ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this note, we study the ill-posedness of nonlinear wave equations (NLW). Namely, we show that NLW experiences norm inflation at every initial data in negative Sobolev spaces. This result covers a gap left open in a paper of Christ, Colliander, and Tao (2003) and extends the result by Oh, Tzvetkov, and the second author (2019) to non-cubic integer nonlinearities. In particular, for some low dimensional cases, we obtain norm inflation above the scaling critical regularity. We also prove ill-posedness for NLW, via norm inflation at general initial data, in negative regularity Fourier-Lebesgue and Fourier-amalgam spaces.
We give examples of small data blow-up for a three-component system of quadratic nonlinear Schr\"odinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.
In 1916 Einstein introduced the first rules for a quantum theory of electromagnetic radiation, and he applied them to a model of matter in thermal equilibrium with radiation to derive Planck's black-body formula. Einstein's treatment is extended here to time-dependent stochastic variables, which leads to a master equation for the probability distribution that describes the irreversible approach of Einstein's model towards thermal equilibrium, and elucidates aspects of the foundation of statistical mechanics. An analytic solution of this equation is obtained in the Fokker-Planck approximation which is in excellent agreement with numerical results. At equilibrium, it is shown that the probability distribution is proportional to the total number of microstates for a given configuration, in accordance with Boltzmann's fundamental postulate of equal a priori probabilities for these states. While the counting of these configurations depends on particle statistics- Boltzmann, Bose-Einstein, or Fermi-Dirac - the corresponding probability is determined here by the dynamics which are embodied in the form of Einstein's quantum transition probabilities for the emission and absorption of radiation. In a special limit, it is shown that the photons in Einstein's model can act as a thermal bath for the evolution of the atoms towards the canonical equilibrium distribution of Gibbs. In this limit, the present model is mathematically equivalent to an extended version of the Ehrenfests' ``dog-flea'' model, which has been discussed recently by Ambegaokar and Clerk.
The thermodynamic uncertainty relation sets the minimal bound of the cost-precision trade-off relation for dissipative processes. Examining the dynamics of an internally coupled system that is driven by a constant thermodynamic force, we however find that the trade-off relation of a sub-system is not constrained by the minimal bound of conventional uncertainty relation. We made our point explicit by using an exactly solvable model of interacting oscillators. As the number (N) of interacting oscillators increases, the uncertainty bound of individual oscillators is reduced to 2k_B T/N upon full synchronization under strong coupling. The cost-precision trade-off for the sub-system is particularly relevant for sub-cellular processes where collective dynamics emerges from multiple energy-expending components interacting with each other.
We reconsider the problem of finding all local symmetries of a Lagrangian. Our approach is completely Hamiltonian without any reference to the associated action. We present a simple algorithm for obtaining the restrictions on the gauge parameters entering in the definition of the generator of gauge transformations.
We describe and discuss remarkable infrared spectra, covering key portions of the $2-5$ $\mu$m wavelength interval, of the probable OH/IR supergiant 2MASS J17470898$-$2829561 (2M1747), located in direction of the Sgr B molecular cloud complex within the Central Molecular Zone (CMZ) of the Galaxy. This star was originally singled out for examination based on its suitability for spectroscopy of lines of H$_3^+$ in the CMZ. Analysis of the spectra shows that 2M1747 is deeply embedded within Sgr B1, with A$_V$ $\gtrsim$ 100 mag, making it the only star within Sgr B for which infrared spectra have been obtained at present, and thereby a unique infrared probe of the dense interstellar medium within the CMZ. Despite the high extinction, spectra of 2M1747 reveal a veiled photosphere in the $K$ band and circumstellar gas in the $M$ band, giving clues as to its nature. Its $ 3.5-4.0$ $\mu$m spectrum contains the strongest absorption lines of H$_3^+$ observed toward any object to date. The $4.5-4.8$ $\mu$m spectrum has impressively deep and wide absorption lines of interstellar CO, most of which arise in dense gas within Sgr B1. The $3-5$ $\mu$m spectrum also contains several solid state absorption features, which are characteristic of both dense and diffuse clouds, and which raise questions about the identifications of some of these features. We discuss the nature of the star, the extinction to it, the extinction law for dust in the CMZ, and the identifications of the various solid-state features and where they are produced along this complex line of sight.
