ShantanuT01/DACTYL-Pretraining huggingface dataset:
Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots \cite{ponomarenko} we investigate the level statistics in the simplest tight-binding model for different dot shapes by computer simulation. The results are in a reasonable agreement with the experiment which confirms qualitatively interpretation of observed level statistics in terms of "Dirac billiards" without taking into account many-body effects. It is shown that edge effects are in general sufficient to produce the observed level distribution and that even strong bulk disorder does not change the results drastically.
In a cold-dark-matter universe, cosmological structure formation proceeds in rough analogy to origami folding. Dark matter occupies a three-dimensional 'sheet' of free- fall observers, non-intersecting in six-dimensional velocity-position phase space. At early times, the sheet was flat like an origami sheet, i.e. velocities were essentially zero, but as time passes, the sheet folds up to form cosmic structure. The present paper further illustrates this analogy, and clarifies a Lagrangian definition of caustics and streams: caustics are two-dimensional surfaces in this initial sheet along which it folds, tessellating Lagrangian space into a set of three-dimensional regions, i.e. streams. The main scientific result of the paper is that streams may be colored by only two colors, with no two neighbouring streams (i.e. streams on either side of a caustic surface) colored the same. The two colors correspond to positive and negative parities of local Lagrangian volumes. This is a severe restriction on the connectivity and therefore arrangement of streams in Lagrangian space, since arbitrarily many colors can be necessary to color a general arrangement of three-dimensional regions. This stream two-colorability has consequences from graph theory, which we explain. Then, using N-body simulations, we test how these caustics correspond in Lagrangian space to the boundaries of haloes, filaments and walls. We also test how well outer caustics correspond to a Zel'dovich-approximation prediction.
The process of stimulated Brillouin scattering is described by the model of two-dimensional oscillator. The phenomenon of entanglement which appears in the photon-phonon modes after the interaction with matter is discussed.
We establish the analytic Hasse principle for Diophantine systems consisting of one diagonal form of degree $k$ and one general form of degree $d$, where $d$ is smaller than $k$. By employing a hybrid method that combines ideas from the study of general forms with techniques adapted to the diagonal case, we are able to obtain bounds that grow exponentially in $d$ but only quadratically in $k$, reflecting the growth rates typically obtained for both problems separately. We also discuss some of the most interesting generalisations of our approach.
Forced desorption of a semiflexible polymer chain on a solid substrate is theoretically investigated. The pulling force versus displacement is studied for different adsorption energy and persistence length P. It is found that the relationships between pulling force and cantilever displacement show a series of characteristic force spikes at different persistence length P. These force spikes becomes more pronounced but the average magnitude of this force decrease as P grows. Our results are of relevance to forced desorption of DNA on an attractive wall in single-molecule pulling experiments.
Deep image relighting allows photo enhancement by illumination-specific retouching without human effort and so it is getting much interest lately. Most of the existing popular methods available for relighting are run-time intensive and memory inefficient. Keeping these issues in mind, we propose the use of Stacked Deep Multi-Scale Hierarchical Network, which aggregates features from each image at different scales. Our solution is differentiable and robust for translating image illumination setting from input image to target image. Additionally, we have also shown that using a multi-step training approach to this problem with two different loss functions can significantly boost performance and can achieve a high quality reconstruction of a relighted image.
The available data on $J/\Psi$ photoproduction are analyzed in terms of pomeron exchange, two gluon exchange and photon-gluon fusion models. Allowing the pomeron-quark interaction to be flavour dependent and introducing the soft and hard pomerons it is possible to reproduce the data at $\sqrt{s}{>}$10 GeV and small $|t|$. The two gluon exchange calculations indicate strong sensitivity to the gluon distribution function. The results obtained with the most modern MRST2001 and DL PDF reproduce the forward $J/\Psi$ photoproduction cross section at $\sqrt{s}{>}$10 GeV. The calculations with the photon-gluon fusion model and with MRST2001 and DL PDF are also in reasonable agreement with the data on the total $J/\Psi$ photoproduction cross section. We allocate the $J/\Psi$ photoproduction at low energies and large $|t|$ to the mechanism different from pomeron or two gluon exchanges. We consider that this might be axial vector trajectory exchange that couples to the axial form factor of the nucleon.
