Soliton Resonances for MKP-II

Using the second flow - the Derivative Reaction-Diffusion system, and the third one of the dissipative SL(2,R) Kaup-Newell hierarchy, we show that the product of two functions, satisfying those systems is a solution of the modified Kadomtsev-Petviashvili equation in 2+1 dimension with negative dispersion (MKP-II). We construct Hirota's bilinear representation for both flows and combine them together as the bilinear system for MKP-II. Using this bilinear form we find one and two soliton solutions for the MKP-II. For special values of parameters our solution shows resonance behaviour with creation of four virtual solitons. Our approach allows one to interpret the resonance soliton as a composite object of two dissipative solitons in 1+1 dimensions.Comment: 11 pages, 2 figures, Talk on International Conference "Nonlinear Physics. Theory and Experiment. III", 24 June-3 July, 2004, Gallipoli(Lecce), Ital

Common gauge origin of discrete symmetries in observable sector and hidden sector

An extra Abelian gauge symmetry is motivated in many new physics models in both supersymmetric and nonsupersymmetric cases. Such a new gauge symmetry may interact with both the observable sector and the hidden sector. We systematically investigate the most general residual discrete symmetries in both sectors from a common Abelian gauge symmetry. Those discrete symmetries can ensure the stability of the proton and the dark matter candidate. A hidden sector dark matter candidate (lightest U-parity particle or LUP) interacts with the standard model fields through the gauge boson Z', which may selectively couple to quarks or leptons only. We make a comment on the implications of the discrete symmetry and the leptonically coupling dark matter candidate, which has been highlighted recently due to the possibility of the simultaneous explanation of the DAMA and the PAMELA results. We also show how to construct the most general U(1) charges for a given discrete symmetry, and discuss the relation between the U(1) gauge symmetry and R-parity.Comment: Version to appear in JHE

Lyman alpha line formation in starbursting galaxies II. Extremely Thick, Dustless, and Static HI Media

The Lya line transfer in an extremely thick medium of neutral hydrogen is investigated by adopting an accelerating scheme in our Monte Carlo code to skip a large number of core or resonant scatterings. This scheme reduces computing time significantly with no sacrifice in the accuracy of the results. We applied this numerical method to the Lya transfer in a static, uniform, dustless, and plane-parallel medium. Two types of photon sources have been considered, the midplane source and the uniformly distributed sources. The emergent profiles show double peaks and absorption trough at the line-center. We compared our results with the analytic solutions derived by previous researchers, and confirmed that both solutions are in good agreement with each other. We investigated the directionality of the emergent Lya photons and found that limb brightening is observed in slightly thick media while limb darkening appears in extremely thick media. The behavior of the directionality is noted to follow that of the Thomson scattered radiation in electron clouds, because both Lya wing scattering and Thomson scattering share the same Rayleigh scattering phase function. The mean number of wing scatterings just before escape is in exact agreement with the prediction of the diffusion approximation. The Lya photons constituting the inner part of the emergent profiles follow the relationship derived from the diffusion approximation. We present a brief discussion on the application of our results to the formation of Lya broad absorption troughs and P-Cygni type Lya profiles seen in the UV spectra of starburst galaxies.Comment: 24 papges, 12 figures, The revised version submitted to Ap

Coulomb corrections to bremsstrahlung in electric field of heavy atom at high energies

The differential and partially integrated cross sections are considered for bremsstrahlung from high-energy electrons in atomic field with the exact account of this field. The consideration exploits the quasiclassical electron Green's function and wave functions in an external electric field. It is shown that the Coulomb corrections to the differential cross section are very susceptible to screening. Nevertheless, the Coulomb corrections to the cross section summed up over the final-electron states are independent of screening in the leading approximation over a small parameter $1/mr_{scr}$ ($r_{scr}$ is a screening radius, $m$ is the electron mass, $\hbar=c=1$). Bremsstrahlung from an electron beam of the finite size on heavy nucleus is considered as well. Again, the Coulomb corrections to the differential probability are very susceptible to the beam shape, while those to the probability integrated over momentum transfer are independent of it, apart from the trivial factor, which is the electron-beam density at zero impact parameter. For the Coulomb corrections to the bremsstrahlung spectrum, the next-to-leading terms with respect to the parameters $m/\epsilon$ ($\epsilon$ is the electron energy) and $1/mr_{scr}$ are obtained.Comment: 13 pages, 4 figure

