ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider two-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a spatial dynamics approach and formulate the steady Euler equations as a Hamiltonian system, where we consider the unbounded horizontal coordinate $x$ as a time-like coordinate. The linearization of the Hamiltonian system is studied, and bifurcation curves in the $(\beta,\alpha)$-plane are obtained, where $\alpha$ and $\beta$ are two parameters. The curves depend on two additional parameters $\rho$ and $h$, where $\rho$ is the ratio of the densities and $h$ is the ratio of the fluid depths. However, the bifurcation diagram is found to be qualitatively the same as for surface waves. In particular we find that a Hamiltonian-Hopf bifurcation and a Hamiltonian real 1:1 resonance occur for certain values of $(\beta,\alpha)$. Of particular interest are solitary wave solutions of the Euler equations. Such solutions correspond to homoclinic solutions of the Hamiltonian system. We investigate the parameter regimes where the Hamiltonian-Hopf bifurcation and the Hamiltonian real 1:1 resonance occur. In both these cases we perform a center manifold reduction of the Hamiltonian system and show that homoclinic solutions of the reduced system exist. In contrast to the case of surface waves we find parameter values $\rho$ and $h$ for which the leading order nonlinear term in the reduced system vanishes. We make a detailed analysis of this phenomenon in the case of the real 1:1 resonance.
Using generalized Konishi anomaly equations, it is known that one can express, in a large class of supersymmetric gauge theories, all the chiral operators expectation values in terms of a finite number of a priori arbitrary constants. We show that these constants are fully determined by the requirement of gauge invariance and an additional anomaly equation. The constraints so obtained turn out to be equivalent to the extremization of the Dijkgraaf-Vafa quantum glueball superpotential, with all terms (including the Veneziano-Yankielowicz part) unambiguously fixed. As an application, we fill non-trivial gaps in existing derivations of the mass gap and confinement properties in super Yang-Mills theories.
Visualizing features in deep neural networks (DNNs) can help understanding their computations. Many previous studies aimed to visualize the selectivity of individual units by finding meaningful images that maximize their activation. However, comparably little attention has been paid to visualizing to what image transformations units in DNNs are invariant. Here we propose a method to discover invariances in the responses of hidden layer units of deep neural networks. Our approach is based on simultaneously searching for a batch of images that strongly activate a unit while at the same time being as distinct from each other as possible. We find that even early convolutional layers in VGG-19 exhibit various forms of response invariance: near-perfect phase invariance in some units and invariance to local diffeomorphic transformations in others. At the same time, we uncover representational differences with ResNet-50 in its corresponding layers. We conclude that invariance transformations are a major computational component learned by DNNs and we provide a systematic method to study them.
We study the existence and nonexistence of normalized solutions $(u_a, \lambda_a)\in H^{1}(\mathbb{R}^N)\times \mathbb{R}$ to the nonlinear Schr\"{o}dinger equation with mixed nonlocal nonlinearities.   This study can be viewed as a counterpart of the Brezis-Nirenberg problem in the context of normalized solutions to the nonlocal Schr\"{o}diger equation with a fixed $L^2$-norm $\|u\|_2=a>0$.   The leading term is $L^2$-supercritical, that is, $p\in (\frac{N+\alpha+2}{N},\frac{N+\alpha}{N-2}]$, where the Hardy-Littlewood-Sobolev critical exponent $p=\frac{N+\alpha}{N-2}$ appears.   We first prove that there exist two normalized solutions if $q\in (\frac{N+\alpha}{N},\frac{N+\alpha+2}{N})$ with $\mu >0$ small, that is, one is at the negative energy level while the other one is at the positive energy level.   For $q=\frac{N+\alpha+2}{N}$, we show that there is a normalized ground state for $0<\mu < \tilde{\mu} $ and there exist no ground states for $\mu >\tilde{\mu}$, where $\tilde{\mu}$ is a sharp positive constant.   If $q\in (\frac{N+\alpha+2}{N},\frac{N+\alpha}{N-2})$, we deduce that there exists a normalized ground state for any $\mu>0$.   We also obtain some existence and nonexistence results for the case $\mu<0$ and $q\in (\frac{N+\alpha}{N},\frac{N+\alpha+2}{N}]$.   Besides, we analyze the asymptotic behavior of normalized ground states as $\mu\rightarrow 0^{+}$.
We report the discovery of a transient and fading hard X-ray emission in the BATSE lightcurves of a sample of short gamma-ray bursts. We have summed each of the four channel BATSE light curves of 76 short bursts to uncover the average overall temporal and spectral evolution of a possible transient signal following the prompt flux. We found an excess emission peaking ~30 s after the prompt one, detectable for ~100 s. The soft power-law spectrum and the time-evolution of this transient signal suggest that it is produced by the deceleration of a relativistic expanding source, as predicted by the afterglow model.
In this paper we describe the structure of the space of parabolic reductions, and their compactifications, of principal $G$-bundles over a smooth projective curve over an algebraically closed field of arbitrary characteristic. We first prove estimates for the dimensions of moduli spaces of stable maps to the twisted flag varieties $E/P$ and Hilbert schemes of closed subschemes of $E/P$ with same Hilbert polynomials as that of a $P$-reductions of $E$. This generalizes the earlier results of Mihnea Popa and Mike Roth to connected reductive groups and the results of Y. I. Holla and M. S. Narasimhan to the case of non-minimal sections. We then prove irreducibility and generic smoothness of the space of reductions for large numerical constraints, using the above result and the methods of G. Harder. We also study these space in more detail for generically stable $G$-bundles. As a consequence we can generalize the lower bound results of H. Lange to $G$.
We study by quantum Monte Carlo simulations the ground state of a harmonically confined dipolar Bose gas with aligned dipole moments, and with the inclusion of a repulsive two-body potential of varying range. Two different limits can be clearly identified, namely a classical one in which the attractive part of the dipolar interaction dominates and the system forms an ordered array of parallel filaments, and a quantum-mechanical one, wherein filaments are destabilized by zero-point motion, and eventually the ground state becomes a uniform cloud. The physical character of the system smoothly evolves from classical to quantum mechanical as the range of the repulsive two-body potential increases. An intermediate regime is observed, in which ordered filaments are still present, albeit forming different structures from the ones predicted classically; quantum-mechanical exchanges of indistinguishable particles across different filaments allow phase coherence to be established, underlying a global superfluid response.
We present recent polarimetric images of the highly variable star R CrB using ExPo and archival WFPC2 images from the HST. We observed R CrB during its current dramatic minimum where it decreased more than 9 mag due to the formation of an obscuring dust cloud. Since the dust cloud is only in the line-of-sight, it mimics a coronograph allowing the imaging of the star's circumstellar environment. Our polarimetric observations surprisingly show another scattering dust cloud at approximately 1.3" or 2000 AU from the star. We find that to obtain a decrease in the stellar light of 9 mag and with 30% of the light being reemitted at infrared wavelengths (from R CrB's SED) the grains in R CrB's circumstellar environment must have a very low albedo of approximately 0.07%. We show that the properties of the dust clouds formed around R CrB are best fitted using a combination of two distinct populations of grains size. The first are the extremely small 5 nm grains, formed in the low density continuous wind, and the second population of large grains (~0.14 {\mu}m) which are found in the ejected dust clouds. The observed scattering cloud, not only contains such large grains, but is exceptionally massive compared to the average cloud.
A probabilistic framework for studying single-particle diffusion in partially absorbing media has recently been developed in terms of an encounter-based approach. The latter computes the joint probability density (generalized propagator) for particle position $\X_t$ and a Brownian functional ${\mathcal U}_t$ that specifies the amount of time the particle is in contact with a reactive component $\calM$. Absorption occurs as soon as $\calU_t$ crosses a randomly distributed threshold (stopping time). Laplace transforming the propagator with respect to $\calU_t$ leads to a classical boundary value problem (BVP) in which the reactive component has a constant rate of absorption $z$, where $z$ is the corresponding Laplace variable. Hence, a crucial step in the encounter-based approach is finding the inverse Laplace transform. In the case of a reactive boundary $\partial \calM$, this can be achieved by solving a classical Robin BVP in terms of the spectral decomposition of a Dirichlet-to-Neumann operator. In this paper we develop the analogous construction in the case of a reactive substrate $\calM$. In particular, we show that the Laplace transformed propagator can be computed in terms of the spectral decomposition of a pair of Dirichlet-to-Neumann operators. However, inverting the Laplace transform with respect to $z$ is more involved. We illustrate the theory by considering a 1D example where the Dirichlet-to-Neumann operators reduce to scalars.
We construct non-BPS dyon solutions of N=4 SU(n) supersymmetric Yang-Mills theory. These solutions are the worldvolume solitons which describe non-BPS Type IIB non-planar string junctions connecting n parallel D3-branes. The solutions are smooth deformations of the 1/4 BPS states which describe planar string junctions.
A superconductor/normal metal/superconductor Josephson junction is a coherent electron system where the thermodynamic entropy depends on temperature and phase difference across the weak-link. Here, exploiting the phase-temperature thermodynamic diagram of a thermally isolated system, we argue that a cooling effect can be achieved when the phase drop across the junction is brought from 0 to $\pi$ in a iso-entropic process. We show that iso-entropic cooling can be enhanced with proper choice of geometrical and electrical parameters of the junction, i.e. by increasing the ratio between supercurrent and total junction volume. We present extensive numerical calculations using quasi-classical Green function methods for a short junction and we compare them with analytical results. Interestingly, we demonstrate that phase-coherent thermodynamic cycles can be implemented by combining iso-entropic and iso-phasic processes acting on the weak-link, thereby engineering the coherent version of thermal machines such as engines and cooling systems. We therefore evaluate their performances and the minimum temperature achievable in a cooling cycle.
The production of charmonia in relativistic heavy-ion collisions is formulated within the framework of a quantum kinetic theory simultaneously accounting for breakup and recombination processes. The survival probability of J/Psi mesons is evaluated for a Mott-Hagedorn resonance gas, whereby the pattern of anomalous J/Psi suppression at CERN-SPS can be explained by a strong coupling to open-charm states and their in-medium modification. Recent data for charmonium suppression from Au-Au collisions at RHIC are discussed.
We investigate the interplay between spin and orbital correlations in monolayer and bilayer manganites using an effective spin-orbital t-J model which treats explicitly the e_g orbital degrees of freedom coupled to classical t_{2g} spins. Using finite clusters with periodic boundary conditions, the orbital many-body problem is solved by exact diagonalization, either by optimizing spin configuration at zero temperature, or by using classical Monte-Carlo for the spin subsystem at finite temperature. In undoped two-dimensional clusters, a complementary behavior of orbital and spin correlations is found - the ferromagnetic spin order coexists with alternating orbital order, while the antiferromagnetic spin order, triggered by t_{2g} spin superexchange, coexists with ferro-orbital order. With finite crystal field term, we introduce a realistic model for La_{1-x}Sr_{1+x}MnO_4, describing a gradual change from predominantly out-of-plane 3z^2-r^2 to in-plane x^2-y^2 orbital occupation under increasing doping. The present electronic model is sufficient to explain the stability of the CE phase in monolayer manganites at doping x=0.5, and also yields the C-type antiferromagnetic phase found in Nd_{1-x}Sr_{1+x}MnO_4 at high doping. Also in bilayer manganites magnetic phases and the accompanying orbital order change with increasing doping. Here the model predicts C-AF and G-AF phases at high doping x>0.75, as found experimentally in La_{2-2x}Sr_{1+2x}Mn_2O_7.
To mitigate climate change, our global society is harnessing direct (solar irradiation) and indirect (wind/water flow) sources of renewable electrical power generation. Emerging direct sources include current-producing thermal gradients in thermoelectric materials, while quantum physics-driven processes to convert quantum information into energy have been demonstrated at very low temperatures. The magnetic state of matter, assembled by ordering the electron's quantum spin property, represents a sizeable source of built-in energy. We propose to create a direct source of electrical power at room temperature (RT) by utilizing magnetic energy to harvest thermal fluctuations on paramagnetic (PM) centers. Our spin engine rectifies current fluctuations across the PM centers' spin states according to the electron spin by utilizing so-called 'spinterfaces' with high spin polarization. As a rare experimental event, we demonstrate how this path can generate 0.1nW at room temperature across a 20 micron-wide spintronic device called the magnetic tunnel junction, assembled using commonplace Co, C and MgO materials. The presence of this path in our experiment, which also generates very high spintronic performance, is confirmed by analytical and ab-initio calculations. Device downscaling, and the ability for other materials systems than the spinterface to select a transport spin channel at RT widens opportunities for routine device reproduction. The challenging control over PM centers within the tunnel barrier's nanotransport path may be addressed using oxide- and organic-based nanojunctions. At present densities in MRAM products, this spin engine could lead to 'always-on' areal power densities well beyond that generated by solar irradiation on earth. Further developing this concept can fundamentally alter our energy-driven society's global economic, social and geopolitical constructs.
We study the 2018 outburst of Aql X-1 via the monitor of all sky X-ray image (MAXI) data. We show that the outburst starting in February 2018 is a member of short-low class in the frame of outburst duration and the peak count rate although the outburst morphology is slightly different from the other fast-rise-exponential-decay (FRED) type outbursts with a milder rising stage. We study the partial accretion in the weak propeller stage of Aql X-1 via the MAXI data of the 2018 outburst. We report on the spectral analysis of 3 observations of Aquila X-1 obtained by Insight - hard X-ray modulation telescope (Insight-HXMT) during the late decay stage of the 2018 outburst. We discuss that the data taken by Insight-HXMT is just after the transition to the weak propeller stage. Our analysis shows the necessity of a comptonization component to take into account the existence of an electron cloud resulting photons partly up-scattered.
The number of apparent double points of an irreducible projective variety $X$ of dimension $n$ in $\mathbb{P}^{2n+1}$ is the number of secant lines to $X$ passing through a general point of $\mathbb{P}^{2n+1}$. This classical notion dates back to Severi.   Smooth threefolds having one apparent double point (shortly OADP threefolds) have been classified in 2004 by Ciliberto, Mella and Russo. In 2011, Ciliberto and Russo have classified normal OADP threefolds such that the so-called fundamental surface is a plane.   In this thesis the case in which the fundamental surface is not a plane is considered. A partial classification is given and several examples are presented.
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.
We study the possibility that the $Z^+(4430)$ state observed by Belle is a $D_1D^*$ (or $D_1'D^*$) resonance in S-wave. Focusing on its decays, We find that the open-charm decay into $D^*D^*\pi$ is dominant. Furthermore, we use the re-scattering mechanism to study its hidden-charm decays and find that the re-scattering effects are significant in $D_1D^*$ channel but not in $D_1'D^*$ channel. For the $J^P=1^-$ candidate, with chosen parameters, we can get $\Gamma(Z^+\to\psi'\pi^+)/\Gamma(Z^+\to J/\psi\pi^+)\thickapprox 5.3$, which tends to account for why the $Z^+(4430)$ is difficult to be found in $J/\psi\pi^+$. However, the $0^-$ candidate can not be ruled out by our calculations.
In this paper we calculate the effective action for neutral particles with anomalous magnetic moment in an external magnetic and electric field. We show that we can take advantage from the Foldy Wouthuysen transformation for such systems, determined in our previous works: indeed, by this transformation we have explicitly evaluated the diagonalized Hamiltonian, allowing to present a closed form for the corresponding effective action and for the partition function at finite temperature from which the thermodynamical potentials can be calculated.
Methods for efficient simulations of multidimensional quantum dynamics are essential for theoretical studies of chemical systems where quantum effects are important, such as those involving rearrangements of protons or electronic configurations. Here, we introduce the functional tensor-train Chebyshev (FTTC) method for rigorous nuclear quantum dynamics simulations. FTTC is essentially the Chebyshev propagation scheme applied to the initial state, represented in continuous analogue tensor-train format. We demonstrate the capabilities of FTTC as applied to simulations of proton quantum dynamics in a 50-dimensional model of hydrogen-bonded DNA base pairs.
Given a pair of graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the smallest $N$ such that every red-blue coloring of the edges of the complete graph $K_N$ contains a red copy of $G$ or a blue copy of $H$. If a graph $G$ is connected, it is well known and easy to show that $R(G,H) \geq (|G|-1)(\chi(H)-1)+\sigma(H)$, where $\chi(H)$ is the chromatic number of $H$ and $\sigma(H)$ is the size of the smallest color class in a $\chi(H)$-coloring of $H$. A graph $G$ is called $H$-good if $R(G,H)= (|G|-1)(\chi(H)-1)+\sigma(H)$. The notion of Ramsey goodness was introduced by Burr and Erd\H{o}s in 1983 and has been extensively studied since then.   In this paper we show that if $n\geq \Omega(|H| \log^4 |H|)$ then every $n$-vertex bounded degree tree $T$ is $H$-good. The dependency between $n$ and $|H|$ is tight up to $\log$ factors. This substantially improves a result of Erd\H{o}s, Faudree, Rousseau, and Schelp from 1985, who proved that $n$-vertex bounded degree trees are $H$-good when when $n \geq \Omega(|H|^4)$.
The evolution of small magnetic features in quiet regions of the Sun provides a unique window to probing solar magneto-convection. Here we analyze small scale magnetic features in the quiet Sun, using the high resolution, seeing-free observations from the Sunrise balloon borne solar observatory. Our aim is to understand the contribution of different physical processes, such as splitting, merging, emergence and cancellation of magnetic fields to the rearrangement, addition and removal of magnetic flux in the photosphere. We employ a statistical approach for the analysis and the evolution studies are carried out using a feature tracking technique. In this paper we provide a detailed description of the feature tracking algorithm that we have newly developed and we present the results of a statistical study of several physical quantities. The results on the fractions of the flux in the emergence, appearance, splitting, merging, disappearance and cancellation qualitatively agrees with other recent studies. To summarize, the total flux gained in unipolar appearance is an order of magnitude larger than the total flux gained in emergence. On the other hand, the bi-polar cancellation contributes nearly an equal amount to the loss of magnetic flux as unipolar disappearance. The total flux lost in cancellation is nearly $6-8$ times larger than the total flux gained in emergence. One big difference between our study and previous similar studies is that thanks to the higher spatial resolution of Sunrise we can track features with fluxes as low as $9\times10^{14}$ Mx. This flux is nearly an order of magnitude lower than the smallest fluxes of the features tracked in the highest resolution previous studies based on Hinode data.
We analyze the quantum quench dynamics in the formation of a phase-biased superconducting nanojunction. We find that in the absence of an external relaxation mechanism and for very general conditions the system gets trapped in a metastable state, corresponding to a non-equilibrium population of the Andreev bound states. The use of the time-dependent Full Counting Statistics (FCS) analysis allows us to extract information on the asymptotic population of even and odd manybody states, demonstrating that a universal behavior, dependent only on the Andreev states energy, is reached in the quantum point contact limit. These results shed light on recent experimental observations on quasiparticle trapping in superconducting atomic contacts.
One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are members of only a handful of parametric families, and each inequivalent matrix, up to transposition, can be identified through its fingerprint.