It has been shown that a realistic level of magnetization of dense molecular cloud cores can suppress the formation of a rotationally supported disk (RSD) through catastrophic magnetic braking in the axisymmetric ideal MHD limit. In this study, we present conditions for the formation of RSDs through non-ideal MHD effects computed self-consistently from an equilibrium chemical network. We find that removing from the standard MRN distribution the large population of very small grains (VSGs) of ~10 $\AA$ to few 100 $\AA$ that dominate the coupling of the bulk neutral matter to the magnetic field increases the ambipolar diffusivity by ~1--2 orders of magnitude at densities below 10$^{10}$ cm$^{-3}$. The enhanced ambipolar diffusion (AD) in the envelope reduces the amount of magnetic flux dragged by the collapse into the circumstellar disk-forming region. Therefore, magnetic braking is weakened and more angular momentum can be retained. With continuous high angular momentum inflow, RSDs of tens of AU are able to form, survive, and even grow in size, depending on other parameters including cosmic-ray ionization rate, magnetic field strength, and rotation speed. Some disks become self-gravitating and evolve into rings in our 2D (axisymmetric) simulations, which have the potential to fragment into (close) multiple systems in 3D. We conclude that disk formation in magnetized cores is highly sensitive to chemistry, especially to grain sizes. A moderate grain coagulation/growth to remove the large population of VSGs, either in the prestellar phase or during free-fall collapse, can greatly promote AD and help formation of tens of AU RSDs.
A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being one of them. In this letter we present the first evidence for the emergence of scaling (and smallworldness) in software architecture graphs from a well-defined local optimization process. Although the rules that define the strategies involved in software engineering should lead to a tree-like structure, the final net is scale-free, perhaps reflecting the presence of conflicting constraints unavoidable in a multidimensional optimization process. The consequences for other complex networks are outlined.
The Relativistic Hartree-Bogoliubov model is applied in the analysis of ground-state properties of Be, B, C, N, F, Ne and Na isotopes. The model uses the NL3 effective interaction in the mean-field Lagrangian, and describes pairing correlations by the pairing part of the finite range Gogny interaction D1S. Neutron separation energies, quadrupole deformations, nuclear matter radii, and differences in radii of proton and neutron distributions are compared with recent experimental data.
We give a brief review of some generalized continuum theories applied to the crystals with complicated microscopic structure. Three different ways of generalization of the classical elasticity theory are discussed. One is the high-gradient theory, another is the micropolar type theory and the third one is the many-field theory. The importance of the first two types of theories has already been established, while the theory of the third type still has to be developed. With the use of 1D and 2D examples we show for each of these theories where they can be and should be applied, separately or in a combination.
We perform the first three-dimensional radiation hydrodynamical simulations that investigate the growth of intermediate-mass BHs (IMBHs) embedded in massive self-gravitating, dusty nuclear accretion disks. We explore the dependence of mass accretion efficiency on the gas metallicity $Z$ and mass injection at super-Eddington accretion rates from the outer galactic disk $\dot{M}_{\rm in}$, and find that the central BH can be fed at rates exceeding the Eddington rate only when the dusty disk becomes sufficiently optically thick to ionizing radiation. In this case, mass outflows from the disk owing to photoevaporation is suppressed and thus a large fraction ($\gtrsim 40\%$) of the mass injection rate can feed the central BH. The conditions are expressed as $\dot{M}_{\rm in} > 2.2\times 10^{-1}~M_\odot ~{\rm yr}^{-1} (1+Z/10^{-2}~Z_\odot)^{-1}(c_{\rm s}/10~{\rm km~s}^{-1})$, where $c_{\rm s}$ is the sound speed in the gaseous disk. With increasing numerical resolution, vigorous disk fragmentation reduces the disk surface density and dynamical heating by formed clumps makes the disk thickness higher. As a result, the photoevaorative mass-loss rate rises and thus the critical injection rate increases for fixed metallicity. This process enables super-Eddington growth of BHs until the BH mass reaches $M_{\rm BH} \sim 10^{7-8}~M_\odot$, depending on the properties of the host dark-matter halo and metal-enrichment history. In the assembly of protogalaxies, seed BHs that form in overdense regions with a mass variance of 3-4$\sigma$ at $z\sim 15-20$ are able to undergo short periods of their rapid growth and transits into the Eddington-limited growth phase afterwards to be supermassive BHs observed at $z>6-7$.
