217 research outputs found
Well-posedness and decay structure of a quantum hydrodynamics system with Bohm potential and linear viscosity
In this paper, a compressible viscous-dispersive Euler system in one space
dimension in the context of quantum hydrodynamics is considered. The purpose of
this study is twofold. First, it is shown that the system is locally
well-posed. For that purpose, the existence of classical solutions which are
perturbation of constant states is established. Second, it is proved that in
the particular case of subsonic equilibrium states, sufficiently small
perturbations decay globally in time. In order to prove this stability
property, the linearized system around the subsonic state is examined. Using an
appropriately constructed compensating matrix symbol in the Fourier space, it
is proved that solutions to the linear system decay globally in time,
underlying a dissipative mechanism of regularity gain type. These linear decay
estimates, together with the local existence result, imply the global existence
and the decay of perturbations to constant subsonic equilibrium states as
solutions to the full nonlinear system.Comment: 42 page
Analytical Models of Exoplanetary Atmospheres. I. Atmospheric Dynamics via the Shallow Water System
Within the context of exoplanetary atmospheres, we present a comprehensive
linear analysis of forced, damped, magnetized shallow water systems, exploring
the effects of dimensionality, geometry (Cartesian, pseudo-spherical and
spherical), rotation, magnetic tension and hydrodynamic and magnetic sources of
friction. Across a broad range of conditions, we find that the key governing
equation for atmospheres and quantum harmonic oscillators are identical, even
when forcing (stellar irradiation), sources of friction (molecular viscosity,
Rayleigh drag and magnetic drag) and magnetic tension are included. The global
atmospheric structure is largely controlled by a single, key parameter that
involves the Rossby and Prandtl numbers. This near-universality breaks down
when either molecular viscosity or magnetic drag acts non-uniformly across
latitude or a poloidal magnetic field is present, suggesting that these effects
will introduce qualitative changes to the familiar chevron-shaped feature
witnessed in simulations of atmospheric circulation. We also find that
hydrodynamic and magnetic sources of friction have dissimilar phase signatures
and affect the flow in fundamentally different ways, implying that using
Rayleigh drag to mimic magnetic drag is inaccurate. We exhaustively lay down
the theoretical formalism (dispersion relations, governing equations and
time-dependent wave solutions) for a broad suite of models. In all situations,
we derive the steady state of an atmosphere, which is relevant to interpreting
infrared phase and eclipse maps of exoplanetary atmospheres. We elucidate a
pinching effect that confines the atmospheric structure to be near the equator.
Our suite of analytical models may be used to decisively develop physical
intuition and as a reference point for three-dimensional, magnetohydrodynamic
(MHD) simulations of atmospheric circulation.Comment: Accepted by ApJS, 36 pages, 6 figures, 3 tables, 273 equation
Complex extreme nonlinear waves: classical and quantum theory for new computing models
The historical role of nonlinear waves in developing the science of complexity, and also their physical feature of being a widespread paradigm in optics, establishes a bridge between two diverse and fundamental fields that can open an immeasurable number of new routes. In what follows, we present our most important results on nonlinear waves in classical and quantum nonlinear optics. About classical phenomenology, we lay the groundwork for establishing one uniform theory of dispersive shock waves, and for controlling complex nonlinear regimes through simple integer topological invariants. The second quantized field theory of optical propagation in nonlinear dispersive media allows us to perform numerical simulations of quantum solitons and the quantum nonlinear box problem. The complexity of light propagation in nonlinear media is here examined from all the main points of view: extreme phenomena, recurrence, control, modulation instability, and so forth. Such an analysis has a major, significant goal: answering the question can nonlinear waves do computation? For this purpose, our study towards the realization of an all-optical computer, able to do computation by implementing machine learning algorithms, is illustrated. The first all-optical realization of the Ising machine and the theoretical foundations of the random optical machine are here reported. We believe that this treatise is a fundamental study for the application of nonlinear waves to new computational techniques, disclosing new procedures to the control of extreme waves, and to the design of new quantum sources and non-classical state generators for future quantum technologies, also giving incredible insights about all-optical reservoir computing. Can nonlinear waves do computation? Our random optical machine draws the route for a positive answer to this question, substituting the randomness either with the uncertainty of quantum noise effects on light propagation or with the arbitrariness of classical, extremely nonlinear regimes, as similarly done by random projection methods and extreme learning machines
Hydrodynamics
The phenomena related to the flow of fluids are generally complex, and difficult to quantify. New approaches - considering points of view still not explored - may introduce useful tools in the study of Hydrodynamics and the related transport phenomena. The details of the flows and the properties of the fluids must be considered on a very small scale perspective. Consequently, new concepts and tools are generated to better describe the fluids and their properties. This volume presents conclusions about advanced topics of calculated and observed flows. It contains eighteen chapters, organized in five sections: 1) Mathematical Models in Fluid Mechanics, 2) Biological Applications and Biohydrodynamics, 3) Detailed Experimental Analyses of Fluids and Flows, 4) Radiation-, Electro-, Magnetohydrodynamics, and Magnetorheology, 5) Special Topics on Simulations and Experimental Data. These chapters present new points of view about methods and tools used in Hydrodynamics
