ShantanuT01/DACTYL-Pretraining huggingface dataset:
We show that the surface tension of fluid near the critical point may be correctly described by taking into consideration the microscopic structure of the system using a {\phi}4 field theory. We revise the theory of the surface tension near criticality to take into account a microscopic structure of the fluid. Focusing on the case of the Lennard-Jones fluid, we express the surface tension in terms of the compressibility of the reference hard-core system and its derivatives with respect to density. We demonstrate that the obtained analytical microscopic expression for the surface tension near the critical point is in a good agreement with numerical experiments, which emphasizes the impact of microscopic structure on the critical behavior of the surface tension in fluids. Our analysis provides a basis for studying the surface tension in small-volume systems important in many technological applications.
We solve a renormalized Wheeler-DeWitt equation for Einstein gravity in D+1 dimensions with D= odd in the strong coupling limit, which is expected to be suited to probe quantum geometry at short distances, in order to test Horava's idea that quantum gravity at short distances will be described by a nonrelativistic system with dynamical critical exponent z>1. Our results support the idea and show that the Wheeler-DeWitt equation possesses a solution associated with a z=2 Lifshitz point but no other z>2 solutions to leading order of the strong coupling expansion.
The hybrid model with a scalar "inflaton" field coupled to a "Higgs" field with a broken symmetry potential is one of the promising models for inflation and (p)reheating after inflation. We consider the nonequilibrium evolution of the quantum fields of this model with quantum back reaction in the Hartree approximation, in particular the transition of the Higgs field from the metastable "false vacuum" to the broken symmetry phase. We have performed the renormalization of the equations of motion, of the gap equations and of the energy density, using dimensional regularization. We study the influence of the back reaction on the evolution of the classical fields and of the quantum fluctuations. We observe that back reaction plays an important role over a wide range of parameters. Some implications of our investigation for the preheating stage after cosmic inflation are presented.
The temperature-dependent phase transitions in Ruddlesden-Popper oxides with perovskite bilayers have been under increased scrutiny in recent years due to the so-called hybrid improper ferroelectricity that some chemical compositions exhibit. However, little is currently understood about the hydrostatic pressure dependence of these phase transitions. Herein we present the results of a high-pressure powder synchrotron X-ray diffraction experiment and $ab~initio$ calculations on the bilayered Ruddlesden-Popper phases Ca$_{3}$Mn$_{2}$O$_{7}$ and Ca$_{3}$Ti$_{2}$O$_{7}$. In both compounds we observe a first-order phase transition between polar $A2_{1}am$ and non-polar $Acaa$ structures. Interestingly, we show that while the application of pressure ultimately favours a non-polar phase -- as is commonly observed for proper ferroelectrics -- regions of response exist where pressure actually acts to increase the polar mode amplitudes. The reason for this can be untangled by considering the varied response of octahedral tilts and rotations to hydrostatic pressure and their trilinear coupling with the polar instability.
Key to advancing lithium-ion battery technology, and in particular fast charging capabilities, is our ability to follow and understand the dynamic processes occurring in operating materials under realistic conditions, in real time, and on the nano- to meso-scale. Currently, operando imaging of lithium-ion dynamics requires sophisticated synchrotron X-ray or electron microscopy techniques, which do not lend themselves to high-throughput material screening. This limits rapid and rational materials improvements. Here we introduce a simple lab-based, optical interferometric scattering microscope to resolve nanoscopic lithium-ion dynamics in battery materials and apply it to follow the repeated cycling of the archetypical cathode material Li$_\textit{x}$CoO$_2$. The method allows us to visualise directly the insulator-metal, solid solution and lithium ordering phase transitions in this material. We determine rates of lithium insertion and removal at the single-particle level and identify different mechanisms that occur on charge vs. discharge. Finally, we capture the dynamic formation of domain boundaries between different crystal orientations associated with the monoclinic lattice distortion at around Li$_{0.5}$CoO$_2$. The high throughput nature of our methodology allows many particles to be sampled across the entire electrode and, moving forward, will enable exploration of the role of dislocations, morphologies and cycling rate on battery degradation. The generality of our imaging concept means that it can be applied to study any battery electrode, and more broadly, systems where the transport of ions is associated with electronic or structural changes, including nanoionic films, ionic conducting polymers, photocatalytic materials and memristors.
