ShantanuT01/DACTYL-Pretraining huggingface dataset:
We compute the boundary state associated with a moving D$p$-brane in the presence of the open string tachyon field as a background field. The effect of the tachyon condensation on the boundary state will be discussed. It leads to a boundary state associated with a lower dimensional moving D-brane or a stationary instantonic D-brane. The former originates from condensation along the spatial directions and the latter comes from the temporal direction of the D-brane's worldvolume. Using the boundary state we also study the interaction amplitude between two arbitrary D$p_1$ and D$p_2$-branes. The long range behavior of the amplitude is investigated which shows an obvious deviation from the conventional form, due to the presence of the background tachyon field.
The subject of this article is a matched microstructure model for Newtonian fluid flows in fractured porous media. This is a homogenized model which takes the form of two coupled parabolic differential equations with boundary conditions in a given (two-scale) domain in Euclidean space. The main objective is to establish the local well-posedness in the strong sense of the flow. Two main settings are investigated: semi-linear systems with linear boundary conditions and semi-linear systems with nonlinear boundary conditions. With the help of analytic semigoups we establish local well-posedness and investigate the long-time behaviour of the solutions in the first case: we establish global existence and show that solutions converge to zero at an exponential rate.
The familiar cascade measures are sequences of random positive measures obtained on $[0,1]$ via $b$-adic independent cascades. To generalize them, this paper allows the random weights invoked in the cascades to take real or complex values. This yields sequences of random functions whose possible strong or weak limits are natural candidates for modeling multifractal phenomena. Their asymptotic behavior is investigated, yielding a sufficient condition for almost sure uniform convergence to nontrivial statistically self-similar limits. Is the limit function a monofractal function in multifractal time? General sufficient conditions are given under which such is the case, as well as examples for which no natural time change can be used. In most cases when the sufficient condition for convergence does not hold, we show that either the limit is 0 or the sequence diverges almost surely. In the later case, a functional central limit theorem holds, under some conditions. It provides a natural normalization making the sequence converge in law to a standard Brownian motion in multifractal time.
It is shown both analytically and numerically that the suggested lattice Boltzmann model on rectangular grids leads to anisotropic dissipation of fluid momentum and thus it does not recover Navier-Stokes equations. Hence, it cannot be used for the simulation of hydrodynamics.
The non-relativistic Chern-Simons theory with the single-valued anyonic field is proposed as an example of q-deformed field theory. The corresponding q-deformed algebra interpolating between bosons and fermions,both in position and momentum spaces, is analyzed.A possible generalization to a space with an arbitrary dimension is suggested.
Decay of the superdeformed bands have been studied mainly concentrating upon the decay-out spin, which is sensitive to the tunneling probability between the super- and normal-deformed wells. Although the basic features are well understood by the calculations, it is difficult to precisely reproduce the decay-out spins in some cases. Comparison of the systematic calculations with experimental data reveals that values of the calculated decay-out spins scatter more broadly around the average value in both the $A \approx$ 150 and 190 regions, which reflects the variety of calculated tunneling probability in each band.
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but challenging issue in modeling structure and dynamics of a broad range of material systems across variable scales. This generalized phase field crystal type approach is based upon the complete expansion of particle direct correlation functions and the concept of isotropic tensors. Through applications to the modeling of various two- and three-dimensional crystalline structures, our study demonstrates the capability of bond angle control in this continuum field theory and its effects on the emergence of ordered phases, and provides a systematic way of tunable angle analysis for crystalline microstructures.
Recently full O(alpha_s^2, alpha_s*beta, beta^2) corrections to the threshold total cross section for e+e- to ttbar have been calculated, and the reported corrections turned out to be unexpectedly large. We study how to reduce theoretical uncertainties of the cross section. We adopt a new mass definition proposed by Beneke, which incorporates a renormalon-pole cancellation in the total energy of a static quark-antiquark pair. This improves the convergence of the 1S resonance mass, while the normalization of the cross section scarcely changes. We argue that resummations of logarithms are indispensable, since two largely separated scales dictate the shape of the cross section. As a first step, we resum logarithms in the Coulombic part of the t-tbar potential and observe a considerable improvement in the convergence of corresponding corrections. There still remain, however, large corrections, which arise from a 1/r^2 term in the ttbar potential. We also calculate full O(alpha_s^2, alpha_s*beta, beta^2) corrections to the momentum distributions of top quarks in the threshold region. Corrections to the distribution shape are small on the 1S resonance. At higher energies, corrections become larger.
In this note, I study a comparison map between a motivic and \'{e}tale cohomology group of an elliptic curve over $\mathbb{Q}$ just outside the range of Voevodsky's isomorphism theorem. I show that the property of an appropriate version of the map being an isomorphism is equivalent to certain arithmetical properties of the elliptic curve.
Nonstandard neutrino properties (masses, mixing, sterile states, electromagnetic interactions, and so forth) can have far-reaching ramifications in astrophysics and cosmology. We look at the most interesting cases in the light of the powerful current indications for neutrino oscillations.
We use N=2 harmonic and projective superspaces to formulate the most general `Ansatz' for the SU(2)_R invariant hypermultiplet low-energy effective action (LEEA) in four dimensions, which describes the two-parametric family of the hyper-K"ahler metrics generalizing the Atiyah-Hitchin metric. We then demonstrate in the very explicit and manifestly N=2 supersymmetric way that the (magnetically charged, massive) single hypermultiplet LEEA in the underlying non-abelian N=2 supersymmetric quantum field theory can receive both perturbative (e.g., in the Coulomb branch) and non-perturbative (e.g., in the Higgs branch) quantum corrections. The manifestly N=2 supersymmetric Feynman rules in harmonic superspace can be used to calculate the perturbative corrections described by the Taub-NUT metric. The non-perturbative corrections (due to instantons and anti-instantons) can be encoded in terms of an elliptic curve, which is very reminiscent to the Seiberg-Witten theory. Our four-dimensional results agree with the three-dimensional Seiberg-Witten theory and instanton calculations.
We present a microscopic magnetic domain imaging study of single-shot all-optical magnetic toggle switching of a ferrimagnetic Gd$_{26}$Fe$_{74}$ film with out-of-plane easy axis of magnetization by x-ray magnetic circular dichroism photoelectron emission microscopy. Individual linearly polarized laser pulses of 800 nm wavelength and 100 fs duration above a certain threshold fluence reverse the sample magnetization, independent of the magnetization direction, the so-called toggle switching. Local deviations from this deterministic behavior close to magnetic domain walls are studied in detail. Reasons for nondeterministic toggle switching are related to extrinsic effects, caused by pulse-to-pulse variations of the exciting laser system, and to intrinsic effects related to the magnetic domain structure of the sample. The latter are, on the one hand, caused by magnetic domain wall elasticity, which leads to a reduction of the domain-wall length at sharp tipped features. These features appear after the optical switching at positions where the line of constant threshold fluence in the Gaussian footprint of the laser pulse comes close to an already-existing domain wall. On the other hand, we identify the presence of laser-induced domain-wall motion in the toggle-switching event as a further cause for local deviations from purely deterministic toggle switching.
We extend basic regularity of the free boundary of the obstacle problem to some classes of heterogeneous quasilinear elliptic operators with variable growth that includes, in particular, the $p(x)$-Laplacian. Under the assumption of Lipschitz continuity of the order of the power growth $p(x)>1$, we use the growth rate of the solution near the free boundary to obtain its porosity, which implies that the free boundary is of Lebesgue measure zero for $p(x)$-Laplacian type heterogeneous obstacle problems.   Under additional assumptions on the operator heterogeneities and on data we show, in two different cases, that up to a negligible singular set of null perimeter the free boundary is the union of at most a countable family of $C^1$ hypersurfaces:   i) by extending directly the finiteness of the $(n-1)$-dimensional Hausdorff measure of the free boundary to the case of heterogeneous $p$-Laplacian type operators with constant $p$; $1<p<\infty$;   ii) by proving the characteristic function of the coincidence set is of bounded variation in the case of non degenerate or non singular operators with variable power growth $p(x)>1$.
After a brief introduction to low-x QCD and to resummation approaches, I illustrate the predictions for the gluon Green function and splitting function of a recent renormalization-group improved small-x resummation scheme. I argue, on this basis, that the range of validity of perturbative calculations is considerably extended in rapidity with respect to leading log expectations. The perturbative high-energy exponents are predicted in a phenomenologically interesting range, and significant preasymptotic effects are found. In particular, the splitting function shows a shallow dip in the moderate-x region, followed by the expected small-x power increase.
In this work a satisfactory, simple theoretical prediction of the data corresponding to observationally (by fine tuning condition) estimated value of the cosmological constant is given. It is supposed (in conceptually analogy with holographic principle) that cosmological constant, like classical surface tension coefficient by a liquid drop, does not correspond to a volume (bulk) vacuum mass (energy) density distribution but that it corresponds to a surface vacuum mass (energy) density distribution. Then form of given surface mass distribution and fine tuning condition imply observed growing (for $\sim$ 61 magnitude order) of the scale factor (from initial, corresponding to Planck length, to recent, at the beginning of the cosmic acceleration, corresponding to 10 Glyr length).
