ShantanuT01/DACTYL-Pretraining huggingface dataset:
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being intuitive and models can be easily simulated on a computer in most cases; however, few analytical tools beyond simulation are available. The motivation for this paper is to develop such tools for the analysis of models in biology. In this paper we have identified a broad class of discrete dynamical systems with a finite phase space for which one can derive strong results about their long-term dynamics in terms of properties of their dependency graphs. We classify completely the limit cycles of semilattice networks with strongly connected dependency graph and provide polynomial upper and lower bounds in the general case.
We study the couplings between collective vibrations such as the isovector giant dipole and isoscalar giant quadrupole resonances in tin isotopes in the framework of the time-dependent Hartree-Fock theory with a Skyrme energy density functional. These couplings are a source of anharmonicity in the multiphonon spectrum. In particular, the residual interaction is known to couple the isovector giant dipole resonance with the isoscalar giant quadrupole resonance built on top of it, inducing a nonlinear evolution of the quadrupole moment after a dipole boost. This coupling also affects the dipole motion in a nucleus with a static or dynamical deformation induced by a quadrupole constraint or boost respectively. Three methods associated with these different manifestations of the coupling are proposed to extract the corresponding matrix elements of the residual interaction. Numerical applications of the different methods to 132Sn are in good agreement with each other. Finally, several tin isotopes are considered to investigate the role of isospin and mass number on this coupling. A simple 1/A dependence of the residual matrix elements is found with no noticeable contribution from the isospin. This result is interpreted within the Goldhaber-Teller model.
First principles calculations based on many-electron perturbation theory methods, such as the \textit{ab initio} GW and GW plus Bethe-Salpeter equation (GW-BSE) approach, are reliable ways to predict quasiparticle and optical properties of materials, respectively. However, these methods involve more care in treating the electron-electron interaction and are considerably more computationally demanding when applied to systems with reduced dimensionality, since the electronic confinement leads a slower convergence of sums over the Brillouin zone due to a much more complicated screening environment that manifests in the "head" and "neck" elements of the dielectric matrix. Here, we present two new schemes to sample the Brillouin zone for GW and GW-BSE calculations: the non-uniform neck subsampling method and the clustered sampling interpolation method, which can respectively be used for a family of single-particle problems, such as GW calculations, and for problems involving the scattering of two-particle states, such as when solving the BSE. We tested these methods on several few-layer semiconductors and graphene and show that they perform a much more efficient sampling of the Brillouin zone and yield two to three orders of magnitude reduction in the computer time. These two methods can be readily incorporated into several \textit{ab initio} packages that compute electronic and optical properties through the GW and GW-BSE approaches.
In this work, we utilize the quasinormal modes (QNMs) of a massless scalar perturbation to probe the Van der Waals-like small and large black holes (SBH/LBH) phase transition of charged topological Anti-de Sitter (AdS) black holes in four-dimensional massive gravity. We find that the signature of this SBH/LBH phase transition is detected in the isobaric as well as in the isothermal process.This further supports the idea that the QNMs can be an efficient tool to investigate the thermodynamical phase transition.
In this paper we investigate the asymptotic behavior of anisotropic fractional energies as the fractional parameter $s\in (0,1)$ approaches both $s\uparrow 1$ and $s\downarrow 0$ in the spirit of the celebrated papers of Bourgain-Brezis-Mironescu \cite{BBM} and Maz'ya-Shaposhnikova \cite{MS}.   Then, focusing con the case $s\uparrow 1$ we analyze the behavior of solutions to the corresponding minimization problems and finally, we also study the problem where a homogenization effect is combined with the localization phenomena that occurs when $s\uparrow 1$.
We prove that the log Iitaka conjecture holds for log canonical fibrations when log canonical divisor of a sufficiently general fiber is abundant.
TMDCs have attracted a lot of attention in recent years due to their unique indirect to direct band gap transition from bulk to monolayer thickness. Strong confinement in the out-of-plane direction enhances the Coulomb potential between the charged particles (e-h pairs) and thus increases the exciton binding energy dramatically. The lattice inversion asymmetry in a monolayer creates two non-equivalent (but degenerate in energy) band edges protected by time reversal polarisation via pseudo-spin. However, the presence of strong spin-orbit coupling in the valence band and weak spin-splitting in the conduction band results in the lowest lying exciton in WX2 (X = S, Se) being spin forbidden and optically dark. Because of their long life times, dark excitons (XD) are highly attractive for quantum optics and optoelectronic applications. To date studying XD emission is limited to cryogenic temperature or required very complex experimental configurations to observe them at room temperature (RT). Here, we demonstrate a novel approach of radiative decay of XD related emissions in 1L-WSe2 studied by micro and nano PL at RT. 1L-WSe2 flakes were sandwiched by noble metal (Au or Ag) substrates and PDMS nano-patches providing a strong local out-of-plane dipole moment with respect to the 2D plane. This strong dipole moment not only enhances the XD in WSe2, it also produces bound excitons due to extrinsic charge defects visible at RT. The spatial distributions of these XD related emissions were studied by TEPL with a spatial resolution < 10 nm confirming the confinement of these excitons within the PDMS nano-patches. Finally, by removing the nano-patches from the top of the flakes we are able to recover the bright excitons in the 1L-WSe2. Our approach paves the way for deep understanding and to harness excitonic properties in low dimensional semiconductors, thus offering a platform towards quantum optics.
In a recent paper, Gallego, Gonz\'{a}lez and Purnaprajna showed that rational 3-ropes can be smoothed. We generalise their proof and obtain smoothability of rational $m$-ropes for $m \geq 3$.
We consider the empirical process G_t of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F. By the central limit theorem for diffusions, the finite-dimensional distributions of G_t converge weakly to those of a zero-mean Gaussian random process G. We prove that the weak convergence G_t\Rightarrow G takes place in \ell^{\infty}(F) if and only if the limit G exists as a tight, Borel measurable map. The proof relies on majorizing measure techniques for continuous martingales. Applications include the weak convergence of the local time density estimator and the empirical distribution function on the full state space.
Depending on the Higgs-boson and top-quark masses, $M_H$ and $M_t$, the effective potential of the {\bf Standard Model} can develop a non-standard minimum for values of the field much larger than the weak scale. In those cases the standard minimum becomes metastable and the possibility of decay to the non-standard one arises. Comparison of the decay rate to the non-standard minimum at finite (and zero) temperature with the corresponding expansion rate of the Universe allows to identify the region, in the ($M_H$, $M_t$) plane, where the Higgs field is sitting at the standard electroweak minimum. In the {\bf Minimal Supersymmetric Standard Model}, approximate analytical expressions for the Higgs mass spectrum and couplings are worked out, providing an excellent approximation to the numerical results which include all next-to-leading-log corrections. An appropriate treatment of squark decoupling allows to consider large values of the stop and/or sbottom mixing parameters and thus fix a reliable upper bound on the mass of the lightest CP-even Higgs boson mass. The discovery of the Higgs boson at LEP~2 might put an upper bound (below the Planck scale) on the scale of new physics $\Lambda$ and eventually disentangle between the Standard Model and the Minimal Supersymmetric Standard Model.
The short time behavior of the 1+1 dimensional KPZ growth equation with a flat initial condition is obtained from the exact expressions of the moments of the partition function of a directed polymer with one endpoint free and the other fixed. From these expressions, the short time expansions of the lowest cumulants of the KPZ height field are exactly derived. The results for these two classes of cumulants are checked in high precision lattice numerical simulations. The short time limit considered here is relevant for the study of the interface growth in the large diffusivity/weak noise limit, and describes the universal crossover between the Edwards-Wilkinson and KPZ universality classes for an initially flat interface.
Classifying pages or text lines into font categories aids transcription because single font Optical Character Recognition (OCR) is generally more accurate than omni-font OCR. We present a simple framework based on Convolutional Neural Networks (CNNs), where a CNN is trained to classify small patches of text into predefined font classes. To classify page or line images, we average the CNN predictions over densely extracted patches. We show that this method achieves state-of-the-art performance on a challenging dataset of 40 Arabic computer fonts with 98.8\% line level accuracy. This same method also achieves the highest reported accuracy of 86.6% in predicting paleographic scribal script classes at the page level on medieval Latin manuscripts. Finally, we analyze what features are learned by the CNN on Latin manuscripts and find evidence that the CNN is learning both the defining morphological differences between scribal script classes as well as overfitting to class-correlated nuisance factors. We propose a novel form of data augmentation that improves robustness to text darkness, further increasing classification performance.
Relative BPS state counts for log Calabi-Yau surface pairs were introduced by Gross-Pandharipande-Siebert. We describe how in the case of del Pezzo surfaces they are linearly related to local BPS state counts by means of generalized Donaldson-Thomas invariants of loop quivers.
The local and global properties of the Goetz thick plane domain wall space-time are studied. It is found that when the surface energy of the wall is greater than a critical value $\sigma_{c}$, the space-time will be closed by intermediate singularities at a finite proper distance. A model is presented in which these singularities will give rise to scalar ones when interacting with null fluids. The maximum extension of the space-time of the wall whose surface energy is less than $\sigma_{c}$ is presented. It is shown that for certain choice of the free parameter the space-time has a black hole structure but with plane symmetry.
We study subcritical two-dimensional oriented percolation seen from its rightmost point on the set of infinite configurations which are bounded above. This a Feller process whose state space is not compact and has no invariant measures. We prove that it converges in distribution to a measure which charges only finite configurations.
In this paper, the overcharging problem and thermodynamics in the extended phase spaces of the five-dimensional spherically symmetric topological black holes are investigated by absorptions of scalar particles and fermions. The cosmological constant is regarded as a variable related to pressure and its conjugate quantity is a thermodynamic volume. The first law of thermodynamics is recovered. The second law is violated in the extended phase space of the extremal and near-extremal black holes. The overcharging problem is tested by the existence of the event horizons. The event horizon is determined by the metric component $f(r)$. The minimal values of the metric component at the final stage show that the extremal and near-extremal black holes can not be overcharged.
We consider properties of quantum channels with use of unified entropies. Extremal unravelings of quantum channel with respect to these entropies are examined. The concept of map entropy is extended in terms of the unified entropies. The map $(q,s)$-entropy is naturally defined as the unified $(q,s)$-entropy of rescaled dynamical matrix of given quantum channel. Inequalities of Fannes type are obtained for introduced entropies in terms of both the trace and Frobenius norms of difference between corresponding dynamical matrices. Additivity properties of introduced map entropies are discussed. The known inequality of Lindblad with the entropy exchange is generalized to many of the unified entropies. For tensor product of a pair of quantum channels, we derive two-sided estimating of the output entropy of a maximally entangled input state.
The ground state of a two-dimensional, harmonically confined mesoscopic assembly of up to thirty polar molecules is studied by computer simulations. As the strength of the confining trap is increased, clusters evolve from superfluid, to supersolid, to insulating crystals. For strong confinement, the crystalline structure can be predicted based on classical energetics. However, clusters of specific numbers of particles (i.e., N=12 and N=19) display a {\it non-classical crystalline structure}, stabilized by quantum effects, in an intermediate range of confinement strength. In these cases, coexistence of quantum and classical crystalline configurations is observed at finite temperature.
This article is the second part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part is concerned with symplectic Galois representations having a huge residual image, by which we mean that a symplectic group of full dimension over the prime field is contained up to conjugation. A key ingredient is a classification of symplectic representations whose image contains a nontrivial transvection: these fall into three very simply describable classes, the reducible ones, the induced ones and those with huge image. Using the idea of an (n,p)-group of Khare, Larsen and Savin we give simple conditions under which a symplectic Galois representation with coefficients in a finite field has a huge image. Finally, we combine this classification result with the main result of the first part to obtain a strenghtened application to the inverse Galois problem.
Evolution equations of YFS and DGLAP types in leading order are considered. They are compared in terms of mathematical properties and solutions. In particular, it is discussed how the properties of evolution kernels affect solutions. Finally, comparison of solutions obtained numerically are presented.
The Nitrogen-to-Oxygen (N/O) abundance ratio is an important diagnostic of galaxy evolution since the ratio is closely tied to the growth of metallicity and the star formation history in galaxies. Estimates for the N/O ratio are traditionally accomplished with optical lines that could suffer from extinction and excitation effects, so the N/O ratio is arguably measured better through far-infrared (far-IR) fine-structure lines. Here we show that the [N III]57$\mu$m/[O III]52$\mu$m line ratio, denoted $N3O3$, is a physically robust probe of N/O. This parameter is insensitive to gas temperature and only weakly dependent on electron density. Though it has a dependence on the hardness of the ionizing radiation field, we show that it is well corrected by including the [Ne III]15.5$\mu$m/[Ne II]12.8$\mu$m line ratio. We verify the method, and characterize its intrinsic uncertainties by comparing the results to photoionization models. We then apply our method to a sample of nearby galaxies using new observations obtained with SOFIA/FIFI-LS in combination with available Herschel/PACS data, and the results are compared with optical N/O estimates. We find evidence for a systematic offset between the far-IR and optically derived N/O ratio. We argue this is likely due to that our far-IR method is biased towards younger and denser H II regions, while the optical methods are biased towards older H II regions as well as diffuse ionized gas. This work provides a local template for studies of ISM abundance in the early Universe.
In hierarchical models of structure formation, an early cosmic UV background (UVB) is produced by the small (T_vir < 10^4 K) halos that collapse before reionization. The UVB at energies below 13.6eV suppresses the formation of stars or black holes inside small halos, by photo-dissociating their only cooling agent, molecular H2. We self-consistently compute the buildup of the early UVB in Press-Schechter models, coupled with H2 photo-dissociation both in the intergalactic medium (IGM), and inside virialized halos. We find that the intergalactic H2 has a negligible effect on the UVB, both because its initial optical depth is small (tau<0.1), and because it is photo-dissociated at an early stage. If the UV sources in the first collapsed halos are stars, then their UV flux suppresses further star-formation inside small halos. This results in a pause in the buildup of the UVB, and reionization is delayed until larger halos (T_vir> 10^4 K) collapse. If the small halos host mini-quasars with hard spectra extending to approximately 1 keV, then their X-rays balance the effects of the UVB, the negative feedback does not occur, and reionization can be caused by the small halos.
We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states.
We report a numerical investigation on the heat transfer through one dimensional arrays of metallic nanoparticles closely spaced in a host material. Our simulations show that the multipolar interactions play a crucial role in the heat transport via collective plasmons. Calculations of the plasmonic thermal conductance and of the thermal conductivity in ballistic and diffusive regime, respectively have been carried out. (a) Using the Landauer-Buttiker formalism we have found that, when the host material dielectric constant takes positive values, the multipolar interactions drastically enhance by several order of magnitude the ballistic thermal conductance of collective plasmons compared with that of a classical dipolar chain. On the contrary, when the host material dielectric constant takes negative values, we have demonstrated the existence of non-ballistic multipolar modes which annihilate the heat transfer through the chains. (b) Using the kinetic theory we have also examined the thermal behavior of chains in the diffusion approximation. We have shown that the plasmonic thermal conductivity of metallic nanoparticle chains can reach 1% of the bulk metal thermal conductivity . This result could explain the anomalously high thermal conductivity observed in many collo\"idal suspensions, the so called nanofluids.
This is a review article for The Review of Particle Physics 2010 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the beginning of 2010. Topics included are Parametrizing the Universe; Extensions to the standard model; Probes; Bringing observations together; Outlook for the future.
We propose a model for isotropization and corresponding thermalization in a nucleon system created in the collision of two nuclei. The model is based on the assumption: during the fireball evolution, two-particle elastic and inelastic collisions give rise to the randomization of the nucleon-momentum transfer which is driven by a proper distribution. As a first approximation, we assume a homogeneous distribution where the values of the momentum transfer is bounded from above. These features have been shown to result in a smearing of the particle momenta about their initial values and, as a consequence, in their partial isotropization and thermalization. The nonequilibrium single-particle distribution function and single-particle spectrum which carry a memory about initial state of nuclei have been obtained.
This paper presents the results of an updated phase-shift analysis of the low-energy (pion laboratory kinetic energy $T \leq 100$ MeV) pion-nucleon data; this solution will be referred to as `ZRH20'.
We demonstrate that our model [Phys.Rev. E91, 032312 (2015)] serves as a useful tool to trace the evolution of equilibrium configurations of one-component charged particles confined in a disk. Our approach reduces significantly the computational effort in minimizing the energy of equilibrium configurations and demonstrates a remarkable agreement with the values provided by molecular dynamics calculations. We show that the Comment misrepresents our paper, and fails to provide plausible arguments against the formation hexagonal structure for n>200 in molecular dynamics calculations.
Let K be a number field. We consider a local-global principle for elliptic curves E/K that admit (or do not admit) a rational isogeny of prime degree n. For suitable K (including K=Q), we prove that this principle holds when n = 1 mod 4, and for n < 7, but find a counterexample when n = 7 for an elliptic curve with j-invariant 2268945/128. For K = Q we show that, up to isomorphism, this is the only counterexample.
Motivated by the general question of existence of open A1-cylinders in higher dimensional pro-jective varieties, we consider the case of Mori Fiber Spaces of relative dimension three, whose general closed fibers are isomorphic to the quintic del Pezzo threefold V5 , the smooth Fano threefold of index two and degree five. We show that the total spaces of these Mori Fiber Spaces always contain relative A2-cylinders, and we characterize those admitting relative A3-cylinders in terms of the existence of certain special lines in their generic fibers.
We report here on physical properties and lattice distortion in the new quasi-one-dimensional spin system TiOBr by x-ray diffraction experiment using synchrotoron radiation. Comparing the crystal structure between TiOBr and TiOCl, the difference of b-axis length plays a key role for physical properties in both systems. By using single crystal of TiOBr, superlattice reflections were observed at (0 1.5 0) and (0 2.5 0). The temperature dependence of superlattice reflections imply the first order transition at $T_{c1}$=27K. We analyzed the data using the simple dimerization model.
We investigate the possibility that the dimension 2 condensate A_mu^2 has a non zero non-perturbative value in Yang-Mills theory. We introduce a multiplicatively renormalisable effective potential for this condensate and show through two loop calculations that a non zero condensate is energetically favoured.