4FGL J0935.3+0901 is a gamma-ray source detected by the Large Area Telescope (LAT) onboard the Fermi Gamma-Ray Space Telescope. We have conducted detailed analysis of the LAT data for this source and multi-wavelength studies of the source field. Its gamma-ray emission can be described with a power law ($\Gamma=2.0\pm0.2$) with an exponential cutoff ($E_c=2.9\pm1.6$ GeV), while the flux shows significant long-term variations. From analysis of archival Neil Gehrels Swift X-ray Telescope data, we find only one X-ray source in the LAT's 2$\sigma$ error region. Within a 3.7" radius error circle of the X-ray source, there is only one optical object down to $r'\sim$23 mag. Time-resolved photometry of the optical object indicates a likely 2.5~hr periodic modulation, while its spectrum shows double-peaked hydrogen and helium emission lines (similar to those seen in accretion discs in low-mass X-ray binaries). Combining these results, we conclude that we have discovered a compact X-ray emitting binary in likely association with 4FGL J0935.3+0901, i.e., a millisecond pulsar (MSP) binary. We discuss the implication of the optical spectral features: this binary could be a transitional MSP system at a sub-luminous disc state, although the other possibility, the binary in a rotation-powered state showing the optical emission lines due to intrabinary interaction processes, can not be excluded. Further observational studies will help determine detailed properties of this candidate MSP binary and thus clarify its current state.
We consider the shape of the posterior distribution to be used when fitting cosmological models to power spectra measured from galaxy surveys. At very large scales, Gaussian posterior distributions in the power do not approximate the posterior distribution $\mathcal{P}_R$ we expect for a Gaussian density field $\delta_k$, even if we vary the covariance matrix according to the model to be tested. We compare alternative posterior distributions with $\mathcal{P}_R$, both mode-by-mode and in terms of expected measurements of primordial non-Gaussianity parameterised by $f_\mathrm{NL}$. Marginalising over a Gaussian posterior distribution $\mathcal{P}_f$ with fixed covariance matrix yields a posterior mean value of $f_\mathrm{NL}$ which, for a data set with the characteristics of Euclid, will be underestimated by $\triangle f_\mathrm{NL}=0.4$, while for the data release 9 (DR9) of the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) it will be underestimated by $\triangle f_\mathrm{NL}=19.1$. Adopting a different form of the posterior function means that we do not necessarily require a different covariance matrix for each model to be tested: this dependence is absorbed into the functional form of the posterior. Thus, the computational burden of analysis is significantly reduced.
We report the detection of multiple quasi-periodic pulsations (QPPs) observed during the flaring activity of KIC 8414845, a young, active solar-type star observed by the Kepler mission launched by NASA. We analyzed the QQP signal using a data-driven, nonparametric method called singular spectrum analysis (SSA), which has never been utilized previously for analyzing solar or stellar QPPs. Because it is not based on a prescribed choice of basis functions, SSA is particularly suitable for analyzing nonstationary, nonlinear signals such as those observed in QPPs during major flares. The analysis has revealed that the apparent anharmonic shape of the QPP in this superflare results from a superposition of two intrinsic modes of periods of 49 min and 86 min, which display quasi-harmonic behaviors and different modulation patterns. The two reconstructed signals are consistent with slow-mode transverse and/or longitudinal magnetohydrodynamic oscillations excited in a coronal loop inducing periodic releases of flaring energy in a nearby loop through a mechanism of repetitive reconnection. The peculiar amplitude modulation of the two modes evinced by SSA favors the interpretation of the observed QPP pattern as due to the excitation in a coronal loop of the second harmonic of a standing slow-mode magnetoacoustic oscillation and a global kink oscillation periodically triggering magnetic reconnection in a nearby loop. Concurrent interpretations cannot however be ruled out on the basis of the available data.
