Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras

Polynomial-in-time dependent symmetries are analysed for polynomial-in-time dependent evolution equations. Graded Lie algebras, especially Virasoro algebras, are used to construct nonlinear variable-coefficient evolution equations, both in 1+1 dimensions and in 2+1 dimensions, which possess higher-degree polynomial-in-time dependent symmetries. The theory also provides a kind of new realisation of graded Lie algebras. Some illustrative examples are given.Comment: 11 pages, latex, to appear in J. Phys. A: Math. Ge

Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP equations

By starting from known graded Lie algebras, including Virasoro algebras, new kinds of time-dependent evolution equations are found possessing graded symmetry algebras. The modified KP equations are taken as an illustrative example: new modified KP equations with $m$ arbitrary time-dependent coefficients are obtained possessing symmetries involving $m$ arbitrary functions of time. A particular graded symmetry algebra for the modified KP equations is derived in this connection homomorphic to the Virasoro algebras.Comment: 19 pages, latex, to appear in J. Nonlinear Math. Phy

Invariant solutions of the supersymmetric sine-Gordon equation

A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to the coefficients of the various powers of the anticommuting independent variables. Next, we consider the super-sine-Gordon equation expressed in terms of a bosonic superfield involving anticommuting independent variables. In each case, a Lie (super)algebra of symmetries is determined and a classification of all subgroups having generic orbits of codimension 1 in the space of independent variables is performed. The method of symmetry reduction is systematically applied in order to derive invariant solutions of the supersymmetric model. Several types of algebraic, hyperbolic and doubly periodic solutions are obtained in explicit form.Comment: 27 pages, major revision, the published versio

A Study Of A New Class Of Discrete Nonlinear Schroedinger Equations

A new class of 1D discrete nonlinear Schr${\ddot{\rm{o}}}$dinger Hamiltonians with tunable nonlinerities is introduced, which includes the integrable Ablowitz-Ladik system as a limit. A new subset of equations, which are derived from these Hamiltonians using a generalized definition of Poisson brackets, and collectively refered to as the N-AL equation, is studied. The symmetry properties of the equation are discussed. These equations are shown to possess propagating localized solutions, having the continuous translational symmetry of the one-soliton solution of the Ablowitz-Ladik nonlinear Schr${\ddot{\rm{o}}}$dinger equation. The N-AL systems are shown to be suitable to study the combined effect of the dynamical imbalance of nonlinearity and dispersion and the Peierls-Nabarro potential, arising from the lattice discreteness, on the propagating solitary wave like profiles. A perturbative analysis shows that the N-AL systems can have discrete breather solutions, due to the presence of saddle center bifurcations in phase portraits. The unstaggered localized states are shown to have positive effective mass. On the other hand, large width but small amplitude staggered localized states have negative effective mass. The collison dynamics of two colliding solitary wave profiles are studied numerically. Notwithstanding colliding solitary wave profiles are seen to exhibit nontrivial nonsolitonic interactions, certain universal features are observed in the collison dynamics. Future scopes of this work and possible applications of the N-AL systems are discussed.Comment: 17 pages, 15 figures, revtex4, xmgr, gn

New Integrable Sectors in Skyrme and 4-dimensional CP^n Model

The application of a weak integrability concept to the Skyrme and $CP^n$ models in 4 dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic solutions, is derived. This procedure can be applied to the massive Skyrme model, as well. Moreover, an example of a family of chiral Lagrangians providing exact, finite energy Skyrme-like solitons with arbitrary value of the topological charge, is given. In the case of $CP^n$ models a tower of integrable subsystems is obtained. In particular, in (2+1) dimensions a one-to-one correspondence between the standard integrable submodel and the BPS sector is proved. Additionally, it is shown that weak integrable submodels allow also for non-BPS solutions. Geometric as well as algebraic interpretations of the integrability conditions are also given.Comment: 23 page

Abnormal Brain Iron Metabolism in Irp2 Deficient Mice Is Associated with Mild Neurological and Behavioral Impairments

