ShantanuT01/DACTYL-Pretraining huggingface dataset:
Self-assembled nanowire (NW) crystals can be grown into nearly defect-free nanomechanical resonators with exceptional properties, including small motional mass, high resonant frequency, and low dissipation. Furthermore, by virtue of slight asymmetries in geometry, a NW's flexural modes are split into doublets oscillating along orthogonal axes. These characteristics make bottom-up grown NWs extremely sensitive vectorial force sensors. Here, taking advantage of its adaptability as a scanning probe, we use a single NW to image a sample surface. By monitoring the frequency shift and direction of oscillation of both modes as we scan above the surface, we construct a map of all spatial tip-sample force derivatives in the plane. Finally, we use the NW to image electric force fields distinguishing between forces arising from the NW charge and polarizability. This universally applicable technique enables a form of atomic force microscopy particularly suited to mapping the size and direction of weak tip-sample forces.
This paper concerns spectral clusters of the Neumann Laplacian on compact Riemannian manifolds with strictly geodesically concave boundary. We prove an inequality which controls the $L^p$ norms of spectral clusters.
We derive a transformation from the usual ADM metric-extrinsic curvature variables on the phase space of Schwarzschild black holes, to new canonical variables which have the interpretation of Kruskal coordinates. We explicitly show that this transformation is non-singular, even at the horizon. The constraints of the theory simplify in terms of the new canonical variables and are equivalent to the vanishing of the canonical momenta. Our work is based on earlier seminal work by Kuchar in which he reconstructed curvature coordinates and a mass function from spherically symmetric canonical data. The key feature in our construction of a nonsingular canonical transformation to Kruskal variables, is the scaling of the curvature coordinate variables by the mass function rather than by the mass at left spatial infinity.
In this thesis, we study three aspects of theories with massive gravitational waves. In the first part, we review to problems and issues of theories with massive gravitons before introducing models where Lorentz invariance is spontaneously broken by the vacuum expectation value of four scalar fields. In the second part, we discuss three aspects of these models: instantaneous interaction, spherically vacuum solutions and cosmological perturbations.
Future applications of antiferromagnets (AFs) in many spintronics devices rely on the precise manipulation of domain walls. The conventional approach using static magnetic fields is inefficient due to the low susceptibility of AFs. Recently proposed electrical manipulation with spin-orbit torques is restricted to metals with a specific crystal structure.   Here we propose an alternative, broadly applicable approach: using asymmetric magnetic field pulses to induce controlled ratchet motion of AF domain walls.   The efficiency of this approach is based on three peculiarities of AF dynamics. First, a time-dependent magnetic field couples with an AF order parameter stronger than a static magnetic field, which leads to higher mobility of the domain walls. Second, the rate of change of the magnetic field couples with the spatial variation of the AF order parameter inside the domain and this enables synchronous motion of multiple domain walls with the same structure. Third, tailored asymmetric field pulses in combination with static friction can prevent backward motion of domain walls and thus lead to the desired controlled ratchet effect.   The proposed use of an external field, rather than internal spin-orbit torques, avoids any restrictions on size, conductivity, and crystal structure of the AF material.   We believe that our approach paves a way for the development of new AF-based devices based on controlled motion of AF domain walls.
The phonon density-of-states (DOS) summarizes the lattice vibrational modes supported by a structure, and gives access to rich information about the material's stability, thermodynamic constants, and thermal transport coefficients. Here, we present an atomistic line graph neural network (ALIGNN) model for the prediction of the phonon density of states and the derived thermal and thermodynamic properties. The model is trained on a database of over 14,000 phonon spectra included in the JARVIS-DFT (Joint Automated Repository for Various Integrated Simulations: Density Functional Theory) database. The model predictions are shown to capture the spectral features of the phonon density-of-states, effectively categorize dynamical stability, and lead to accurate predictions of DOS-derived thermal and thermodynamic properties, including heat capacity $C_{\mathrm{V}}$, vibrational entropy $S_{\mathrm{vib}}$, and the isotopic phonon scattering rate $\tau^{-1}_{\mathrm{i}}$. The DOS-mediated ALIGNN model provides superior predictions when compared to a direct deep-learning prediction of these material properties as well as predictions based on analytic simplifications of the phonon DOS, including the Debye or Born-von Karman models. Finally, the ALIGNN model is used to predict the phonon spectra and properties for about 40,000 additional materials listed in the JARVIS-DFT database, which are validated as far as possible against other open-sourced high-throughput DFT phonon databases.
I. Raptis and R. Zapatrin in the quant-ph/0010104 show possibility to express general state of $l$-qubits quantum register as sum at most $2^l-l$ product states. In the comment is suggested more simple construction with possibility of generalization for decomposition of tensor product of Hilbert spaces with arbitrary dimension $n$ (here simplicial complexes used in the article mentioned above would not be applied directly). In this case it is decomposition with $n^l-(n^2-n)l/2$ product states.
We study exactly the effect of an impurity in the interacting quantum spin chain at low temperature by solving the integrable spin-1/2 XXZ periodic chain with an impurity through the algebraic and thermal Bethe ansatz methods. In particular, we investigate how the crossover temperature for the impurity specific heat depends on the impurity parameter, i.e. the coupling of the impurity to other spins, and show that it is consistent with the analytic expression that is obtained by setting the impurity susceptibility to be proportional to the inverse of the crossover temperature. In the model, two types of crossover behavior appear: one from the high-temperature regime to the low-temperature Kondo regime and another from the N-site homogeneous chain to the (N-1)-site chain with a decoupled free impurity spin, with respect to the temperature and the impurity parameter, respectively.
We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power $p$, for $p\in[0,2)$. The asymptotic behaviour of the right-most particle for this system is already known; in this article we give large deviations probabilities for particles following "difficult" paths, growth rates along "easy" paths, the total population growth rate, and we derive the optimal paths which particles must follow to achieve this growth rate.
Using Eulerian and Euler numbers, we establish congruences concerning sums involving harmonic numbers, tangent numbers and Genocchi numbers.
For a spectrally negative positive self-similar Markov process with an a.s. finite overall supremum we provide, in tractable detail, a kind of conditional Wiener-Hopf factorization at the maximum of the absorption time at zero, the conditioning being on the overall supremum and the jump at the overall supremum. In a companion result the Laplace transform of said absorption time (on the event that the process does not go above a given level) is identified under no other assumptions (such as the process admitting a recurrent extension and/or hitting zero continuously), generalizing some existent results in the literature.
The origin of the breakdown scale in an effective field theory treatment of nuclear forces is investigated. Different organizational schemes used in the nonperturbative calculation of nucleon-nucleon scattering seem to break down for different physical reasons. It is argued that the same physics is actually responsible, namely strong two-pion exchange as also observed in the pion scalar form factor. The prospect of extending the applicability of the effective field theory beyond this breakdown point is discussed.
In this report we consider brane-world universe (New Brane World) where an arbitrary large $N$ quantum CFT exists on the domain wall. This corresponds to implementing of Randall-Sundrum compactification within the context of AdS/CFT correspondence. Using anomaly induced effective action for domain wall CFT, the possibility of self-consistent quantum creation of 4d de Sitter wall universe (inflation) is demonstrated. In case of maximally SUSY Yang-Mills theory the exact correspondence with radius and effective tension found by Hawking-Hertog-Reall is obtained.   We also discuss the bosonic sector of 5d gauged supergravity with single scalar and taking the boundary action as predicted by supersymmetry and discuss the possibility to supersymmetrize dilatonic New Brane World. It is demonstrated that for a number of superpotentials the flat SUSY dilatonic brane-world (with dynamically induced brane dilaton) or quantum-induced de Sitter dilatonic brane-world (not Anti-de Sitter one) where SUSY is broken by the quantum effects occurs. The analysis of graviton perturbations indicates that gravity is localized on such branes.   New Brane World is useful in the study of FRW dynamics and cosmological entropy bounds. Brane stress tensor is induced by quantum effects of dual CFT and brane crosses the horizon of AdS black hole. The similarity between CFT entropy at the horizon and FRW equations is extended on the quantum level. This suggests the way to understand cosmological entropy bounds in quantum gravity.
We prove logarithmic Sobolev inequalities and concentration results for convex functions and a class of product random vectors. The results are used to derive tail and moment inequalities for chaos variables (in spirit of Talagrand and Arcones, Gine). We also show that the same proof may be used for chaoses generated by log-concave random variables, recovering results by Lochowski and present an application to exponential integrability of Rademacher chaos.
We calculate the thermal photon distribution from the hot QCD matter produced by high energy nuclear collisions based on a hydrodynamical model, and compare it with the recent experimental data obtained by CERN WA80. Through the asymptotic value of the slope parameter of the transverse momentum distribution, we investigate the characteristic temperature of the QCD fluid.
Coherent state photon sources are widely used in quantum information processing. In many applications, such as quantum key distribution (QKD), a coherent state is functioned as a mixture of Fock states by assuming its phase is continuously randomized. In practice, such a crucial assumption is often not satisfied and, therefore, the security of existing QKD experiments is not guaranteed. To bridge this gap, we provide a rigorous security proof of QKD with discrete-phase-randomized coherent state sources. Our results show that the performance of the discrete-phase randomization case is close to its continuous counterpart with only a small number (say, 10) of discrete phases. Comparing to the conventional continuous phase randomization case, where an infinite amount of random bits are required, our result shows that only a small amount (say, 4 bits) of randomness is needed.
The large-time asymptotics of weak solutions to Maxwell--Stefan diffusion systems for chemically reacting fluids with different molar masses and reversible reactions are investigated. The diffusion matrix of the system is generally neither symmetric nor positive definite, but the equations admit a formal gradient-flow structure which provides entropy (free energy) estimates. The main result is the exponential decay to the unique equilibrium with a rate that is constructive up to a finite-dimensional inequality. The key elements of the proof are the existence of a unique detailed-balanced equilibrium and the derivation of an inequality relating the entropy and the entropy production. The main difficulty comes from the fact that the reactions are represented by molar fractions while the conservation laws hold for the concentrations. The idea is to enlarge the space of $n$ partial concentrations by adding the total concentration, viewed as an independent variable, thus working with $n+1$ variables. Further results concern the existence of global bounded weak solutions to the parabolic system and an extension of the results to complex-balanced systems.
We study a system of nonlinear partial differential equations describing the unsteady motions of incompressible chemically reacting non-Newtonian fluids. The system under consideration consists of the generalized Navier-Stokes equations with a power-law type stress-strain relation, where the power-law index depends on the concentration of a chemical, coupled to a convection-diffusion equation for the concentration. This system of equations arises in the rheology of the synovial fluid found in the cavities of synovial joints. We prove the existence of global weak solutions of the non-stationary model by using the Galerkin method combined with generalized monotone operator theory and parabolic De Giorgi-Nash-Moser theory. As the governing equations involve a nonlinearity with a variable power-law index, our proofs exploit the framework of generalized Sobolev spaces with variable integrability exponent.
We study the long-range, long-time behavior of the reactive-telegraph equation and a related reactive-kinetic model. The two problems are equivalent in one spatial dimension. We point out that the reactive-telegraph equation, meant to model a population density, does not preserve positivity in higher dimensions. In view of this, in dimensions larger than one, we consider a reactive-kinetic model and investigate the long-range, long-time limit of the solutions. We provide a general characterization of the speed of propagation and we compute it explicitly in one and two dimensions. We show that a phase transition between parabolic and hyperbolic behavior takes place only in one dimension. Finally, we investigate the hydrodynamic limit of the limiting problem.
Intermetallic compounds are key materials for energy transition as they form reversible hydrides that can be used for solid state hydrogen storage or as anodes in batteries. ABy compounds (A = Rare Earth (RE); B = transition metal; 2 < y < 5) are good candidates to fulfill the required properties for practical applications. They can be described as stacking of AB5 and AB2 sub-units along the c crystallographic axis. The latter sub-unit brings a larger capacity, while the former one provides a better cycling stability. However, ABy binaries do not show good enough properties for applications. Upon hydrogenation, they exhibit multiplateau behavior and poor reversibility, attributed to H induced amorphization. These drawbacks can be overcome by chemical substitutions on the A and/or the B sites leading to stabilized reversible hydrides. The present work focuses on the pseudo-binary Sm2MnxNi7-x system (0 <= x < 0.5). The structural, thermodynamic and corrosion properties are analyzed and interpreted by means of X-ray diffraction, chemical analysis, scanning electron microscopy, thermogravimetric analysis and magnetic measurements. Unexpected cell parameter variations are reported and interpreted regarding possible formation of structural defects and uneven Mn distribution within the Ni sublattice. Reversible capacity is improved for x > 0.3 leading to larger and flatter isotherm curves, allowing for reversible capacity >1.4 wt %. Regarding corrosion, the binary compound corrodes in alkaline medium to form rare earth hydroxide and nanoporous nickel. As for the Mn-substituted compounds, a new corrosion product is formed in addition to those above mentioned, as manganese initiates a sacrificial anode mechanism taking place at the early corrosion stage.
High-strain piezoelectric materials are often ceramics with a complicated constitution. In particular, PZT is used with compositions near to a so-called morphotropic phase boundary, where not only different variants of the same phase (domains), but different phases may coexist. Micro-mechanical models for ferroelectric ceramics would be much more realistic, if these effects could be incorporated.   In this paper, we consider the conditions of mechanical and electrical compatibility of ferroelectric domain structures. We are able to address the question of coexistence of different crystallographic phases within the very same crystallite. In general, the spontaneous strain and spontaneous polarization of different phases are not compatible. The numerical analysis of the derived relationships are susceptible to the crystallographic description of the phases in question. In this presentation, a simple analysis and analytical, composition dependent fit of strain and polarization of PZT at room temperature for available data are used.   The outlined approach can be used to model the overall behavior of multi-variant and multi-phase crystallites with certain, simplified geometrical arrangements of the constituents.