In this work, we obtain the hydrostatic approximation by taking the small aspect ratio limit to the Navier-Stokes equations. The aspect ratio (the ratio of the depth to horizontal width) is a geometrical constraint in general large scale geophysical motions that the vertical scale is significantly smaller than horizontal. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier-Stokes equations to the compressible Primitive Equations. This is the first work to use relative entropy inequality for proving hydrostatic approximation and derive the compressible Primitive Equations.
Generalizing a result of S.V. Konyagin and D.R. Heath--Brown, we prove, in particular, that for any multiplicative subgroup R of Z/pZ and any nonzero elements mu_1,...,mu_k the following holds |R \cap (R+mu_1) \cap ... \cap (R+mu_k)| \ll_k |R|^{1/2+alpha_k}, provided by 1 \ll_k |R| \ll_k p^{1-\beta_k}, where alpha_k, beta_k are some sequences of positive reals and alpha_k, beta_k tend to zero. Besides we show that for an arbitrary subgroup R, |R| < p^{1/2} one have |R\pm R| > |R|^{5/3} \log^{-1/2} |R|.
We theoretically study the transmittance for normal incidence of linearly polarized light between two media separated by a strained graphene monolayer. We analytically characterize the degree of dichroism and the transparency of graphene as a function of an arbitrary uniform strain and the incident polarization. We discuss how measurements of dichroism and transparency for two different polarization directions can be used to determine the magnitude and direction of strain. Ours findings result in very useful tools to tune the graphene absorption by mechanical strain, as well as to design nano-devices to determine crack propagation in materials.
We study the distribution of the maximum $M$ of a random walk whose increments have a distribution with negative mean and belonging, for some $\gamma>0$, to a subclass of the class $\mathcal{S}_\gamma$--see, for example, Chover, Ney, and Wainger (1973). For this subclass we give a probabilistic derivation of the asymptotic tail distribution of $M$, and show that extreme values of $M$ are in general attained through some single large increment in the random walk near the beginning of its trajectory. We also give some results concerning the ``spatially local'' asymptotics of the distribution of $M$, the maximum of the stopped random walk for various stopping times, and various bounds.
The present paper extends the thermodynamic dislocation theory developed by Langer, Bouchbinder, and Lookmann to non-uniform plastic deformations. The free energy density as well as the positive definite dissipation function are proposed. The governing equations are derived from the variational equation. As illustration, the problem of plane strain constrained shear of single crystal deforming in single slip is solved within the proposed theory.
Quantum computing is a rapidly expanding field with applications ranging from optimization all the way to complex machine learning tasks. Quantum memories, while lacking in practical quantum computers, have the potential to bring quantum advantage. In quantum machine learning applications for example, a quantum memory can simplify the data loading process and potentially accelerate the learning task. Quantum memory can also store intermediate quantum state of qubits that can be reused for computation. However, the depth, gate count and compilation time of quantum memories such as, Quantum Read Only Memory (QROM) scale exponentially with the number of address lines making them impractical in state-of-the-art Noisy Intermediate-Scale Quantum (NISQ) computers beyond 4-bit addresses. In this paper, we propose techniques such as, predecoding logic and qubit reset to reduce the depth and gate count of QROM circuits to target wider address ranges such as, 8-bits. The proposed approach reduces the number of gates and depth count by at least 2X compared to the naive implementation at only 36% qubit overhead. A reduction in circuit depth and gate count as high as 75X and compilation time by 85X at the cost of a maximum of 2.28X qubit overhead is observed. Experimentally, the fidelity with the proposed predecoding circuit compared to existing optimization approach is also higher (as much as 73% compared to 40.8%) under reduced error rates.
Hot subdwarf stars (sdO/Bs) are evolved core helium-burning stars with very thin hydrogen envelopes, which can be formed by common envelope ejection. Close sdB binaries with massive white dwarf (WD) companions are potential progenitors of thermonuclear supernovae type Ia (SN~Ia). We discovered such a progenitor candidate as well as a candidate for a surviving companion star, which escapes from the Galaxy. More candidates for both types of objects have been found by crossmatching known sdB stars with proper motion and light curve catalogues. We found 72 sdO/B candidates with high Galactic restframe velocities, 12 of them might be unbound to our Galaxy. Furthermore, we discovered the second-most compact sdB+WD binary known. However, due to the low mass of the WD companion, it is unlikely to be a SN\,Ia progenitor.