Towards better understanding of the Smoothed Particle Hydrodynamic Method
Numerous approaches have been proposed for solving partial differential equations; all these methods have their own advantages and disadvantages depending on the problems being treated. In recent years there has been much development of particle methods for mechanical problems. Among these are the Smoothed Particle Hydrodynamics (SPH), Reproducing Kernel Particle Method (RKPM), Element Free Galerkin (EFG) and Moving Least Squares (MLS) methods. This development is motivated by the extension of their applications to mechanical and engineering problems. Since numerical experiments are one of the basic tools used in computational mechanics, in physics, in biology etc, a robust spatial discretization would be a significant contribution towards solutions of a number of problems. Even a well-defined stable and convergent formulation of a continuous model does not guarantee a perfect numerical solution to the problem under investigation. Particle methods especially SPH and RKPM have advantages over meshed methods for problems, in which large distortions and high discontinuities occur, such as high velocity impact, fragmentation, hydrodynamic ram. These methods are also convenient for open problems. Recently, SPH and its family have grown into a successful simulation tools and the extension of these methods to initial boundary value problems requires further research in numerical fields. In this thesis, several problem areas of the SPH formulation were examined. Firstly, a new approach based on ‘Hamilton’s variational principle’ is used to derive the equations of motion in the SPH form. Secondly, the application of a complex Von Neumann analysis to SPH method reveals the existence of a number of physical mechanisms accountable for the stability of the method. Finally, the notion of the amplification matrix is used to detect how numerical errors propagate permits the identification of the mechanisms responsible for the delimitation of the domain of numerical stability. By doing so, we were able to erect a link between the physics and the numerics that govern the SPH formulation.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Fundamentals and applications of spatial dissipative solitons in photonic devices : [Chapter 6]
We review the properties of optical spatial dissipative solitons (SDS). These are stable, self‐localized optical excitations sitting on a uniform, or quasi‐uniform, background in a dissipative environment like a nonlinear optical cavity. Indeed, in optics they are often termed “cavity solitons.” We discuss their dynamics and interactions in both ideal and imperfect systems, making comparison with experiments. SDS in lasers offer important advantages for applications. We review candidate schemes and the tremendous recent progress in semiconductor‐based cavity soliton lasers. We examine SDS in periodic structures, and we show how SDS can be quantitatively related to the locking of fronts. We conclude with an assessment of potential applications of SDS in photonics, arguing that best use of their particular features is made by exploiting their mobility, for example in all‐optical delay lines
Results towards a Scalable Multiphase Navier-Stokes Solver for High Reynolds Number Flows
The incompressible Navier-Stokes equations have proven formidable for nearly a century. The present difficulties are mathematical and computational in nature; the computational requirements, in particular, are exponentially exacerbated in the presence of high Reynolds number. The issues are further compounded with the introduction of markers or an immiscible fluid intended to be tracked in an ambient high Reynolds number flow; despite the overwhelming pragmatism of problems in this regime, and increasing computational efficacy, even modest problems remain outside the realm of direct approaches.
Herein three approaches are presented which embody direct application to problems of this nature. An LES model based on an entropy-viscosity serves to abet the computational resolution requirements imposed by high Reynolds numbers and a one-stage compressive flux, also utilizing an entropy-viscosity, aids in accurate, efficient, conservative transport, free of low order dispersive error, of an immiscible fluid or tracer. Finally, an integral commutator and the theory of anti-dispersive spaces is introduced as a novel theoretical tool for consistency error analysis; in addition the material engenders the construction of error-correction techniques for mass lumping schemes
Ion Acceleration by Solitary and Shock Waves Driven by Laser- Plasma Interactions
This thesis presents a theoretical study of the interaction of intense, ultrashort laser pulses with overdense
plasmas. Main objectives are to understand the basic phenomenon which leads to the formation
of non-linear electrostatic coherent wave structures in form of either solitary ion acoustic waves (SAW)
or collisionless shock waves (CSW). These different types of waves have been classified according to
Sagdeev’s theory and related formulas have been used for comparison with the numerical results. The
particular focus is on the effect on ion acceleration, by means of ion refection by the moving electrostatic
field associated to the shocks/solitons. An extensive numerical study by 1D PIC simulations has
been performed and in particular the differences arising between linearly polarized pulses and circularly
polarized pulses have been discussed. In a cold plasma, ion bunches produced by “hole boring” (HB)
radiation pressure acceleration at the target surface may propagate in the bulk as solitary waves. The acceleration
mechanism of these ion bunches has been discussed pointing out a distinction between shock
acceleration (SA) and HB acceleration, also with respect to some recent experimental results. Stability
of (SAW) or (CSW) and ion reflection from them has been found to be strongly dependent on the initial
velocity distribution of ions. The effect of both the ion and the electron temperature on the generation
and evolution of solitary acoustic waves have been discussed
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