Give Scaling Laws Research Articles

Are we ready to transfer optical light to gamma-rays?

Scattering relativistic electrons with optical lasers can result in a significant frequency upshift of photons, potentially producing γ-rays. This is what linear Compton scattering taught us. Ultra-intense lasers offer nowadays a new paradigm where multiphoton absorption effects come into play. These effects can result in higher harmonics, higher yields, and also electron-positron pairs. This article intends to discriminate the different laser scenarios that have been proposed over the past few years as well as to give scaling laws for future experiments. The energy conversion from lasers or particles to high-frequency photons is addressed for both the well-known counter propagating electron beam-laser interaction and quantum-electrodynamics cascades triggered by various lasers. Constructing bright and energetic gamma-ray sources in controlled conditions is within an ace of seeing the light of day.

Critical phase behavior in multi-component fluid mixtures: Complete scaling analysis.

We analyze the critical gas-liquid phase behavior of arbitrary fluid mixtures in their coexistence region. We focus on the setting relevant for polydisperse colloids, where the overall density and composition of the system are being controlled, in addition to temperature. Our analysis uses the complete scaling formalism and thus includes pressure mixing effects in the mapping from thermodynamic fields to the effective fields of 3D Ising criticality. Because of fractionation, where mixture components are distributed unevenly across coexisting phases, the critical behavior is remarkably rich. We give scaling laws for a number of important loci in the phase diagram. These include the cloud and shadow curves, which characterise the onset of phase coexistence, a more general set of curves defined by fixing the fractional volumes of the coexisting phases to arbitrary values, and conventional coexistence curves of the densities of coexisting phases for fixed overall density. We identify suitable observables (distinct from the Yang-Yang anomalies discussed in the literature) for detecting pressure mixing effects. Our analytical predictions are checked against numerics using a set of mapping parameters fitted to simulation data for a polydisperse Lennard-Jones fluid, allowing us to highlight crossovers where pressure mixing becomes relevant close to the critical point.

Lubrication of soft viscoelastic solids

Lubrication flows appear in many applications in engineering, biophysics and nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubricating fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin–Voigt, standard linear and power law rheology. It is shown how the solid viscoelasticity affects the lubrication process when the time scale of loading becomes comparable to the rheological time scale. We derive asymptotic relations between the lift force and the sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.

Vortex Dynamics and Shear-Layer Instability in High-Intensity Cyclotrons.

We show that the space-charge dynamics of high-intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics gives a unified and intuitive framework to explain the beam spiraling and beam breakup behavior observed in experiments and in simulations. Specifically, we demonstrate that beam breakup is the result of a classical instability occurring in fluids subject to a sheared flow. We give scaling laws for the instability and predict the nonlinear evolution of beams subject to it. Our work suggests that cyclotrons may be uniquely suited for the experimental study of shear layers and vortex distributions that are not achievable in Penning-Malmberg traps.

A plasma wiggler beamline for 100 TW to 10 PW lasers

We introduce the theoretical framework of laser wakefield acceleration and plasma wiggler radiation generation in the matched regime, give scaling laws and apply the scheme to laser systems planned for the near future. We compare the anticipated electron and x-ray beam parameters for a 100 TW, 1 PW and 10 PW short pulse Ti:Sapphire laser with previous experimental results. Depending on the chosen laser configuration, x-rays from a plasma wiggler beamline (PWB) can be several orders of magnitude brighter than current betatron sources, and comparable to or better than 3rd generation synchrotron facilities. Furthermore, increasing the laser power from 0.1 to 10 PW, the spectral peak of the betatron radiation shifts into the hard x-ray and γ-ray regime. We also discuss a basic layout of a PWB and motivate 100 TW, 1 PW and 10 PW beamlines with a wide range of uses, experiments and applications. The ability to couple the PWBs with various optical laser drivers has the potential to facilitate uses across the spectrum of light source applications.

Pattern formation arising from condensation of a homogeneous gas into a binary, phase-separating liquid

We examine the nucleated growth of a binary, immiscible liquid drop within a homogeneous gas. The system couples the growth of the liquid drop with the phase separation of the immiscible components and, thus, can potentially reveal novel pattern formation. To carry out this study, we first characterize the thermodynamic properties of the system in terms of an appropriate Ginzburg-Landau free energy density. By minimizing this free energy, we construct the equilibrium phase diagram for the system. We then use a lattice Boltzmann algorithm to solve the hydrodynamic equations describing the dynamical evolution of the fluid. We observe intriguing tentaclelike structures within the nucleation and growth regime and explore how the formation of these structures depends on the thermodynamic and transport properties of the system. We give scaling laws describing domain growth in both the diffusion- and flow-limited regimes. The results highlight the novel physics that can emerge when there is interplay between the ordering of a density and a concentration field.

Modulational instabilities in Josephson oscillations of elongated coupled condensates

We study the Josephson oscillations of two coupled elongated condensates. Linearized calculations show that the oscillating mode uniform over the length of the condensates (uniform Josephson mode) is unstable : modes of non zero longitudinal momentum grow exponentially. In the limit of strong atom interactions, we give scaling laws for the instability time constant and unstable wave vectors. Beyond the linearized approach, numerical calculations show a damped recurrence behavior : the energy in the Josephson mode presents damped oscillations. Finally, we derive conditions on the confinement of the condensates to prevent instabilities.

Theory of 1-N-way phase-locked resonators with perturbations in the array elements

The recently proposed 1-N-way resonator based on beam splitting and beam combining effects in rectangular cross-sectional multimode waveguides offers a valuable way in which N low-power laser elements can be combined in a coherent fashion. We develop a theory of such resonators in the presence of perturbations in the N-element array. We demonstrate that despite the presence of perturbations there is only one possible mode of the resonator. The theory is used to provide an understanding of the effects of a number of possible perturbations that could arise as a result of manufacturing processes and operational effects. The results give scaling laws for the design tolerances on array element mirror tilt, array element optical path length control, and the effects of array element malfunction and their need for gain balance.