A new method of combined loading was developed for manufacturing large - scale ingot of alpha-beta titanium alloy Ti-6Al-4V with the diameter of the gauge 120 mm and the length 300 mm. The process includes torsion with simultaneous tensile deformation, followed by a single compression and drawing of the ingot in alpha-beta temperature phase fields. Ingot structure and mechanical property evaluation was performed after deformation and post-deformation heating. The ingots had completely homogeneous macrostructure. The ingot microstructures were alpha plus beta with a mean grain size of d=10 m. There has not been any significant difference in microstructure of central and periphery areas in the cross section of the ingot.
Let $c$ be a positive constant. We show that if $r=\lfloor cn^{1/3}\rfloor$ and the members of ${[n]\choose r}$ are chosen sequentially at random to form an intersecting hypergraph then with limiting probability $(1+c^3)^{-1}$, as $n\to\infty$, the resulting family will be of maximum size ${n-1\choose r-1}$.
We study the generation and evolution of density perturbations and peculiar velocities due to primordial magnetic fields. We assume that a random magnetic field was present before recombination and follow the field's effect on the baryon fluid starting at recombination. We find that magnetic fields generate growing density perturbations on length scales larger than the magnetic Jeans length, $\lambda_B$, and damped oscillations for scales smaller than $\lambda_B$. For small wavenumbers $k$ (large length scales), we find the magnetic field-induced density power spectrum generally scales as $k^4$. We derive the magnetic Jeans length explicitly by including the back--reaction of the velocity field onto the magnetic field by decomposing the magnetic field into a force-free background field and perturbations about it. Depending on the strength of the magnetic field and the ultraviolet cutoff of its spectrum, structure can be generated on small or intermediate scales early in the history of the universe. For a present {\it rms} magnetic field of $10^{-10}$ G on intergalactic scales, we find that perturbations on galactic scales could have gone non--linear at $z \simeq 6$. Finally, we discuss how primordial magnetic fields affect scenarios of structure formation with non--baryonic dark matter.
In a recent paper Gunnells, Scott and Walden have determined the complete spectrum of the Schreier graph on the symmetric group corresponding to the Young subgroup $S_{n-2}\times S_2$ and generated by initial reversals. In particular they find that the first nonzero eigenvalue, or spectral gap, of the Laplacian is always 1, and report that "empirical evidence" suggests that this also holds for the corresponding Cayley graph. We provide a simple proof of this last assertion, based on the decomposition of the Laplacian of Cayley graphs, into a direct sum of irreducible representation matrices of the symmetric group.
Within a covariant effective one-boson exchange model for the $T$ matrix of $NN$ interactions we present detailed calculations of bremsstrahlung cross sections for proton - proton and proton - neutron reactions at beam energies in the 1 GeV region. Besides pure bremsstrahlung processes we consider photons from $\Delta$ decays and contributions from the $\eta \to \gamma \gamma$ process. At beam energies above 700 MeV the $\Delta$ decay channel dominates the spectra at large photon energies, where the interference between non-resonance processes and the $\Delta$ decay channel becomes also important. Low energy photons stem from pure bremsstrahlung processes. The available experimental data at 730 MeV beam energy is well described. We extrapolate the model down to 280 MeV, where more detailed experimental data exist, and find agreement with angular distributions.
In the present paper some consequences of the assumption that in the center of the Galaxy there is a supermassive compact object without the events horizon are considered. The possibility of existence of such object has been argued earlier. It is shown, that accretion of a surrounding gas onto the object can cause nuclear burning in a superficial layer which owing to comptonization in a hotter layer, laying above, can manifest itself in observable IR and X spectra. The contribution of an intrinsic magnetic moment of the object in the observable synchrotron radiation is considered, using transfer equations, taking into account influence of gravitation on the energy and movement of photons.
A new integral with respect to an integer-valued random measure is introduced. In contrast to the finite variation integral ubiquitous in semimartingale theory (Jacod and Shiryaev, 2003, II.1.5), the new integral is closed under stochastic integration, composition, and smooth transformations. The new integral gives rise to a previously unstudied class of pure-jump processes: the sigma-locally finite variation pure-jump processes. As an application, it is shown that every semimartingale $X$ has a unique decomposition $$X = X_0 + X^{\mathrm{qc}}+X^{\mathrm{dp}},$$ where $X^{\mathrm{qc}}$ is quasi-left-continuous and $X^{\mathrm{dp}}$ is a sigma-locally finite variation pure-jump process that jumps only at predictable times, both starting at zero. The decomposition mirrors the classical result for local martingales (Yoeurp, 1976, Theoreme~1.4) and gives a rigorous meaning to the notions of continuous-time and discrete-time components of a semimartingale. Against this backdrop, the paper investigates a wider class of processes that are equal to the sum of their jumps in the semimartingale topology and constructs a taxonomic hierarchy of pure-jump semimartingales.
