Integrability and Algebraic Solutions for Planar Polynomial Differential Systems with Emphasis on the Quadratic Systems

The paper is divided into two parts. In the first one we present a survey about the theory of Darboux for the integrability of polynomial differential equations

A Budding-Defective M2 Mutant Exhibits Reduced Membrane Interaction, Insensitivity To Cholesterol, And Perturbed Interdomain Coupling

Influenza A M2 is a membrane-associated protein with a C-terminal amphipathic helix that plays a cholesterol-dependent role in viral budding. An M2 mutant with alanine substitutions in the C-terminal amphipathic helix is deficient in viral scission. With the goal of providing atomic-level understanding of how the wild-type protein functions, we used a multipronged site-directed spin labeling electron paramagnetic resonance spectroscopy (SDSL-EPR) approach to characterize the conformational properties of the alanine mutant. We spin-labeled sites in the transmembrane (TM) domain and the C-terminal amphipathic helix (AH) of wild-type (WT) and mutant M2, and collected information on line shapes, relaxation rates, membrane topology, and distances within the homotetramer in membranes with and without cholesterol. Our results identify marked differences in the conformation and dynamics between the WT and the alanine mutant. Compared to WT, the dominant population of the mutant AH is more dynamic, shallower in the membrane, and has altered quaternary arrangement of the C-terminal domain. While the AH becomes more dynamic, the dominant population of the TM domain of the mutant is immobilized. The presence of cholesterol changes the conformation and dynamics of the WT protein, while the alanine mutant is insensitive to cholesterol. These findings provide new insight into how M2 may facilitate budding. We propose the AH–membrane interaction modulates the arrangement of the TM helices, effectively stabilizing a conformational state that enables M2 to facilitate viral budding. Antagonizing the properties of the AH that enable interdomain coupling within M2 may therefore present a novel strategy for anti-influenza drug design

Numerical simulation of a negative ion plasma expansion into vacuum

The expansion into vacuum of a one-dimensional, collisionless, negative ion plasma is investigated in the framework of the Vlasov–Poisson model. The basic equations are written in a ‘‘new time space’’ by use of a rescaling transformation and, subsequently, solved numerically through a fully Eulerian code. As in the case of a two species plasma, the time-asymptotic regime is found to be self-similar with the temperature decreasing as t22. The numerical results exhibit clearly the physically expected effects produced by the variation of parameters such as initial temperatures, mass ratios and charge of the negative ions

Influence of Collision Cascade Statistics on Pattern Formation of Ion-Sputtered Surfaces

Theoretical continuum models that describe the formation of patterns on surfaces of targets undergoing ion-beam sputtering, are based on Sigmund's formula, which describes the spatial distribution of the energy deposited by the ion. For small angles of incidence and amorphous or polycrystalline materials, this description seems to be suitable, and leads to the classic BH morphological theory [R.M. Bradley and J.M.E. Harper, J. Vac. Sci. Technol. A 6, 2390 (1988)]. Here we study the sputtering of Cu crystals by means of numerical simulations under the binary-collision approximation. We observe significant deviations from Sigmund's energy distribution. In particular, the distribution that best fits our simulations has a minimum near the position where the ion penetrates the surface, and the decay of energy deposition with distance to ion trajectory is exponential rather than Gaussian. We provide a modified continuum theory which takes these effects into account and explores the implications of the modified energy distribution for the surface morphology. In marked contrast with BH's theory, the dependence of the sputtering yield with the angle of incidence is non-monotonous, with a maximum for non-grazing incidence angles.Comment: 12 pages, 13 figures, RevTe

Is Gravitational Lensing by Intercluster Filaments Always Negligible?