We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators which are subject to individual heat baths modeled by a collection of harmonic oscillators, and show that this master equation in general contains non-local Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator, and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled, and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.
In this work we study the process of energy dissipation triggered by a slow large scale motion of a magnetized conducting fluid. Our consideration is motivated by the problem of heating the solar corona, which is believed to be governed by fast reconnection events set off by the slow motion of magnetic field lines anchored in the photospheric plasma. To elucidate the physics governing the disruption of the imposed laminar motion and the energy transfer to small scales, we propose a simplified model where the large-scale motion of magnetic field lines is prescribed not at the footpoints but rather imposed volumetrically. As a result, the problem can be treated numerically with an efficient, highly-accurate spectral method, allowing us to use a resolution and statistical ensemble exceeding those of the previous work. We find that, even though the large-scale deformations are slow, they eventually lead to reconnection events that drive a turbulent state at smaller scales. The small-scale turbulence displays many of the universal features of field-guided MHD turbulence like a well developed inertial range spectrum. Based on these observations, we construct a phenomenological model that gives the scalings of the amplitude of the fluctuations and the energy dissipation rate as functions of the input parameters. We find a good agreement between the numerical results and the predictions of the model.
The energy-momentum tensor for a massless conformally coupled scalar field in de Sitter spacetime in the presence of a couple curved branes is investigated. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.
We discuss an alternative form of the supersymmetric D-$p$-brane action which is quadratic in derivatives of $X$ and linear in $F_{\mu \nu}$. This action involves an auxiliary worldvolume tensor and generalises the simplification of the Nambu-Goto action for $p$-branes using a symmetric metric. When the worldvolume gauge field is abelian, it appears as a Lagrange multiplier, and solving the constraint gives the dual form of the ($p+1$)-dimensional action with a $p-2$ form gauge field instead of a vector gauge field. This is illustrated by the example of the dual D-2-brane action, for which the known result is recovered.
The evolution equations of the Yukawa couplings and quark mixings are derived for the one-loop renormalization group equations in the 5D Minimal Supersymmetric Standard Model on an {$S^1 / Z_2$} orbifold. Different possibilities for the matter fields are discussed such as the cases of bulk propagating or brane localised fields. We discuss in both cases the evolution of the mass ratios and the implications for the mixing angles.
We consider in more detail a model previously proposed for the hard X-ray (>10 keV) emission observed from the supernova remnant Cas A, whereby electrons are accelerated by lower-hybrid waves and radiate bremsstrahlung. We consider both cold and thermal plasma limits of the modified two-stream instability that generates the lower-hybrid waves, and by studying time dependent ionization balance for various components of the Cas A ejecta and shocked circumstellar medium, find locations within the shell where one or other of the instabilities may occur. Either instability can be effective, with the cold plasma instability imposing fewer constraints on the shocked reflected ion population responsible for exciting the waves. The instability must be located in the ejecta shocked at the earliest times and therefore closest to the contact discontinuity where magnetic fields are expected to be the strongest. The energy deposited in this ejecta by collisions between accelerated and ambient electrons is broadly consistent with that required to reheat this ejecta to observed temperatures.
We present an approach to the four laws of black hole thermodynamics by utilizing the thermodynamics of quantum coherence. Firstly, Hawking effect is attributed to the decoherence of the two-mode squeezed state in a black hole spacetime. Then use is made of the relative entropy between undecohered and decohered squeezed states whose monotonicity gives the zeroth and the second law, while the first law can be obtained either by the vanishing of the first derivative of relative entropy or by studying the effective thermal model generated by the modular Hamiltonian. Futhermore, information-theoretic arguments give a Planck's form of the third law of black hole thermodynamics. With this approach we can understand the laboratory analogues of black holes solely by quantum theory, and find a way to detect the thermodynamics of black holes produced in colliders.
We review the latest progress in understanding the phase structure of static and neutral Kaluza-Klein black holes, i.e. static and neutral solutions of pure gravity with an event horizon that asymptote to a d-dimensional Minkowski-space times a circle. We start by reviewing the (mu,n) phase diagram and the split-up of the phase structure into solutions with an internal SO(d-1) symmetry and solutions with Kaluza-Klein bubbles. We then discuss the uniform black string, non-uniform black string and localized black hole phases, and how those three phases are connected, involving issues such as classical instability and horizon-topology changing transitions. Finally, we review the bubble-black hole sequences, their place in the phase structure and interesting aspects such as the continuously infinite non-uniqueness of solutions for a given mass and relative tension.
The goal of this paper is to introduce one of the versions of the electromagnetic Lagrangian on a causal set in such a way that would address the non-locality issues inherent to causal set theory. The key idea is that Lagrangian density is assigned to the edges rather than points, and there is a way of defining the concept of "neighboring edges" of a given edge in such a way that each edge has only finitely many neighboring edges which would ultimately allow for the theory to be local. That is to be contrasted with points where every point has infinitely many direct neighbors which is a source of non-locality. The edges are needed in order to define electromagnetic Lagrangian anyway, regardless of the consideration of locality; the novelty of this paper is to assign Lagrangian density to the edges as well. Also, in the other papers edges were both spacelike and timelike, while in this paper they are only timelike. This makes calculations considerably more complicated, but it is crucial in preserving locality since the Lorentz group in a hyperplane perpendicular to the edge is compact only if the edge is timelike.
With the advent of relativistic mechanics, the Lorentz transformation replaced the Galilean transformation based on classical Newtonian mechanics among inertial frames at high uniform velocities, but both transformations are based on Cartesian coordinate system, hence position of particles obtaining linear velocities in space can be obtained. In case where frames are rotating with constant angular velocity, use of Galilean rotational transformation (GRT) is replaced by Franklin transformation, proposed by Philip Franklin in 1922. The modified transformation introduced the concept of rotational motion of points in a rigid body. Both the transformations are based on cylindrical coordinate system. Here we moved a step further for making a relativistic transformation using spherical coordinate system for understanding the behaviour of rotating frames along any axis in the space passing through the center of mass of a symmetrical object (Sphere). We finally came to an understanding about how Special Theory of relativity is found to be applicable in rotational motion using different co-ordinate system.
We study the energy spectrum and the quantized Hall conductance of electrons in a two-dimensional periodic potential with perpendicular magnetic field WITHOUT neglecting the coupling of the Landau bands. Remarkably, even for weak Landau band coupling significant changes in the Hall conductance compared to the one-band approximation of Hofstadter's butterfly are found. The principal deviations are the rearrangement of subbands and unexpected subband contributions to the Hall conductance.
We report on the correlation between the flux, color and polarization variations on time scales of days--months in blazars, and discuss their universal aspects. We performed monitoring of 42 blazars in the optical and near-infrared bands from 2008 to 2010 using TRISPEC attached to the "Kanata" 1.5-m telescope. We found that 28 blazars exhibited "bluer-when-brighter" trends in their whole or a part of time-series data sets. This corresponds to 88% of objects that were observed for >10 days. Thus, our observation unambiguously confirmed that the "bluer-when-brighter" trend is common in the emission from blazar jets. This trend was apparently generated by a variation component with a constant and relatively blue color and an underlying red component. Prominent short-term flares on time scales of days--weeks tended to exhibit a spectral hysteresis; their rising phases were bluer than their decay phases around the flare maxima. In contrast to the strong flux--color correlation, the correlation of the flux and polarization degree was relatively weak; only 10 objects showed significant positive correlations. Rotations of polarization were detected only in three objects: PKS 1510-089, 3C 454.3, and PKS 1749+096, and possibly in S5 0716+714. We also investigated the dependence of the degree of variability on the luminosity and the synchrotron peak frequency, \nu_peak. As a result, we found that lower luminosity and higher \nu_peak objects had smaller variations in their amplitudes both in the flux, color, and polarization degree. Our observation suggests the presence of several distinct emitting sources, which have different variation time-scales, colors, and polarizations. We propose that the energy injection by, for example, internal shocks in relativistic shells is a major factor for blazar variations on time scales of both days and months.
The production of charm quark jets in association with electroweak gauge bosons at the LHC can be used as a tool to constrain quark parton distribution functions. Motivated by recent measurements at the LHC, we calculate cross sections for W/Z +c, comparing these to W/Z+jet, for various PDF sets. The cross-section differences can be understood in terms of the different underlying PDFs, with the strange quark distribution being particularly important for W +c production. We discuss appropriately defined ratios and comment on how the measurements at the LHC can be used to extract information on the strange and charm content of the proton at high scales.