Instability of potential jet streams

A Hamiltonian version has been formulated for the model of a potential jet stream of a homogeneous incompressible fluid with a free boundary. In the framework of this model, instability regimes have been analyzed. It has been shown that self-similar solutions with a compact support can be dominant structures. Analysis of the instability mechanism shows that two collapse scenarios are possible. The first scenario occurs without the deformation of the shape and leads to an intensification of the vortex sheet according to the law (t ₀ ? t)^?1, where t ₀ is the collapse time. The second scenario leads to the formation of a singularity for the surface shape and to a decrease in the intensity of the vortex sheet according to the laws (t ₀ ? t)^?1/5 and (t ₀ ? t)^1/5, respectively. The integral collapse criterion has been found.     

A nonlinear scenario for development of vortex layer instability in gravity field

A Hamiltonian version of contour dynamics is formulated for models of constant-vorticity plane flows with interfaces. The proposed approach is used as a framework for a nonlinear scenario for instability development. Localized vortex blobs are analyzed as structural elements of a strongly perturbed wall layer of a vorticity-carrying fluid with free boundary in gravity field. Gravity and vorticity effects on the geometry and velocity of vortex structures are examined. It is shown that compactly supported nonlinear solutions (compactons) are candidates for the role of particle-like vortex structures in models of flow breakdown. An analysis of the instability mechanism demonstrates the possibility of a self-similar collapse. It is found that the vortex shape stabilizes at the final stage of the collapse, while the vortex sheet strength on its boundary increases as (t ₀ ? t)^?1, where t ₀ is the collapse time.     

Collapse of vortex lines in hydrodynamics

A new mechanism is proposed for collapse in hydrodynamics associated with the “breaking” of vortex lines. The collapse results in the formation of point singularities of the vorticity field, i.e., a generalized momentum curl. At the point of collapse the vorticity |Ω| increases as ((t ₀ ? t)^?1 and its spatial distribution for t → t ₀ approaches quasi-two-dimensional: in the “soft” direction contraction obeys the law l ₁ → (t ₀ ? t)^3/2 whereas in the other two “hard” directions it obeys l ₂ → (t ₀ ? t)^1/2. It has been shown that this collapse scenario takes place in the general case for three-dimensional integrable hydrodynamics with the Hamiltonian ? = ∫|Ω| d r.     

Boundary Conditions for the Dynamical Equations of Quantum Mechanics

We discuss the problem whether the time evolution in quantum physics should be represented by the time-symmetric unitary-group evolution, i.e., whether time t extends over???∞?<?t?<?+∞ or it is more realistic to describe quantum systems by a mathematical theory, for which time t starts from a finite value t ₀: t ₀?≤?t?<?+∞, for which the mathematicians would choose t ₀?=?0,¹ but which could be any finite value. If the quantum system in the lab should be described by some kind of quantum theory, one should also admit the possibility that the solution of the dynamical equations needs to be found under boundary conditions that admit a semigroup evolution. It is remarkable that results in lab experiments indicate the existence of an ensemble of finite beginnings of time $ t_0^{(i) } $ for an ensemble of individual quanta.     

Blow-up instability in shallow water flows with horizontally-nonuniform density

The mechanisms of instability, whose development leads to the occurrence of the collapse (blow up), have been studied in the scope of the rotating shallow water flows with horizontal density gradient. Analysis shows that collapses in such models are initiated by the Rayleigh-Taylor instability and two scenarios are possible. Both the scenarios evolve according to a power law (t ₀ ? t)^??, where t ₀ is the collapse time, with ?? = ?1, ?2, and ?? = ?2/3, ?1 for the isotropic and anisotropic collapses, respectively. The rigorous criterion of collapse is found on the base of integrals of motion.     

Nonself-similar regimes of isothermal collapse of protostellar clouds

We consider the development of inhomogeneity in the isothermal collapse of protostellar clouds. The initial and boundary conditions correspond to the classical statement of the problem on the contraction of a homogeneous cloud from a given volume. A centered rarefaction wave is shown to propagate from the outer boundary of the cloud toward its center at the first collapse stage. Analysis reveals two possible regimes of isothermal collapse, depending on the relationship between the rarefaction wave focusing time t^* and the cloud free-fall collapse time t_ff. For cold clouds, t^*=t _ff and the rarefaction wave is not reflected. In this case, as time elapses, the cloud collapse becomes self-similar with the characteristic density profile ρ～r^?2. In hot clouds, t*<t _ff and the focusing can take place before the formation of an opaque core. Since the velocities of the rarefaction wave along and across magnetic field lines in a magnetized cloud are different, its front assumes a shape elongated along magnetic field lines. Depending on the initial conditions, based on analytical estimates, we investigate various possible scenarios for the collapse of magnetic protostellar clouds.     