Classical study of single-electron capture and ionization processes inAq++(H,H2)collisions

Using a classical method, cross sections in ${A}^{q+}+(\mathrm{H},{\mathrm{H}}_{2}) (q=1,\dots{},8)$ collisions are obtained for impact energy ranges $9 {\mathrm{keV}\mathrm{}\mathrm{amu}}^{\ensuremath{-}1}--6.4 {\mathrm{MeV}\mathrm{}\mathrm{amu}}^{\ensuremath{-}1}$ (ionization), $--600 {\mathrm{KeV}\mathrm{}\mathrm{amu}}^{\ensuremath{-}1}$ (electron capture). For bare ion impact on H, comparison to experiment and to the results of accurate semiclassical calculations shows that total and partial cross sections, as well as transition probabilities, obtained with the classical trajectory Monte Carlo approach, are more accurate than usually assumed. From the characteristics of the mechanisms, we are led to use our data as estimates for the case of dressed-ion impact at the higher nuclear velocities. We successfully apply a very simple model for ${\mathrm{H}}_{2}$ targets, in which the relevant quantities are the charge of the projectile and the vertical ionization potential of the molecule. For practical purposes, we give scaling laws to benchmark $({\mathrm{H}}^{+},{\mathrm{He}}^{2+})$ cases, and for ionization we relate them, at higher $v,$ to the behavior of the transition probabilities.

Diffusion-limited binary reactions: the hierarchy of nonclassical regimes for random initial conditions

We derive a hierarchy of kinetic regimes and crossover conditions for elementary A + A → 0 and A + B → 0 batch reactions from a nonclassical reaction—diffusion formalism that includes spatial fluctuations. This paper addresses the case of a spatially random initial distribution of reactants; correlated initial conditions are discussed in another paper. For low dimensions ( d⩽2) we find that both A + A → 0 and A + B → 0 reactions depart (swiftly) from the classical behavior toward a “depletion zone regime” with non-Hertzian nearest neighbor distributions and nonclassical rate laws. Eventually the (A – B) density difference fluctuations take over in the A + B → 0 case and lead to the segregated Ovchinnikov—Zeldovich asymptotic behavior with its peculiar rate laws. We give scaling laws for the crossover time and crossover density, with explicit dependencies on the initial density and on the dimension. Similarly, in three dimensions the crossover from the classical to the segregated Zeldovich regime is derived for the A + B → 0 reaction. Finite size effects differ significantly for the segregated and nonsegregated regimes. In the former case we obtain a relation between aggregate sizes and lattice sizes. Monte Carlo simulations bear out the scaling laws and provide the scaling coefficients.

Adsorption of polymeric brushes: Bridging

We study the adsorption of grafted polymer layers on a planar surface parallel to the grafting surface. The layer consists of two types of chains: nonadsorbed chains with a free end and adsorbed chains forming bridges between the two plates. In the limit of strong adsorption a dead zone exists in the vicinity of the adsorbing plate; its size increases with the adsorption strength. Two adsorption mechanisms are possible: adsorption of the last monomer only and adsorption of all the monomers. In both cases the adsorption regimes at equilibrium (when no external force acts on the plates) are discussed within the framework of the self-consistent mean-field theory. We also give scaling laws taking into account excluded volume correlations. Finally, we consider situations where a finite external force, either tangential or normal to the plates, is applied on the adsorbing plate. Pulling and tangential forces both reduce the fraction of bridges and eventually lead to rupture, whereas compressional forces favor bridging. For normal forces, force vs distance profiles between planes and crossed cylinders are given.

Features of the turbulent boundary layer pressure field on an elastic surface

In any approach to calculation of the wall pressure spectrum of a TBL based on an inhomogeneous (Lighthill) wave equation, singularities of the spectral density arise along various lines or surfaces in (k,ω) space. These lines of surfaces correspond to the acoustic or structural dispersion relations, and the singularities may be controlled by such mechanisms as surface finiteness, dissipation in the structure or fluid, and surface compliance. This paper will examine the way in which these various mechanisms control the singularities in different regimes of the spatial and dynamical parameters involved, and will give scaling laws for the pressure spectral densities at the critical conditions in (k,ω) space. [Work supported by ONR, Code 425.]

Renormalization group and critical localization

The renormalization-group (RG) method is applied to the problem of formation of a localized state of a particle moving in a given potential. It is shown that RG transformation on the particle's Green's function can be performed exactly. The fixed-point equations yield information on the critical binding strength, while the transformation equations near the fixed points give scaling laws and critical exponents, e.g., for the dependence of the localization radius on the energy and the potential strength. The general theory is illustrated by considering the simplest case of the Slater-Koster problem in detail. We find that it is possible to take all the irrelevant variables into account and thus obtain the exact result for the critical binding point. Critical exponents and scaling laws are, however, universal in character. The method is then extended to the case of motion in random potentials, and some applications are pointed out. In particular it is shown that the RG properties of the averaged absolute value squared ($〈{|G|}^{2}〉$) of the Green's function do not correspond to a simple second-order phase transition. The analysis illustrates certain features of RG methods which have not heretofore been encountered in other problems and which are likely to be found in treatments of disordered materials. In particular, the runaway behavior observed in the RG transformation of $〈G〉$ and $〈{|G|}^{2}〉$ as well as in many random-spin systems, might be associated with the formation of bound states in the band tail for any amount of randomness.