Pairs of consecutive integers have the same height in the Collatz problem with surprising frequency. Garner gave a conjectural family of conditions for exactly when this occurs. Our main result is an infinite family of counterexamples to Garner's conjecture.
We investigate the cosmic dynamics of Rastall gravity in non-flat Friedmann-Robertson-Walker (FRW) space-time with barotropic fluid. In this context, we are concerned about the class of model satisfying the affine equation of state. We derive the autonomous system for the Rastall model with barotropic fluid. We apply the derived system to investigate the critical points for expanding and bouncing cosmologies and their stable nature and cosmological properties. The expanding cosmology yields de Sitter universe at late times with decelerating past having matter and radiation dominated phases. Investigation of autonomous system for bouncing cosmology yields oscillating solutions in positive spatial curvature region. We also investigate the consequences of setting-up a model of non-singular universe by using energy conditions. The distinct features of the Rastall model compared to the standard model have been discussed in detail.
In the dynamical models of gamma-ray burst (GRB) afterglows, the uniform assumption of the shocked region is known as provoking total energy conservation problem. In this work we consider shocks originating from magnetized ejecta, extend the energy-conserving hydrodynamical model of Yan et al. (2007) to the MHD limit by applying the magnetized jump conditions from Zhang & Kobayashi (2005). Compared with the non-conservative models, our Lorentz factor of the whole shocked region is larger by a factor $\lesssim\sqrt{2}$. The total pressure of the forward shocked region is higher than the reversed shocked region, in the relativistic regime with a factor of about 3 in our interstellar medium (ISM) cases while ejecta magnetization degree $\sigma<1$, and a factor of about 2.4 in the wind cases. For $\sigma\le 1$, the non-conservative model loses $32-42$% of its total energy for ISM cases, and for wind cases $25-38$%, which happens specifically in the forward shocked region, making the shock synchrotron emission from the forward shock less luminous than expected. Once the energy conservation problem is fixed, the late time light curves from the forward shock become nearly independent of the ejecta magnetization. The reverse shocked region doesn't suffer from the energy conservation problem since the changes of the Lorentz factor are recompensed by the changes of the shocked particle number density. The early light curves from the reverse shock are sensitive to the magnetization of the ejecta, thus are an important probe of the magnetization degree.
Let $\Gamma\subset \bar{\mathbb Q}^{\times}$ be a finitely generated multiplicative group of algebraic numbers. Let $\alpha_1,\ldots,\alpha_r\in\bar{\mathbb Q}^\times$ be algebraic numbers which are $\mathbb{Q}$-linearly independent and let $\epsilon>0$ be a given real number. One of the main results that we prove in this article is as follows; There exist only finitely many tuples $(u, q, p_1,\ldots,p_r)\in\Gamma\times\mathbb{Z}^{r+1}$ with $d = [\mathbb{Q}(u):\mathbb{Q}]$ for some integer $d\geq 1$ satisfying $|\alpha_i q u|>1$, $\alpha_i q u$ is not a pseudo-Pisot number for some integer $i\in\{1, \ldots, r\}$ and $$ 0<|\alpha_j qu-p_j|<\frac{1}{H^\epsilon(u)|q|^{\frac{d}{r}+\varepsilon}} $$ for all integers $j = 1, 2,\ldots, r$, where $H(u)$ is the absolute Weil height. In particular, when $r =1$, this result was proved by Corvaja and Zannier in [3]. As an application of our result, we also prove a transcendence criterion which generalizes a result of Han\v{c}l, Kolouch, Pulcerov\'a and \v{S}t\v{e}pni\v{c}ka in [4]. The proofs rely on the clever use of the subspace theorem and the underlying ideas from the work of Corvaja and Zannier.
Two-dimensional materials are considered for future quantum devices and are usually produced by extensive methods like molecular beam epitaxy. We report on the fabrication of field-effect transistors using individual ultra-thin lead sulfide nanostructures with lateral dimensions in the micrometer range and a height of a few nanometers as conductive channel produced by a comparatively fast, inexpensive, and scalable colloidal chemistry approach. Contacted with gold electrodes, such devices exhibit p-type behavior and temperature-dependent photoconductivity. Trap states play a crucial role in the conduction mechanism. The performance of the transistors is among the ones of the best devices based on colloidal nanostructures.
Consider the nonautonomous semilinear evolution equation of type: $(\star) \; u'(t)=A(t)u(t)+f(t,u(t)), \; t \in \mathbb{R},$ where $ A(t), \ t\in \mathbb{R} $ is a family of closed linear operators in a Banach space $X$, the nonlinear term $f$, acting on some real interpolation spaces, is assumed to be almost periodic just in a weak sense (i.e. in Stepanov sense) with respect to $t$ and Lipschitzian in bounded sets with respect to the second variable. We prove the existence and uniqueness of almost periodic solutions in the strong sense (Bohr sense) for equation $ (\star) $ using the exponential dichotomy approach. Then, we establish a new composition result of Stepanov almost periodic functions by assuming just the continuity of $f$ in the second variable. Moreover, we provide an application to a nonautonomous system of reaction-diffusion equations describing a Lotka-Volterra predator-prey model with diffusion and time-dependent parameters in a generalized almost periodic environment.
The Fornax dwarf spheroidal galaxy is the most massive satellites of the Milky Way, claimed to be embedded in a huge dark matter halo, and the only among the Milky Way satellites hosting five globular clusters. Interestingly, their estimated masses, ages and positions seem hardly compatible with the presence of a significant dark matter component, as expected in the $\Lambda$ CDM scheme. Indeed, if Fornax would have a CDM halo with a standard density profile, all its globular clusters should have sunk to the galactic centre many Gyr ago due to dynamical friction. Due to this, some authors proposed that the most massive clusters may have formed out of Fornax and later tidally captured. In this paper we investigate the past evolution of the Fornax GC system by using both a recently developed, semi-analytical treatment of dynamical friction and direct $N$-body simulations of the orbital evolution of the globular clusters within Fornax and of Fornax galaxy around the Milky Way. Our results suggest that an "in-situ" origin for all the clusters is likely if their observed positions are close to their spatial ones and their orbits are almost circular. Moreover, the Milky Way seems to accelerate the GC decay reducing the decay time of $15\%$. Nevertheless, our results indicate that the GCs survival probability exceeds $50\%$, even in the case of cuspy density profiles. We conclude that more detailed data are required to shed light on the Fornax dark matter content, to distinguish between a cuspy or a cored profile.
We model a 21 cm intensity mapping survey in the redshift range 0.01<z<1.5 designed to simulate the skies as seen by future radio telescopes such as the Square Kilometre Array (SKA), including instrumental noise and Galactic foregrounds. In our pipeline, we remove the introduced Galactic foregrounds with a fast independent component analysis (fastica) technique. We present the power spectrum of the large-scale matter distribution, C(l), before and after the application of this foreground removal method and calculate the resulting systematic errors. We attempt to reduce systematics in the foreground subtraction by optimally masking the maps to remove high foregrounds in the Galactic plane. Our simulations show a certain level of bias remains in the power spectrum at all scales l<400. At large-scales l<30 this bias is particularly significant. We measure the impact of these systematic effects in two different ways: firstly we fit cosmological parameters to the broadband shape of the power spectrum and secondly we extract the position of the Baryon Acoustic Oscillations (BAO). In the first analysis, we find that the systematics introduce an significant shift in the best fit cosmological parameters at the 2 to 3 sigma level which depends on the masking and noise levels. However, cosmic distances can be recovered in an unbiased way after foreground removal at all simulated redshifts by fitting the BAOs in the power spectrum. We conclude that further advances in foreground removal are needed in order to recover unbiased information from the broadband shape of the power spectrum, however, intensity mapping experiments will be a powerful tool for mapping cosmic distances across a wide redshift range.
This paper is a continuation of our accompanying paper [Talbi, Touzi and Zhang (2021)], where we characterized the mean field optimal stopping problem by an obstacle equation on the Wasserstein space of probability measures, provided that the value function is smooth. Our purpose here is to establish this characterization under weaker regularity requirements. We shall define a notion of viscosity solutions for such equation, and prove existence, stability, and comparison principle.