norm inequalities for accretive–dissipative operator matrices

An open question raised in Lin and Zhou (2013) [13] is answered.     

An approach to generate deterministic Brownian motion

We propose an approach for generation of deterministic Brownian motion. By adding an additional degree of freedom to the Langevin equation and transforming it into a system of three linear differential equations, we determine the position of switching surfaces, which act as a multi-well potential with a short fluctuation escape time. Although the model is based on the Langevin equation, the final system does not contain a stochastic term, and therefore the obtained motion is deterministic. Nevertheless, the system behavior exhibits important characteristic properties of Brownian motion, namely, a linear growth in time of the mean square displacement, a Gaussian distribution, and a −2 power law of the frequency spectrum. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion.