Role of f(G) Gravity in the Study of Non-Static Complex Systems

The concept of complexity for dynamical spherically symmetric dissipative self-gravitating configuration [1] is generalized in the scenario of modified Gauss-Bonnet gravity. For this purpose, a spherically symmetric fluid with locally anisotropic, dissipative, and non-dissipative configuration is considered. We choose the same complexity factor for the structure as we did for the static case, while we consider the homologous condition for the simplest pattern of evolution. In this approach, we formulate structure scalars that demonstrate the essential properties of the system. A fluid distribution that fulfills the vanishing complexity constraint and proceeds homologously corresponds to isotropic, geodesic, homogeneous, and shear-free fluid. In the dissipative case, the fluid is still geodesic but it is shearing, and there is a wide range of solutions. In the last, the stability of vanishing complexity is examined.

New results on Blow-up of solutions for Emden-Fowler type degenerate wave equation with memory

In this article we consider a new class of a Emden-Fowler type semilinear degenerate wave equation with memory. The main contributions here is to show that the memory lets the global solutions of the degenerate problem still non-exist without any conditions on the nature of growth of the relaxation function. This is to extend the paper in \cite{L11} for the dissipative case.

Force reversal and energy dissipation in composite tubes through nonlinear viscoelasticity of component materials

Fibre-reinforced, fluid-filled structures are commonly found in nature and emulated in devices. Researchers in the field of soft robotics have used such structures to build lightweight, impact-resistant and safe robots. The polymers and biological materials in many soft actuators have these advantageous characteristics because of viscoelastic energy dissipation. Yet, the gross effects of these underlying viscoelastic properties have not been studied. We explore nonlinear viscoelasticity in soft, pressurized fibre-reinforced tubes, which are a popular type of soft actuation and a common biological architecture. Relative properties of the reinforcement and matrix materials lead to a rich parameter space connecting actuator inputs, loading response and energy dissipation. We solve a mechanical problem in which both the fibre and the matrix are nonlinearly viscoelastic, and the tube deforms into component materials’ nonlinear response regimes. We show that stress relaxation of an actuator can cause the relationship between the working fluid input and the output force to reverse over time compared to the equivalent, non-dissipative case. We further show that differences in design parameter and viscoelastic material properties can affect energy dissipation throughout the use cycle. This approach bridges the gap between viscoelastic behaviour of fibre-reinforced materials and time-dependent soft robot actuation.

Asymptotic to systems with memory and non-local initial data

We study the existence and the asymptotic behavior of the solution of an abstract viscoelastic system submitted to non-local initial data. [Formula: see text] [Formula: see text] where [Formula: see text] and [Formula: see text] are differential operators satisfying [Formula: see text] for [Formula: see text]. We prove that the model is well-posed. Concerning the asymptotic behavior, we show that the exponential decay holds if and only if [Formula: see text] and [Formula: see text] goes to zero exponentially. Otherwise if [Formula: see text] or the kernel goes to zero polynomially, then the solution only decays polynomially. We show the optimality of our result. Finally, we consider the non-dissipative case.

General Solution of the Rayleigh Equation for the Description of Bubble Oscillations Near a Wall

We consider a generalization of the Rayleigh equation for the description of the dynamics of a spherical gas bubble oscillating near an elastic or rigid wall. We show that in the non–dissipative case, i.e. neglecting the liquid viscosity and compressibility, it is possible to construct the general analytical solution of this equation. The corresponding general solution is expressed via the Weierstrass elliptic function. We analyze the dependence of this solution properties on the physical parameters.

Optical and spin-optical superpositions modulated by Aharonov–Bohm effect

Generation of Aharonov–Bohm (AB) phase has achieved a state-of-the-art in mesoscopic systems with manipulation and control of the AB effect. The possibility of transfer information encoded in such systems to nonclassical states of light increases the possible scenarios where the information can be manipulated and transferred. In this paper, we propose a quantum transfer of the AB phase generated in a spintronic device, a topological spin transistor (TST), to an quantum optical device, a coherent state superposition in high-Q cavity and discuss optical and spin-optical superpositions in the presence of an AB phase. We demonstrate that the AB phase generated in the TST can be transferred to the coherent state superposition, considering the interaction with the spin state and the quantum optical manipulation of the coherent state superposition. We show that these cases provide examples of two-qubit states modulated by AB effect and that the phase parameter can be used to control the degree of rotation of the qubit state. We also show under a measurement on the spin basis, an optical one-qubit state that can be modulated by the AB effect. In these cases, we consider a dispersive interaction between a coherent state and a spin state with an acquired AB phase and also discuss a dissipative case where a given Lindblad equation is achieved and solved.

Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces

As an essential extension of the well known case {\beta\kern-1.0pt\in\kern-1.0pt({\frac{1}{2}},1]} to the hyper-dissipative case {\beta\kern-1.0pt\in\kern-1.0pt(1,\infty)} , this paper establishes both well-posedness and ill-posedness (not only norm inflation but also indifferentiability of the solution map) for the mild solutions of the incompressible Navier–Stokes system with dissipation {(-\Delta)^{{\frac{1}{2}}<\beta<\infty}} through the generalized Carleson measure spaces of initial data that unify many diverse spaces, including the Q space {(Q_{-s=-\alpha})^{n}} , the BMO-Sobolev space {((-\Delta)^{-{\frac{s}{2}}}\mathrm{BMO})^{n}} , the Lip-Sobolev space {((-\Delta)^{-{\frac{s}{2}}}\mathrm{Lip}\alpha)^{n}} , and the Besov space {(\dot{B}^{s}_{\infty,\infty})^{n}} .

The general peakon–antipeakon solution for the Camassa–Holm equation

We compute explicitly the peakon–antipeakon solution of the Camassa–Holm (CH) equation [Formula: see text] in the non-symmetric and [Formula: see text]-dissipative case. The solution experiences wave breaking in finite time, and the explicit solution illuminates the interplay between the various variables.

A dissipative random velocity field for fully developed fluid turbulence

We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field (Chevillardet al.,Europhys. Lett., vol. 89, 2010, 54002) of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectories. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model dependent on a single free parameter,${\it\gamma}$, that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments (i.e. the structure functions) including the intermittent corrections and the existence of energy transfer across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter${\it\gamma}$and derive analytically the spectrum of exponents of the structure functions in a simplified non-dissipative case. A perturbative expansion in power of${\it\gamma}$shows that energy transfer, at leading order, indeed take place, justifying the dissipative nature of this random field.