We consider a Poisson equation in $\mathbb R^d$ for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect to the parameter are obtained under mild conditions on the coefficients. The result is then applied to establish a general diffusion approximation for fully coupled multi-time-scales stochastic differential equations with only H\"older continuous coefficients. Four different averaged equations as well as rates of convergence are obtained. Moreover, the convergence is shown to rely only on the regularities of the coefficients with respect to the slow variable, and does not depend on their regularities with respect to the fast component.
The Mitsui model for the order-disorder type ferroelectrics is studied within the mean field approximation. The phase diagram of the model is obtained, its dependence on the transverse field is obtained. A scheme of setting the values of the model parameters is proposed; all the dielectric characteristics of Rochelle salt are calculated with the found parameters. Within the Mitsui model we study the physical characteristics of RbHSO4 type crystals; the found values of the model parameters provide a good description of both dielectric and thermodynamic properties of these compounds.
We prove new borderline regularity results for solutions to fully nonlinear elliptic equations together with pointwise gradient potential estimates.
The decay of a massive pseudoscalar, scalar and U(1) boson into an electron-positron pair in the presence of strong electromagnetic backgrounds is calculated. Of particular interest is the constant-crossed-field limit, relevant for experiments that aim to measure high-energy axion-like-particle conversion into electron-positron pairs in a magnetic field. The total probability depends on the quantum nonlinearity parameter - a product of field and lightfront momentum invariants. Depending on the seed particle mass, different decay regimes are identified. In the below-threshold case, we find the probability depends on a non-perturbative tunnelling exponent depending on the quantum parameter and the particle mass. In the above-threshold case, we find that when the quantum parameter is varied linearly, the probability oscillates nonlinearly around the spontaneous decay probability. A strong-field limit is identified in which the threshold is found to disappear. In modelling the fall-off of a quasi-constant-crossed magnetic field, we calculate probabilities beyond the constant limit and investigate when the decay probability can be regarded as locally constant.
Quantum nonreciprocal devices have received extensive attention in recent years because they can be used to realize unidirectional quantum routing and noise isolation. In this work, we show that the shift of resonance frequencies of propagating phonons induced by spin-orbit interactions (SOI) of phonons in a rotating acoustic ring cavity can be used to realize nonreciprocal phonon blockade. When driving the cavity from different directions, nonreciprocal single-, two-phonon blockade and phonon-induced tunneling can take place by varying the parameters of the system to an appropriate value. To realize phonon blockade, the sublevels of the lower orbit branch of the ground state of silicon-vacancy (SiV) color centers in the diamond membrane are employed to induce self-interactions of phonons in the cavity. This work provides a way to achieve acoustic nonreciprocal devices, such as directional acoustic switches and quantum noise isolation, which may help acoustic information network processing.
The history of the local medium, within a few hundred parsecs, is dominated by the evolution of the Gould Belt. The event that triggered this star-forming region and molded the gas distribution is still unknown. Its orientation and extent are reasonably well determined and its expansion matches the space and velocity distributions of many large HI and H2 clouds within half a kiloparsec. The present rim coincides with most of the nearby OB associations, but their mean velocity does not seem to be related to the Belt expansion. The Belt age is uncertain by a factor of 2 because of the discrepancy found between the dynamical timescale (20 to 30 Myr) and the stellar ages (30 to 60 Myr). The stellar content is derived from kinematic studies for massive stars and from X-ray observations for young solar-mass ones. Whether star formation is active along the rim or spread over a larger fraction of the disc is debated. The Belt flatness and its tilt remain very difficult to interpret. Various scenarii involve the impact of a high-velocity cloud, a cascade of supernovae, the dissolution of a rotating system, or the braking of a supercloud entering the spiral arm. Because of the enhanced star formation, the Belt supernova rate over the past few million years has been 3 to 4 times larger than the local Galactic rate. The corresponding pulsars may be responsible for the population of unknown gamma-ray sources associated with the Belt. The higher rate also implies an enhanced cosmic-ray production locally.