Pseudorandom Generators for Width-3 Branching Programs

We construct pseudorandom generators of seed length $\tilde{O}(\log(n)\cdot \log(1/\epsilon))$ that $\epsilon$-fool ordered read-once branching programs (ROBPs) of width $3$ and length $n$. For unordered ROBPs, we construct pseudorandom generators with seed length $\tilde{O}(\log(n) \cdot \mathrm{poly}(1/\epsilon))$. This is the first improvement for pseudorandom generators fooling width $3$ ROBPs since the work of Nisan [Combinatorica, 1992]. Our constructions are based on the `iterated milder restrictions' approach of Gopalan et al. [FOCS, 2012] (which further extends the Ajtai-Wigderson framework [FOCS, 1985]), combined with the INW-generator [STOC, 1994] at the last step (as analyzed by Braverman et al. [SICOMP, 2014]). For the unordered case, we combine iterated milder restrictions with the generator of Chattopadhyay et al. [CCC, 2018]. Two conceptual ideas that play an important role in our analysis are: (1) A relabeling technique allowing us to analyze a relabeled version of the given branching program, which turns out to be much easier. (2) Treating the number of colliding layers in a branching program as a progress measure and showing that it reduces significantly under pseudorandom restrictions. In addition, we achieve nearly optimal seed-length $\tilde{O}(\log(n/\epsilon))$ for the classes of: (1) read-once polynomials on $n$ variables, (2) locally-monotone ROBPs of length $n$ and width $3$ (generalizing read-once CNFs and DNFs), and (3) constant-width ROBPs of length $n$ having a layer of width $2$ in every consecutive $\mathrm{poly}\log(n)$ layers.Comment: 51 page

How dsDNA breathing enhances its flexibility and instability on short length scales

We study the unexpected high flexibility of short dsDNA which recently has been reported by a number of experiments. Via the Langevin dynamics simulation of our Breathing DNA model, first we observe the formation of bubbles within the duplex and also forks at the ends, with the size distributions independent of the contour length. We find that these local denaturations at a physiological temperature, despite their rare and transient presence, can lower the persistence length drastically for a short DNA segment in agreement with experiment

Wavelength- and material-dependent absorption in GaAs and AlGaAs microcavities

The quality factors of modes in nearly identical GaAs and Al_{0.18}Ga_{0.82}As microdisks are tracked over three wavelength ranges centered at 980 nm, 1460 nm, and 1600 nm, with quality factors measured as high as 6.62x10^5 in the 1600-nm band. After accounting for surface scattering, the remaining loss is due to sub-bandgap absorption in the bulk and on the surfaces. We observe the absorption is, on average, 80 percent greater in AlGaAs than in GaAs and in both materials is 540 percent higher at 980 nm than at 1600nm.Comment: 4 pages, 2 figures, 1 table, minor changes to disucssion of Qrad and Urbach tai

SPH Simulations of Galactic Gaseous Disk with Bar: Distribution and Kinematic Structure of Molecular Clouds toward the Galactic Center

We have performed Smoothed Particle Hydrodynamic (SPH) simulations to study the response of molecular clouds in the Galactic disk to a rotating bar and their subsequent evolution in the Galactic Center (GC) region. The Galactic potential in our models is contributed by three axisymmetric components (massive halo, exponential disk, compact bulge) and a non-axisymmetric bar. These components are assumed to be invariant in time in the frame corotating with the bar. Some noticeable features such as an elliptical outer ring, spiral arms, a gas-depletion region, and a central concentration have been developed due to the influence of the bar. The rotating bar induces non-circular motions of the SPH particles, but hydrodynamic collisions tend to suppress the random components of the velocity. The velocity field of the SPH particles is consistent with the kinematics of molecular clouds observed in HCN (1-0) transition; these clouds are thought to be very dense clouds. However, the l-v diagram of the clouds traced by CO is quite different from that of our SPH simulation, being more similar to that obtained from simulations using collisionless particles. The $l-v$ diagram of a mixture of collisional and collisionless particles gives better reproduction of the kinematic structures of the GC clouds observed in the CO line. The fact that the kinematics of HCN clouds can be reproduced by the SPH particles suggests that the dense clouds in the GC are formed via cloud collisions induced by rotating bar.Comment: 31 pages, 10 pigures, accepted for publication in Ap

Water Use Efficiency in a Furrow System

An existing volumetric balance approach in conjunction with the Kostiakov infiltration equation for determining soil infiltration parameters in a furrow is used to study furrow irrigation in the local environment. Other parameters required include furrow geometry, assumed subsurface profile and flow advance data. A set of adjacent furrows is used to indicate the performance of the field system. The procedure outlined here can be used to evaluate efficiency of continuous mode furrow irrigation. The spatial and temporal variation of infiltration characteristics of a soil are well known. As such, the performance of a furrow irrigation system which uses the soil as a medium of conveyance varies with the ever-changing infiltration behaviour. There is therefore a need for an evaluation procedure to determine water use efficiency which can be followed throughout the irrigation season so as to enable the irrigator to make any necessary changes to improve its performance. This determination of irrigation performance hinges very much on the correct evaluation of the infiltration process, in this case, in dynamic infiltration water flowing overland in small channels. An evaluation example is given