Iron Regulatory Protein 2 (Irp2, Ireb2) is a central regulator of cellular iron homeostasis in vertebrates. Two global knockout mouse models have been generated to explore the role of Irp2 in regulating iron metabolism. While both mouse models show that loss of Irp2 results in microcytic anemia and altered body iron distribution, discrepant results have drawn into question the role of Irp2 in regulating brain iron metabolism. One model shows that aged Irp2 deficient mice develop adult-onset progressive neurodegeneration that is associated with axonal degeneration and loss of Purkinje cells in the central nervous system. These mice show iron deposition in white matter tracts and oligodendrocyte soma throughout the brain. A contrasting model of global Irp2 deficiency shows no overt or pathological signs of neurodegeneration or brain iron accumulation, and display only mild motor coordination and balance deficits when challenged by specific tests. Explanations for conflicting findings in the severity of the clinical phenotype, brain iron accumulation and neuronal degeneration remain unclear. Here, we describe an additional mouse model of global Irp2 deficiency. Our aged Irp2−/− mice show marked iron deposition in white matter and in oligodendrocytes while iron content is significantly reduced in neurons. Ferritin and transferrin receptor 1 (TfR1, Tfrc), expression are increased and decreased, respectively, in the brain from Irp2−/− mice. These mice show impairments in locomotion, exploration, motor coordination/balance and nociception when assessed by neurological and behavioral tests, but lack overt signs of neurodegenerative disease. Ultrastructural studies of specific brain regions show no evidence of neurodegeneration. Our data suggest that Irp2 deficiency dysregulates brain iron metabolism causing cellular dysfunction that ultimately leads to mild neurological, behavioral and nociceptive impairments

Cavity-induced coherence effects in spontaneous emission from pre-Selection of polarization

Spontaneous emission can create coherences in a multilevel atom having close lying levels, subject to the condition that the atomic dipole matrix elements are non-orthogonal. This condition is rarely met in atomic systems. We report the possibility of bypassing this condition and thereby creating coherences by letting the atom with orthogonal dipoles to interact with the vacuum of a pre-selected polarized cavity mode rather than the free space vacuum. We derive a master equation for the reduced density operator of a model four level atomic system, and obtain its analytical solution to describe the interference effects. We report the quantum beat structure in the populations.Comment: 6 pages in REVTEX multicolumn format, 5 figures, new references added, journal reference adde

A New Nonlinear Liquid Drop Model. Clusters as Solitons on The Nuclear Surface

By introducing in the hydrodynamic model, i.e. in the hydrodynamic equations and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equation (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by the ratio of the square amplitudes in the two minima.Comment: 27 pages, LateX, 8 figures, Submitted J. Phys. G: Nucl. Part. Phys., PACS: 23.60.+e, 21.60.Gx, 24.30.-v, 25.70.e

Anthropogenic Space Weather

Anthropogenic effects on the space environment started in the late 19th century and reached their peak in the 1960s when high-altitude nuclear explosions were carried out by the USA and the Soviet Union. These explosions created artificial radiation belts near Earth that resulted in major damages to several satellites. Another, unexpected impact of the high-altitude nuclear tests was the electromagnetic pulse (EMP) that can have devastating effects over a large geographic area (as large as the continental United States). Other anthropogenic impacts on the space environment include chemical release ex- periments, high-frequency wave heating of the ionosphere and the interaction of VLF waves with the radiation belts. This paper reviews the fundamental physical process behind these phenomena and discusses the observations of their impacts.Comment: 71 pages, 35 figure

Structural and functional consequences of removing the N-terminal domain from the magnesium chelatase ChlH subunit of Thermosynechococcus elongatus

Magnesium chelatase (MgCH) initiates chlorophyll biosynthesis by catalysing the ATP-dependent insertion of Mg2+ into protoporphyrin. This large enzyme complex comprises ChlH, I and D subunits, with I and D involved in ATP hydrolysis, and H the protein that handles the substrate and product. The 148 kDa ChlH subunit has a globular N-terminal domain attached by a narrow linker to a hollow cage-like structure. Following deletion of this ~18 kDa domain from the Thermosynechoccus elongatus ChlH, we used single particle reconstruction to show that the apo- and porphyrin-bound forms of the mutant subunit consist of a hollow globular protein with three connected lobes; superposition of the mutant and native ChlH structures shows that, despite the clear absence of the N-terminal ‘head’ region, the rest of the protein appears to be correctly folded. Analyses of dissociation constants shows that the ΔN159ChlH mutant retains the ability to bind protoporphyrin and the Gun4 enhancer protein, although the addition of I and D subunits yields an extremely impaired active enzyme complex. Addition of the Gun4 enhancer protein, which stimulates MgCH activity significantly especially at low Mg2+ concentrations, partially reactivates the ΔN159ChlH–I–D mutant enzyme complex, suggesting that the binding site or sites for Gun4 on H do not wholly depend on the N-terminal domain