(Abridged) Star formation-driven outflows are a critical phenomenon in theoretical treatments of galaxy evolution, despite the limited ability of observations to trace them across cosmological timescales. If the strongest MgII absorption-line systems detected in the spectra of background quasars arise in such outflows, "ultra-strong" MgII (USMgII) absorbers would identify significant numbers of galactic winds over a huge baseline in cosmic time, in a manner independent of the luminous properties of the galaxy. To this end, we present the first detailed imaging and spectroscopic study of the fields of two USMgII absorber systems culled from a statistical absorber catalog, with the goal of understanding the physical processes leading to the large velocity spreads that define such systems. Each field contains two bright emission-line galaxies at similar redshift (dv < 300 km/s) to that of the absorption. Lower-limits on their instantaneous star formation rates (SFR) from the observed OII and Hb line fluxes, and stellar masses from spectral template fitting indicate specific SFRs among the highest for their masses at z~0.7. Additionally, their 4000A break and Balmer absorption strengths imply they have undergone recent (~0.01 - 1 Gyr) starbursts. The concomitant presence of two rare phenomena - starbursts and USMgII absorbers - strongly implies a causal connection. We consider these data and USMgII absorbers in general in the context of various popular models, and conclude that galactic outflows are generally necessary to account for the velocity extent of the absorption. We favour starburst driven outflows over tidally-stripped gas from a major interaction which triggered the starburst as the energy source for the majority of systems. Finally, we discuss the implications of these results and speculate on the overall contribution of such systems to the global SFR density at z~0.7.
The main open problem in the physics of Lambda-hypernuclei is the lack of a sound theoretical interpretation of the large experimental values for the ratio G_n/G_p. To approach the problem, we have incorporated a Lambda N-> nN one-meson-exchange model in an intranuclear cascade code for a finite nucleus calculation of the nucleon-nucleon (angular and energy) coincidence distributions in the non-mesonic weak decay of 5_Lambda-He and 12_Lambda-C hypernuclei. The two-nucleon induced decay mechanism, Lambda np-> nnp, has been taken into account by means of the polarization propagator formalism in local density approximation. With respect to single nucleon spectra studies, the treatment of two-nucleon correlations allow a cleaner and more direct determination, from data, of G_n/G_p. Our results agree with the preliminary coincidence data of KEK-E462 for 5_Lambda-He. This allows us to conclude that G_n/G_p for 5_Lambda-He should be close to 0.46, the value predicted by our one-meson-exchange model for this hypernucleus. Unfortunately, to disentangle one- and two-body induced decay channels from experimental non-mesonic decay events, three-nucleon coincidences should be measured.
We demonstrate strain-tuning of magnetocrystalline anisotropy over a range of more than one thousand Gauss in epitaxial Y3Fe5O12 films of excellent crystalline quality grown on lattice-mismatched Y3Al5O12 substrates. Ferromagnetic resonance (FMR) measurements reveal a linear dependence of both out-of-plane and in-plane uniaxial anisotropy on the strain-induced tetragonal distortion of Y3Fe5O12. Importantly, we find the spin mixing conductance G_r determined from inverse spin Hall effect and FMR linewidth broadening remains large: G_r = 3.33 x 10^14 Ohm^-1m^-2 in Pt/Y3Fe5O12/Y3Al5O12 heterostructures, quite comparable to the value found in Pt/Y3Fe5O12 grown on lattice-matched Gd3Ga5O12 substrates.