Numerical modeling of collapse in ideal incompressible hydrodynamics

The appearance of a singularity in the velocity-field vorticity ω at an isolated point irrespective of the symmetry of initial distribution is demonstrated numerically. The behavior of maximal vorticity |ω| near the collapse point is well approximated by the dependence (t ₀?t)^?1, where t ₀ is the collapse time. This is consistent with the interpretation of collapse as the breaking of vortex lines.     

A measurement of the KL0p → KS0p reaction between 4 and 14 GeV/c in the range 0.1 ⩽|t|⩽ 2 GeV2

We present experimental data on the K_L⁰p → K_S⁰p reaction between 4 and 14 GeV/c in the range 0.1 ? |t| ? 2 GeV². This experiment has been performed at the CERN PS, using spark chambers and a large aperture magnet. The results show a break of slope at t = ?0.3 GeV². The ω trajectory deduced from the data has an intercept α(0) = 0.5 and a slope α′ = 0.88. A comparison with various models shows that the non-flip amplitude is dominant.     

Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid ⁴He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ(t) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ(t)≈A(κ|t−t₀|)^1/2, where κ=h/m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ(t)=B|t−t₀|^α and (b) a correction-factor expression δ(t)=A(κ|t−t₀|)^1/2(1+c|t−t₀|). The measured frequency distribution of α is peaked at the predicted value α=0.5, although the half-height values are α=0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24±0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c=0 with a half-height range of −0.9 s⁻¹ to 1.5 s⁻¹. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.     

Instability of gravity flows on a slope

A Hamiltonian version of contour dynamics is formulated for the model of a potential slope flow of homogeneous incompressible fluid. The particle-like solutions that play the role of structural elements in the disintegration of strongly perturbed slope flows are studied in terms of this approach. Investigation of the solution instability mechanism has shown that two collapse scenarios are realized, depending on the slope steepness. The singularity for the surface shape develops according to the law (t − t ₀)^−1/3 on a vertical slope and slightly more slowly, according to the law (t − t ₀)^−2/7, where t ₀ is the collapse time, on a nonvertical slope. A sufficient collapse criterion that allows this effect to be judged from the first three integrals of motion has been established.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Roles of initial condition and vortex pairing in jet noise

This is a study of the effect of initial condition on sound generated by vortex pairing in a low Mach number, cold air jet (0·15 ⩽ M ⩽ 0·35). Data has been taken, both flow velocity fields and sound pressure far fields, in a quality anechoic facility, with careful documentation of the effect of initial condition on the sound field of jets of two different geometries (i.e., circular and elliptic). Explanations are presented for most of the observed effects by applying Möhring's theory of vortex sound to vortex filament models of coherent structures in the jets. The explanations also draw upon experience with coherent structure dynamics. The sound source of interest here is that associated with the pairing of shear layer vortices. The evolution of these vortices is greatly affected by the initial condition as is their resultant sound field. The elliptic jets with laminar boundary layers show azimuthal directivity, namely, sound pressure levels in the minor axis plane were greater than in the major axis plane. This difference decreases as the nozzle boundary layer undergoes natural transition with increasing jet speed. When the nozzle boundary layer is tripped, making it fully turbulent and removing the shear layer mode of pairing, the elliptic jet sound fields become nearly axisymmetric. What appears to be the most acoustically active phase of vortex pairing has been modeled, and the resulting sound field calculated for the circular jet. Supporting evidence is found in the experimental data for the validity of this model. The model explains the connection between the initial condition and the far field sound of jets. Interestingly, a general result of Möhring's theory is that motions of vortex rings (of any arbitrary shape) can produce only axisymmetric sound fields if the rings remain in a plane. This implies that the observed asymmetric directivity of the laminar elliptic jet sound field must be due to non-planar ring motions of the vortical structures. The primary contribution of this paper is to examine quantitatively the role of vortex pairing in the production of jet noise; the results are used to reemphasize that “pairing noise” cannot be dominant in most practical jet sound fields, contrary to claims by other researchers.     

Process dependence of the target jet remnants in the photoproduction of large transverse momentum jets

We use the quark recombination model of Das and Hwa to predict the inclusive meson spectra (π⁺, π^?,K ⁺,K ^?) in the target fragmentation region for processes in which a large transverse momentum jet is produced by a nearly real photon. We find that the antiparticle ratios of such target jet mesons are sensitive to the type of process which has produced the largep _t jet. By comparing the ratios found in photoproduction to those in deep inelastic scattering we point out that it is in principle possible to identify the presence of the Bethe-Heitler photoproduction subprocess. We conclude that the target jet remnants can contribute to separating the subprocesses responsible for the photoproduction of largep _t jets.     

The effect of an external field on an interface,entropic repulsion

We consider the effects of an external potential -h∑f(S _x ) withh>0,f increasing, on the equilibrium state of a system with a Hamiltonian of the form $$H^0 (S) = \sum\limits_{\left\langle {xy} \right\rangle } {\Phi (S_x - S_y )} ,S_x \in R,x \in Z^d ,d \geqslant 3$$ Φ even and convex, e.g.,Φ(t)=1/2t ² andf(t)=signt. This can be thought of as a model of the interactions between a random interface S _x and a “soft” wall. We show that the random surface is (entropically) repelled to infinity for allh>0, i.e., with probability one,S _x ≥K, for anyK ε R.     

Quantum gravity at very high energies

The problem of time and the quantization of three-dimensional gravity in the strong coupling regime is studied following path integral methods. The time is identified with the volume of spacetime. We show that the effective action describes an infinite set of massless relativistic particles moving in a curved three-dimensional target space, i.e., a tensionless 3-brane on a curved background. If the cosmological constant is zero the target space is flat and there is no ‘‘ graviton" propagation (i.e., G[g_ij(2),g_ij(1)]=0). If the cosmological constant is different from zero, 3D gravity is both classical and quantum mechanically soluble. Indeed, we find the following results: (i) the general exact solutions of the Einstein equations are singular at t=0 showing the existence of a big-bang in this regime and (ii) the propagation amplitude between two geometries 〈g_ij(2),t₂|g_ij(1),t₁〉 vanishes as t→0, suggesting that big-bang is suppressed quantum mechanically. This result is also valid for D>3.     

High-temperature impedance and modulus spectroscopy characterization of La/Mn modified PbTiO3 nanoceramics

Nanocrystalline samples of Pb_1−yLa_y(Ti_1−xMn_x)_(1−y/4)O₃ (PLMT) (y=0.06, x=0, 0.04, 0.07 and 0.10) were prepared by mechanical activation process (i.e., ball milling) followed by some annealing. The formation of single phase tetragonal crystal structure is confirmed by high-resolution X-ray diffraction study and by High resolution transmission electron micrographs (HRTEM), nano-scale compounds. The electrical behavior (i.e., impedance (Z) and electrical modulus (M)) of PLMT ceramics was studied by impedance spectroscopy technique in high temperature range. This study was carried out by means of the simultaneous analysis of the complex impedance (Z^?) and electrical modulus (M^*) functions in a wide frequency range (1 kHz-1 MHz). Impedance analysis has shown the grain and grain boundary contributions by an equivalent circuit model. Modulus analysis has provided vast information on charge transport processes. The simultaneous representation of the imaginary part of impedance and electric modulus (Z″, M″) vs. frequency revealed the localization of relaxation. The activation energy obtained from relaxation data may be attributed to oxygen ion vacancies.     

Sur l'evolution des proprietes physiques de la perovskite GdCoO3 entre 77 et 1200 K

GdCoO₃, which has the GdFeO₃ structure, has been studied between 77 and 1200 K by D.T.A., X-ray diffraction, magnetic susceptibility, electric conductivity and thermoelectric power. All properties observed, although different from those of LaCoO₃, fit with the corresponding Goodenough localized electron model. With rising temperature cobalt ions pass progressively from a low-spin Co^III(t⁶_2ge_g⁰) state to a Co³⁺(t⁴_2ge_g²) high-spin state.     

Orbital Divergence and Relaxation in the Gravitational N-Body Problem

One of the fundamental aspects of statistical behaviour in many-body systems is exponential divergence of neighbouring orbits, which is often discussed in terms of Liapounov exponents. Here we study this topic for the classical gravitational N-body problem. The application we have in mind is to old stellar systems such as globular star clusters, where N10⁶, and so we concentrate on spherical, centrally concentrated systems with total energy E<0. Hitherto no connection has been made between the time scale for divergence (denoted here by t _e ) and the time scale on which the energies of the particles evolve because of two-body encounters (i.e., the two-body relaxation time scale, t _r ), even though both may be calculated by similar considerations. In this paper we give a simplified model showing that divergence in phase space is initially roughly exponential, on a timescale proportional to the crossing time (defined as a mean time for a star to cross from one side of the system to another). In this phase t _e <<t _r , if N is not too small (i.e., N30). After several e-folding times, the model shows that the divergence slows down. Thereafter the divergence (measured by the energies of the bodies) varies with time as t ^1/2, on a timescale nearly proportional to the familiar two-body relaxation timescale, i.e., t _e t _r in this phase. These conclusions are illustrated by numerical results.     

Self-similar distribution in “giant” magnetic flux creep

The problem of magnetic field penetration into the half-space is considered in parallel geometry in an external magnetic field increasing with time in accordance with the law B(0, t, τ₀ = B _{c 1} (1 + t/τ₀) ^m , m ≥ 0, t ≥ 0 (τ ₀ is the time of magnetic flux redistribution and B _{c 1} is the lower critical field). It is assumed that the flow of vortices is thermally activated in the “giant” creep mode (i.e., for weak pinning creep and high temperatures). A model equation is derived for describing the magnetic flux evolution. Analytic formulas are obtained for the depth and velocity of magnetic field penetration. It is shown that the giant creep regime is stable for 0 ≤ m ≤ 1/2.