We perform a systematic study of Gushel-Mukai varieties---quadratic sections of linear sections of cones over the Grassmannian Gr(2,5). This class of varieties includes Clifford general curves of genus 6, Brill-Noether general polarized K3 surfaces of genus 6, prime Fano threefolds of genus 6, and their higher-dimensional analogues.   We establish an intrinsic characterization of normal Gushel-Mukai varieties in terms of their excess conormal sheaves, which leads to a new proof of the classification theorem of Gushel and Mukai. We give a description of isomorphism classes of Gushel-Mukai varieties and their automorphism groups in terms of linear algebraic data naturally associated to these varieties.   We carefully develop the relation between Gushel-Mukai varieties and Eisenbud-Popescu-Walter sextics introduced earlier by Iliev-Manivel and O'Grady. We describe explicitly all Gushel-Mukai varieties whose associated EPW sextics are isomorphic or dual (we call them period partners or dual varieties respectively). Finally, we show that in dimension 3 and higher, period partners/dual varieties are always birationally isomorphic.
The general relativistic corrections in the equations of motion and associated energy of a binary system of point-like masses are derived at the third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian expansion of the metric in harmonic coordinates at the 3PN approximation. The metric is parametrized by appropriate non-linear potentials, which are evaluated in the case of two point-particles using a Lorentzian version of an Hadamard regularization which has been defined in previous works. Distributional forms and distributional derivatives constructed from this regularization are employed systematically. The equations of motion of the particles are geodesic-like with respect to the regularized metric. Crucial contributions to the acceleration are associated with the non-distributivity of the Hadamard regularization and the violation of the Leibniz rule by the distributional derivative. The final equations of motion at the 3PN order are invariant under global Lorentz transformations, and admit a conserved energy (neglecting the radiation reaction force at the 2.5PN order). However, they are not fully determined, as they depend on one arbitrary constant, which reflects probably a physical incompleteness of the point-mass regularization. The results of this paper should be useful when comparing theory to the observations of gravitational waves from binary systems in future detectors VIRGO and LIGO.
We study the Cauchy problem with small initial data for a system of semilinear wave equations $\square u = |v|^p$, $\square v = |\partial_t u|^p$ in $n$-dimensional space. When $n \geq 2$, we prove that blow-up can occur for arbitrarily small data if $(p, q)$ lies below a curve in $p$-$q$ plane. On the other hand, we show a global existence result for $n=3$ which asserts that a portion of the curve is in fact the borderline between global-in-time existence and finite time blow-up. We also estimate the maximal existence time and get an upper bound, which is sharp at least for $(n, p, q)=(2, 2, 2)$ and $(3, 2, 2)$.
We concur with de Castro's observation that the gauge considerations of our approach are not valid. Nevertheless, except for an error that will be corrected, all of our findings are accurate independent of those considerations.
We present the first investigation of the Blue Straggler star (BSS) population in two isolated dwarf spheroidal galaxies of the Local Group, Cetus and Tucana. Deep HST/ACS photometry allowed us to identify samples of 940 and 1214 candidates, respectively. The analysis of the star formation histories of the two galaxies suggests that both host a population of BSSs. Specifically, if the BSS candidates are interpreted as young main sequence stars, they do not conform to their galaxy's age-metallicity relationship. The analysis of the luminosity function and the radial distributions support this conclusion, and suggest a non-collisional mechanism for the BSS formation, from the evolution of primordial binaries. This scenario is also supported by the results of new dynamical simulations presented here. Both galaxies coincide with the relationship between the BSS frequency and the absolute visual magnitude Mv found by Momany et al (2007). If this relationship is confirmed by larger sample, then it could be a valuable tool to discriminate between the presence of BSSs and galaxies hosting truly young populations.
This paper studies risk balancing features in an insurance market by evaluating ruin probabilities for single and multiple components of a multivariate compound Poisson risk process. The dependence of the components of the process is induced by a random bipartite network. In analogy with the non-network scenario, a network ruin parameter is introduced. This random parameter, which depends on the bipartite network, is crucial for the ruin probabilities. Under certain conditions on the network and for light-tailed claim size distributions we obtain Lundberg bounds and, for exponential claim size distributions, exact results for the ruin probabilities. For large sparse networks, the network ruin parameter is approximated by a function of independent Poisson variables. T
We perform non-abelian T-duality for a generic Green-Schwarz string with respect to an isometry (super)group G, and we derive the transformation rules for the supergravity background fields. Specializing to G bosonic, or G fermionic but abelian, our results reproduce those available in the literature. We discuss also continuous deformations of the T-dual models, obtained by adding a closed B-field before the dualization. This idea can also be used to generate deformations of the original (un-dualized) model, when the 2-cocycle identified from the closed B is invertible. The latter construction is the natural generalization of the so-called Yang-Baxter deformations, based on solutions of the classical Yang-Baxter equation on the Lie algebra of G and originally constructed for group manifolds and (super)coset sigma models. We find that the deformed metric and B-field are obtained through a generalization of the Seiberg-Witten map. When applied to integrable sigma models these deformations preserve the integrability.