Quasars have been proposed as a new class of standard candles analogous to Supernovae, as their large redshift range and high luminosities make them excellent candidates. Reverberation mapping (RM) method enables to estimate the distance to the source from the time delay measurement of the emission lines with respect to the continuum, since the time delay depends on the absolute luminosity of the source. This radius-luminosity (RL) relation exhibits a low scatter and it was thus proposed for cosmological purposes. However, in recent years the increase in the studied sample, and in particular the inclusion of highly accreting QSO has increased the dispersion in the RL relation, with many objects showing time delays shorter than the expected. Using H$\beta$ RM measurements for 117 sources with $0.002<z<0.9$ and $41.5<\mathrm{log}~L_{5100}<45.9$, we find a correction for the time delay based on the dimensionless accretion rate considering the virial factor anti-correlated with the FWHM of H$\beta$. This correction decreases the scattering in the accretion parameters compared with the typical value used, which is directly reflected by suppressing the RL relation dispersion. We also confirm the anti-correlation between the excess of variability and the accretion parameters. With this correction we are able to build the Hubble diagram and estimate the cosmological constants $\Omega_m$ and $\Omega_\Lambda$, which are consistent with the standard cosmological model at 2$\sigma$ confidence level. Therefore, RM results can be used to constrain cosmological models in the future.
Charged, rotating black hole solutions of Einstein's gravitational equations are investigated in the presence of a cosmological constant. A pair of wave equations governing the electromagnetic and gravitational perturbations are derived.
Experiments with $\Xi^-$ atoms are proposed in order to study the nuclear interaction of $\Xi$ hyperons. The production of $\Xi^-$ in the ($K^{-}$, $K^{+}$) reaction, the $\Xi^-$ stopping in matter, and its atomic cascade are incorporated within a realistic evaluation of the results expected for $\Xi^-$ X-ray spectra across the periodic table, using an assumed $\Xi$-nucleus optical potential $V_{opt}$. Several optimal targets for measuring the strong-interaction shift and width of the X-ray transition to the `last' atomic level observed are singled out: F, Cl, I, Pb. The sensitivity of these observables to the parameters of $V_{opt}$ is considered. The relevance of such experiments is discussed in the context of strangeness -2 nuclear physics and multistrange nuclear matter. Finally, with particular reference to searches for the $H$ dibaryon, the properties of $\Xi^-d$ atoms are also discussed. The role of Stark mixing, its effect on $S$ and $P$ state capture of $\Xi^-$ by the deuteron, together with estimates of the resulting probability for producing the $H$ dibaryon are considered in detail.
We propose an entanglement-based protocol for two people to simultaneously exchange their messages. We show that the protocol is asymptotically secure against the disturbance attack, the intercept-and-resend attack and the entangle-and-measure attack. Our protocol is experimentally feasible within current technologies.
LiDAR point cloud streams are usually sparse in time dimension, which is limited by hardware performance. Generally, the frame rates of mechanical LiDAR sensors are 10 to 20 Hz, which is much lower than other commonly used sensors like cameras. To overcome the temporal limitations of LiDAR sensors, a novel task named Point Cloud Frame Interpolation is studied in this paper. Given two consecutive point cloud frames, Point Cloud Frame Interpolation aims to generate intermediate frame(s) between them. To achieve that, we propose a novel framework, namely Point Cloud Frame Interpolation Network (PointINet). Based on the proposed method, the low frame rate point cloud streams can be upsampled to higher frame rates. We start by estimating bi-directional 3D scene flow between the two point clouds and then warp them to the given time step based on the 3D scene flow. To fuse the two warped frames and generate intermediate point cloud(s), we propose a novel learning-based points fusion module, which simultaneously takes two warped point clouds into consideration. We design both quantitative and qualitative experiments to evaluate the performance of the point cloud frame interpolation method and extensive experiments on two large scale outdoor LiDAR datasets demonstrate the effectiveness of the proposed PointINet. Our code is available at https://github.com/ispc-lab/PointINet.git.
As the fundamental quantum mechanical theory predicts, it is believed that electronic states can be bound only to potential wells and not to potential barriers in any dimension and their energies should be below the background potential. However, with the help of atomic lattice potentials with a flat electron band in momentum space in the background, an atomically thin 1D potential barrier can possess barrier-centered bound states above the background potential. Here we provide a theoretical proof using Green function pole analysis with Dyson equation that shows the existence of barrier-bound-states whose energy is elevated from the flat band energy nearly by the barrier height. The phenomenon is believed to be independently confirmed in a system of Pd monolayer on a flat oxide substrate with Stoner ferromagnetism using spin-polarized STM technique and through comparison with real-space QPI simulations using realistic 2D Pd band structure.
Classical solutions to PDEs with discrete state-dependent delay are studied. We prove the well-posedness in a set $X_F$ which is an analogous to the solution manifold used for ordinary differential equations with state-dependent delay. We prove that the evolution operators are $C^1$-smooth on the solution manifold.
IC 310 has recently been identified as a gamma-ray emitter based on observations at GeV energies with Fermi-LAT and at very high energies (VHE, E > 100 GeV) with the MAGIC telescopes. Despite IC 310 having been classified as a radio galaxy with the jet observed at an angle > 10 degrees, it exhibits a mixture of multiwavelength properties of a radio galaxy and a blazar, possibly making it a transitional object. On the night of 12/13th of November 2012 the MAGIC telescopes observed a series of violent outbursts from the direction of IC 310 with flux-doubling time scales faster than 5 min and a peculiar spectrum spreading over 2 orders of magnitude. Such fast variability constrains the size of the emission region to be smaller than 20% of the gravitational radius of its central black hole, challenging the shock acceleration models, commonly used in explanation of gamma-ray radiation from active galaxies. Here we will show that this emission can be associated with pulsar-like particle acceleration by the electric field across a magnetospheric gap at the base of the jet.
We prove that every place of an algebraic function field F|K of arbitrary characteristic admits local uniformization in a finite extension F' of F. We show that F'|F can be chosen to be normal. If K is perfect and P is of rank 1, then alternatively, F' can be obtained from F by at most two Galois extensions; if in addition P is zero-dimensional, then we only need one Galois extension. Certain rational places of rank 1 can be uniformized already on F. We introduce the notion of "relative uniformization" for arbitrary finitely generated extensions of valued fields. Our proofs are based solely on valuation theoretical theorems, which are of fundamental importance in positive characteristic.
In this paper, we introduce a quantum walk whose local scattering at each vertex is denoted by a unitary circulant matrix; namely the circulant quantum walk. We also introduce another quantum walk induced by the circulant quantum walk; namely the optical quantum walk, whose underlying graph is a $2$-regular directed graph and obtained by blowing up the original graph in some way. We propose a design of an optical circuit which implements the stationary state of the optical quantum walk. We show that if the induced optical quantum walk does not have $+1$ eigenvalue, then the stationary state of the optical quantum walk gives that of the original circulant quantum walk. From this result, we give a useful condition for the setting of the circulant quantum walks which can be implemented by this optical circuit.
The influence of different boundary conditions on the density of random packings of disks is studied. Packings are generated using the random sequential adsorption algorithm with three different types of boundary conditions: periodic, open, and wall. It is found that the finite size effects are smallest for periodic boundary conditions, as expected. On the other hand, in the case of open and wall boundaries it is possible to introduce an effective packing size and a constant correction term to significantly improve the packing densities.
We describe a method to construct hypersurfaces of the complex affine $n$-space with isomorphic $\mathbb{C}^*$-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent Cancellation Problem, i.e. hypersurfaces that are non isomorphic, although their $\mathbb{C}^*$-cylinders are isomorphic as abstract algebraic varieties. We also provide examples of non isomorphic varieties $X$ and $Y$ with isomorphic cartesian squares $X\times X$ and $Y\times Y$.
We consider the family of singularly nonautonomous plate equation with structural damping \[ u_{tt} + a(t,x)u_{t} + (- \Delta) u_{t} + (-\Delta)^{2} u + \lambda u = f(u), \] in a bounded domain $\Omega \subset \R^n$, with Navier boundary conditions. When the nonlinearity $f$ is dissipative we show that this problem is globally well posed in $H^2_0(\Omega) \times L^2(\Omega)$ and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping $a$.