Intercluster filaments negligibly contribute to the weak lensing signal in general relativity (GR), $\gamma_{N}\sim 10^{-4}-10^{-3}$. In the context of relativistic modified Newtonian dynamics (MOND) introduced by Bekenstein, however, a single filament inclined by $\approx 45^\circ$ from the line of sight can cause substantial distortion of background sources pointing towards the filament's axis ($\kappa=\gamma=(1-A^{-1})/2\sim 0.01$); this is rigorous for infinitely long uniform filaments, but also qualitatively true for short filaments ($\sim 30$Mpc), and even in regions where the projected matter density of the filament is equal to zero. Since galaxies and galaxy clusters are generally embedded in filaments or are projected on such structures, this contribution complicates the interpretation of the weak lensing shear map in the context of MOND. While our analysis is of mainly theoretical interest providing order-of-magnitude estimates only, it seems safe to conclude that when modeling systems with anomalous weak lensing signals, e.g. the "bullet cluster" of Clowe et al., the "cosmic train wreck" of Abell 520 from Mahdavi et al., and the "dark clusters" of Erben et al., filamentary structures might contribute in a significant and likely complex fashion. On the other hand, our predictions of a (conceptual) difference in the weak lensing signal could, in principle, be used to falsify MOND/TeVeS and its variations.Comment: 11 pages, 6 figures, published versio

Nonlinear Dirac operator and quaternionic analysis

Properties of the Cauchy-Riemann-Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3-surface to the cotangent bundle of a complex projective space are computed. A relationship between harmonic spinors of a generalized nonlinear Dirac operator and solutions of the Cauchy-Riemann-Fueter equation are established.Comment: Cosmetic changes onl

A direct probe of cosmological power spectra of the peculiar velocity field and the gravitational lensing magnification from photometric redshift surveys

The cosmological peculiar velocity field (deviations from the pure Hubble flow) of matter carries significant information on dark energy, dark matter and the underlying theory of gravity on large scales. Peculiar motions of galaxies introduce systematic deviations between the observed galaxy redshifts z and the corresponding cosmological redshifts z_cos. A novel method for estimating the angular power spectrum of the peculiar velocity field based on observations of galaxy redshifts and apparent magnitudes m (or equivalently fluxes) is presented. This method exploits the fact that a mean relation between z_cos and m of galaxies can be derived from all galaxies in a redshift-magnitude survey. Given a galaxy magnitude, it is shown that the z_cos(m) relation yields its cosmological redshift with a 1-sigma error of sigma_z~0.3 for a survey like Euclid (~10^9 galaxies at z<~2), and can be used to constrain the angular power spectrum of z-z_cos(m) with a high signal-to-noise ratio. At large angular separations corresponding to l<~15, we obtain significant constraints on the power spectrum of the peculiar velocity field. At 15<~l<~60, magnitude shifts in the z_cos(m) relation caused by gravitational lensing magnification dominate, allowing us to probe the line-of-sight integral of the gravitational potential. Effects related to the environmental dependence in the luminosity function can easily be computed and their contamination removed from the estimated power spectra. The amplitude of the combined velocity and lensing power spectra at z~1 can be measured with <~5% accuracy.Comment: 22 pages, 3 figures; added a discussion of systematic errors, accepted for publication in JCA

Global Structure of Moduli Space for BPS Walls

We study the global structure of the moduli space of BPS walls in the Higgs branch of supersymmetric theories with eight supercharges. We examine the structure in the neighborhood of a special Lagrangian submanifold M, and find that the dimension of the moduli space can be larger than that naively suggested by the index theorem, contrary to previous examples of BPS solitons. We investigate BPS wall solutions in an explicit example of M using Abelian gauge theory. Its Higgs branch turns out to contain several special Lagrangian submanifolds including M. We show that the total moduli space of BPS walls is the union of these submanifolds. We also find interesting dynamics between BPS walls as a byproduct of the analysis. Namely, mutual repulsion and attraction between BPS walls sometimes forbid a movement of a wall and lock it in a certain position; we also find that a pair of walls can transmute to another pair of walls with different tension after they pass through.Comment: 42 pages, 11 figures; a few comments adde

A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators

We explore a nonlocal connection between certain linear and nonlinear ordinary differential equations (ODEs), representing physically important oscillator systems, and identify a class of integrable nonlinear ODEs of any order. We also devise a method to derive explicit general solutions of the nonlinear ODEs. Interestingly, many well known integrable models can be accommodated into our scheme and our procedure thereby provides further understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres