Wave Breaking in a Class of Nonlocal Dispersive Wave Equations

Abstract

The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in di!erent physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which also incorporate physics of short wavelength scales. The model is identified by a renormalization of an infinite dispersive di!erential operator, followed by further specifications in terms of conservation laws associated with the underlying equation. Several well-known models are thus rediscovered. Wave breaking criteria are obtained for several models including the Burgers-Poisson system, the Camassa-Holm type equation and an Euler-Poisson system. The wave breaking criteria for these models are shown to depend only on the negativity of the initial velocity slope relative to other global quantities.     

Construction of the effective Lagrangian of pionic processes for arbitrary SU(2)×SU(2) breaking

By assuming that SU(2)×SU(2) symmetry is broken by the isoscalar element of the representation (l, l), effective Lagrangians reproducing the results of current algebra and the PCAC assumption can be constructed by a direct method suggested byR. Dashen andM. Weinstein. The symmetry-breaking parts of these Lagrangians are the solutions (in closed form) of the differential equation for the breaking parts in Weinberg’s formalism.

     

Dipole bands in the oblate-shaped195Pb

The nucleus¹⁹⁵Pb has been populated with the¹⁸⁴W+¹⁶O reaction at 113 MeV. Two dipole γ-ray cascades have been observed using the EUROGAM spectrometer. A comprehensive level scheme related to these structures has been established. Multiparticle configurations are attributed to these high-spin structures from detailed comparison with the neighbouring nuclei,¹⁹³Hg,¹⁹⁴Pb and¹⁹⁵Tl. Band crossings due to i13/2 neutron pair breaking are observed in¹⁹⁵Pb at about the same frequencies as in the isotone¹⁹³Hg.

     

Lie Symmetries,Infinite-Dimensional Lie Algebras and Similarity Reductions of Certain (2+1)-Dimensional Nonlinear Evolution Equations

Abstract

The Lie point symmetries associated with a number of (2 + 1)-dimensional generalizations of soliton equations are investigated. These include the Niznik – Novikov – Veselov equation and the breaking soliton equation, which are symmetric and asymmetric generalizations respectively of the KDV equation, the (2+1)-dimensional generalization of the nonlinear Schrödinger equation by Fokas as well as the (2+1)-dimensional generalized sine-Gordon equation of Konopelchenko and Rogers. We show that in all these cases the Lie symmetry algebra is infinite-dimensional; however, in the case of the breaking soliton equation they do not possess a centerless Virasorotype subalgebra as in the case of other typical integrable (2+1)-dimensional evolution equations. We work out the similarity variables and special similarity reductions and investigate them.     

Technical Reports: Atoms to Aerosols—The Chemical Dynamics Beamline

Chemical dynamics is the study of the elementary processes and interactions in chemistry. Fundamental properties such as dipole moments, ionization energies, electron affinities, proton affinities, and electronic structure all contribute to the photochemistry, radiationless processes and reactivity underlying all physical processes. The making and breaking of chemical bonds, and the energy partitioning in chemical systems after transformation, are also in the domain of chemical dynamics.

The valence shell, the outermost shell of electrons in a system, contributes most to the physical properties of material. It is these electrons that are shared in covalent bonding, transferred in ionic systems, coupled to form bands in bulk material, and interact most strongly with the environment.     

Plastic coating of glass fibers and its influence on strength

Abstract

Sodium borosilicate glass fibers pulled from the melt were plastic coated “on-line” to preserve the fiber strength. By the use of tapered nozzles within the coating applicator the coating could be made concentric around the fiber, and a 40-μm concentric coating was found to be sufficient for the fiber to withstand a mild abrasion test with no deterioration in strength. Strength measurements made in ambient conditions showed that the fiber had a uniform breaking strain of 4% elongation. The same fiber measured at liquid nitrogen temperatures had a breaking strain of 14%, even after extensive handling, which is close to the theoretical glass cohesive strength.     

Effect on Jarlskog Determinant Above the GUT Scale Within Four Flavor Neutrino Framework

We study the Planck scale effects on Jarlskog determiant in the four flavor framework. On electroweak symmetry breaking, quantum gravitational effects lead to an effective SU(2) × U(1) invariant dimension-5 Lagrangian including neutrino and Higgs forces, which perturbed the neutrino mass term and produce an extra terms in the neutrino mass matrix. We consider that gravitational interaction is independent from flavor and compute the Jarlskog determiant due to Planck scale effects. In the case of leptonic sector, the strentgh of CP violation is measured by Jarlskog determiant. We applied our approach to study Jarlskog determinant in the four flavor neutrino mixing above the GUT scale.

     

The breaking of O(6) symmetry in 118Xe and 120Xe

The spectra of the isotopes of xenon are analysed from the point of view of O(6) symmetry breaking. It is pointed out that the excitation energies of the states 0 ₃ ⁺ can be used in detecting breaking of the symmetry. The nature of symmetry breaking in ¹¹⁸Xe and ¹²⁰Xe is indicated.     

Dislocation damping in alkali halides

In the amplitude independent region the dislocation damping is attributed to either phonon-drag (Granato-Lücke theory) or to the compensating charge-cloud surrounding electrically charged dislocations (Robinson-Birnbaum theory). The experimental results for the dependence of the damping on temperature, frequency and dislocation charge are compared with the two theories. Since it is found that in some cases it is necessary to include both forms of damping, a more complete theory is developed which includes both terms.

In the amplitude dependent region the dislocation damping was thought to be due to the dislocations breaking away from pinning points or breaking through the compensating charge-cloud. Using the piezoelectric defect results for electrically charged dislocation in KCl the force-displacement hysteresis loop for the moving dislocations is determined together with the force-displacement curves for dislocations assuming phonon and charge-cloud damping. These results are found to be inconsistent with the “break away” models for amplitude dependence but instead to be consistent with the restoring force due to an elliptical compensation charge cloud, with a size proportional to the square root of the dislocation charge.     

Grand unification with local supersymmetry

We study general conditions for obtaining spontaneous breaking of local supersymmetry in N = 1 supergravity coupled to supersymmetric matter. We consider in particular the coupling of N = 1 supergravity to grand unified theories like SU(5) and study the conditions which must be met in order to obtain a realistic model. Specific models are built in which local supersymmetry is broken at a scale √M_Wm_p ～ 10¹⁰ GeV. This breaking of supersymmetry is only detected at low energies through soft terms breaking explicitly the global supersymmetry. These soft terms (scalar masses, gaugino masses and trilinear scalar couplings) are renormalized at low energies according to the renormalization group. The (mass)² of the Higgs doublet evolve towards negative values at low energies giving rise to SU(2) × U(1) breaking as a radiative effect of local supersymmetry breaking. We finally point out the possible relevance of non-renormalizable superpotentials for the problem of fermion masses.     

The Influence of Quantum Field Fluctuations on Chaotic Dynamics of Yang–Mills System

Abstract

On example of the model field system we demonstrate that quantum fluctuations of non-abelian gauge fields leading to radiative corrections to Higgs potential and spontaneous symmetry breaking can generate order region in phase space of inherently chaotic classical field system. We demonstrate on the example of another model field system that quantum fluctuations do not influence on the chaotic dynamics of non-abelian Yang–Mills fields if the ratio of bare coupling constants of Yang–Mills and Higgs fields is larger then some critical value. This critical value is estimated.     

Bose condensation and spontaneous breaking of the uniformity of time

The spontaneous breaking of gauge invariance accompanying Bose condensation in mesoscopic systems corresponds to thermodynamically equilibrium ground states with nonintegral average particle number and results in a spontaneous breaking of the uniformity of time. In Fermi systems, the breaking of gauge invariance can be also accompanied by spontaneous breaking of invariances with respect to spatial rotations by an angle of 2π and double time reversal. Possible experiments are discussed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 963–969 (25 June 1996)     

Brillouin and raman scattering from glasses under high pressure

Abstract

Brillouin and Raman Scattering Spectra in SiO₂ and GeO₂ glasses have been measured in a diamond anvil cell up to pressures of 14 GPa. The elastic properties and equation of state for each glass type were obtained from the Brillouin scattering measurements with respect to pressure. Both elastic constants and compressibility of SiO₂ and GeO₂ showed anomalous behavior with respect to pressure. This anomalous behavior is reconciled with a model based on the pressure dependent bending of the oxygen angles in both glass types. The Raman measurements corroborate the conclusions from the Brillouin scattering results, namely that the SiO₂ and GeO₂ bond angles are changing with pressure or the oxygen angle distribution is changed without bond breaking.     

Monopoles and holography

Several lattice collaborations performing simulations with 2+1 light dynamical quarks have experienced difficulties in fitting their data with standard N _f = 3 chiral expansions at next-to-leading order, yielding low values of the quark condensate and/ or the decay constant in the N _f = 3 chiral limit. A reordering of these expansions seems required to analyse these data in a consistent way. We discuss such a reordering, known as Resummed Chiral Perturbation Theory, in the case of pseudoscalar masses and decay constants, pion and kaon electromagnetic form factors and K _ℓ3 form factors. We show that it provides a good fit of the recent results of two lattice collaborations (PACS-CS and RBC/UKQCD). We describe the emerging picture for the pattern of chiral symmetry breaking, marked by a strong dependence of the observables on the strange quark mass and thus a significant difference between chiral symmetry breaking in the N _f = 2 and N _f =3 chiral limits. We discuss the consequences for the ratio of decay constants F _K /F _π and the K ℓ3 form factor at vanishing momentum transfer.

     

STUDY OF HEAVY ION MODIFIED CR-39 (DIETHYLENEGLYCOL BISALLYL CARBONATE)

The commercially available solid state nuclear track detector CR-39 was bombarded with 100 MeV Si⁸⁺ ions. The Fourier transfonned infrared (FTIR) spectroscopic technique was employed for studying the changes in chemical properties whereas differential scanning calorimetry was used for studying the changes in thermal properties. It was observed that there were substantial chemical modifications in the sample, such as the breaking of C-0 single bonds and the formation of phenolic 0-H bonds. lt was further observed that CR-39 is amorphous and rigid and shows no glass transition temperature.     

Gauge hierarchies of SU(N) grand unification

The structure of spontaneous breaking of SU(N) gauge symmetry for grand unification is investigated. The results obtained are applied to the analysis of SU(8) symmetry for which possible ways of breaking and intermediate symmetries are considered. It is assumed that the SU(8) group unifies the subgroups of colour, standard electroweak and horizontal symmetries. We find conditions which it is necessary to impose on the vacuum expectation values of Higgs multiplets to provide an arbitrary breaking pattern of SU(N) symmetry and conserve any intermediate symmetry. If in the SU(8) models considered fermions and mirror fermions do not violate the (V-A) and (V+A) structure of weak interactions, then their masses should not be greater than ～10² GeV. It is also shown that the contributions of fermion and Higgs multiplets to the renormalization group equation for the coupling constant of any subgroup of SU(N) are identical. Renormalization group identities for the case of arbitrary SU(N) breaking are given where the contribution of Higgs multiplets have been taken into account (but they cancel each other). Using these identities one can calculate the mass values for the breaking of the intermediate symmetries in the SU(8) models, and also exclude part of the possible breaking patterns.     

Spontaneous symmetry breaking of a Boseben Fermi mixture in a two-dimensional double-well potential

We study the spontaneous symmetry breaking of a superfluid Bose-Fermi mixture in a two-dimensional double-well potential. The mixture is described by a set of coupled Gross-Pitaevskii equations. The symmetry breaking phenomenon is demonstrated in the two-dimensional double-well potential in the mixture. The results are summarized in the phase diagrams of the mixture particle numbers, which are divided into symmetric and asymmetric regions by the asymmetry ratios. The dynamical pictures of the spontaneous symmetry breaking induced by a gradual transformation of the single-well potential into a double-well one are also illustrated. The properties of the quantum degenerate mixture are explored using the realistic parameters for a ⁴⁰K-⁸⁷Rb system.     

Weak equivalence principle from a spontaneously broken gauge theory of gravity

Further consequences of a finite topological field theory for gravity based on the SL(5,R) gauge group are reported. After symmetry breaking, it induces four-dimensional Einstein spaces with a cosmological constant related to the tiny scale of the symmetry breaking. It is shown that not only a ‘background’ metric emerges from a Higgs-like mechanism, but also consistently the geodesic equation central to Einstein?s equivalence principle. In next order of the symmetry breaking scale, the induced torsion could even provoke a tiny Lorentz violation.     

Split light composite supermultiplets

The splitting induced by soft supersymmetry (SUSY) breaking inside the light composite supermultiplets of confining SUSY gauge theories is studied by effective lagrangian methods. Examples with and without unbroken chiral symmetries are considered. In the former case, for a suitable breaking, the lightest states are $\text{spin}\text{-}\text{1}\text{2}$ fermions. A prototype model for one leptonic family is discussed.