We argue that inhomogeneity inherent to the presence of periodic supercurrents in the vortex lattice sorts excitations by energies into the ones that are spatially localized and those that perform motion along large Larmour orbits. This energy threshold results in a new mechanism for the de Haas-van Alphen oscillations which enhances oscillations at B<<Hc2, even for an isotropic superconductor with a constant gap. We suggest that the mechanism is of a general character and can cause the slow decay of the de Haas-van Alphen effect when the field, B, decreases below Hc2.
We present a compelling case for a systematic and comprehensive study of the resolved and unresolved stellar populations, ISM, and immediate environments of galaxies throughout the local volume, defined here as D < 20 Mpc. This volume is our cosmic backyard and the smallest volume that encompasses environments as different as the Virgo, Ursa Major, Fornax and (perhaps) Eridanus clusters of galaxies, a large number and variety of galaxy groups, and several cosmic void regions. In each galaxy, through a pan-chromatic (160--1100nm) set of broad-band and diagnostic narrow-band filters, ISM structures and individual luminous stars to >~1 mag below the TRGB should be resolved on scales of <5 pc (at D <~ 20 Mpc, lambda ~ 800nm, for mu_I >~ 24 mag/arcsec^2 and m_{I,TRGB} <~ 27.5 mag). Resolved and unresolved stellar populations would be analyzed through color-magnitude and color-color diagram fitting and population synthesis modeling of multi-band colors and would yield physical properties such as spatially resolved star formation histories. The ISM within and around each galaxy would be analyzed using key narrow-band filters that distinguish photospheric from shock heating and provide information on the metallicity of the gas. Such a study would finally allow unraveling the global and spatially resolved star formation histories of galaxies, their assembly, satellite systems, and the dependences thereof on local and global environment within a truly representative cosmic volume. The proposed study is not feasible with current instrumentation but argues for a wide-field (>~250 arcmin^2), high-resolution (<~0.020"--0.065" [300--1000nm]), ultraviolet--near-infrared imaging facility on a 4m-class space-based observatory.
The next generation of Imaging Atmospheric Cherenkov Telescopes (IACTs) will open the regime between approx. 30 GeV and 200 GeV to ground-based gamma observations with unprecedented point source sensitivity and source location accuracy. I examine the prospects of observing the unidentified objects (UNIDs) of the Third EGRET Catalog using the IACT observatories currently under construction by the CANGAROO, HESS, MAGIC and VERITAS collaborations. Assuming a modest spectral steepening similar to that observed in the inverse Compton component of the Crab Nebula spectrum and taking into account the sensitivity of the instruments and its zenith angle dependence, a detailed list of 78 observable objects is derived which is then further constrained to 38 prime candidates. The characteristics of this agenda are discussed.
An adsorption-desorption (or parking-lot) model can reproduce qualitatively the densification kinetics and other features of a weakly vibrated granular material. Here we study the the two-time correlation and response functions of the model and demonstrate that their behavior is consistent with recently observed memory effects in granular materials. Although the densification kinetics and hysteresis are robust properties, we show that the aging behavior of the adsorption-desorption model is different from other models of granular compaction. We propose an experimental test to distinguish the possible aging behaviors.
We consider a thin accretion disc warped due to the Bardeen-Petterson effect, presenting both analytical and numerical solutions for the situation that the two viscosity coefficients vary with radius as power law, with the two power law indices not necessarily equal. The analytical solutions are compared with numerical ones, showing that our new analytical solution is more accurate than previous one, which overestimates the inclination changing in the outer disc. Our new analytical solution is appropriate for moderately warped discs, while for extremely misaligned disc, only numerical solution is appropriate.
We study frustrated spin-1/2 dimer systems in two dimensions with a bilayer structure, where spins are ferromagnetically coupled in dimers. Our model includes frustrated two-spin exchange interactions as well as four-spin interaction. We pay particular attention to the spin nematic phase, which does not exhibit any magnetic (spin-dipole) order but has a spin-quadrupolar long-range order. Employing a perturbation calculation, a mean-field approximation, and a numerical many-variable variational Monte Carlo method, we determine ground-state phase diagrams on various two-dimensional lattices. It is found that the model exhibits the spin nematic phase with ferro-quadrupolar order in a wide parameter region, in addition to conventional magnetically-ordered phases. In particular, it is shown that even when the four-spin interactions are absent, frustrated two-spin exchange interactions can realize the spin nematic phase as a result of strong interdimer correlations. It is also found that the phase transitions between the spin nematic phase and antiferromagnetic phases can be continuous. Furthermore, we present some exact arguments that various phases including the spin nematic phase and the vector chiral (p-type nematic) phase emerge from an SU(4) symmetric point in the model by the addition of appropriate perturbative interactions. The spin nematic phase generated from the SU(4) point is connected with the spin nematic phase found numerically in the system with only two-spin interactions.