ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origami-based metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origami-based metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system. We also demonstrate the existence of numerically exact traveling rarefaction waves. Origami-based metamaterials can be highly useful for mitigating shock waves, potentially enabling a wide variety of engineering applications.
We present first-principles calculations of the coupling of quasiparticles to spin fluctuations in iron selenide and discuss which types of superconducting instabilities this coupling gives rise to. We find that strong antiferromagnetic stripe-phase spin fluctuations lead to large coupling constants for superconducting gaps with $s_\pm$-symmetry, but these coupling constants are significantly reduced by other spin fluctuations with small wave vectors. An accurate description of this competition and an inclusion of band structure and Stoner parameter renormalization effects lead to a value of the coupling constant for an $s_\pm$-symmetric gap which can produce a superconducting transition temperature consistent with experimental measurements.
Generating mocks for future sky surveys requires large volumes and high resolutions, which is computationally expensive even for fast simulations. In this work we try to develop numerical schemes to calibrate various halo and matter statistics in fast low resolution simulations compared to high resolution N-body and hydrodynamic simulations. For the halos, we improve the initial condition accuracy and develop a halo finder "relaxed-FOF", where we allow different linking length for different halo mass and velocity dispersions. We show that our relaxed-FoF halo finder improves the common statistics, such as halo bias, halo mass function, halo auto power spectrum in real space and in redshift space, cross correlation coefficient with the reference halo catalog, and halo-matter cross power spectrum. We also incorporate the potential gradient descent (PGD) method into fast simulations to improve the matter distribution at nonlinear scale. By building a lightcone output, we show that the PGD method significantly improves the weak lensing convergence tomographic power spectrum. With these improvements FastPM is comparable to the high resolution full N-body simulation of the same mass resolution, with two orders of magnitude fewer time steps. These techniques can be used to improve the halo and matter statistics of FastPM simulations for mock catalogs of future surveys such as DESI and LSST.
Using high resolution X-Ray diffraction (XRD) on high purity powders, we resolved the structure and $ab$ symmetry of the intriguing compound \svo$ $ from room temperature down to 20 K to an unprecedented level of accuracy. Upon cooling, this new set of data unambiguously reveals a second order phase transition lowering the symmetry from tetragonal to orthorhombic at a temperature $T_{c2}=136$ K. The observation of an orthorhombic distortion of the $ab$-plane is attributed to nematic phase formation supported by local Jahn-Teller (JT) dynamical instability. At $T_{N}=105$ K, spins order and at $T_{c1}=100$ K the tetragonal structure is recovered with an elongated c-axis.
The Faddeev technique is employed to study the influence of both particle-particle and particle-hole phonons on the one-hole spectral function of O16.   Collective excitations are accounted for at a random phase approximation level and subsequently summed to all orders by the Faddeev equations to obtain the nucleon self-energy. An iterative procedure is applied to investigate the effects of the self-consistent inclusion of the fragmentation in the determination of the phonons and the corresponding self-energy. The present results indicate that the characteristics of hole fragmentation are related to the low-lying states of O16.
An arbitrary-depth reduction theorem for the `convolution' multiple L-values of Euler-Zagier type is proven by an analytic method. To this end, generalized polylogarithms associated to Dirichlet characters are defined. The proof uses the monodromies of these functions and the parities of generating functions of generalized Bernoulli numbers. Some general formulas for resulting reductions in the depth 2 case are provided.
We present a direct detection of the stellar halo of the edge-on S0 galaxy NGC 3957, using ultra-deep VLT/VIMOS V and R images. This is achieved with a sky subtraction strategy based on infrared techniques. These observations allow us to reach unprecedented high signal-to-noise ratios up to 15 kpc away from the galaxy center, rendering photon-noise negligible. The 1 sigma detection limits are R = 30.6 mag/arcsec^2 and V = 31.4 mag/arcsec^2. We conduct a thorough analysis of the possible sources of systematic errors that could affect the data: flat-fielding, differences in CCD responses, scaling of the sky background, the extended halo itself, and PSF wings. We conclude that the V-R colour of the NGC 3957 halo, calculated between 5 and 8 kpc above the disc plane where the systematic errors are modest, is consistent with an old and preferentially metal-poor normal stellar population, like that revealed in nearby galaxy halos from studies of their resolved stellar content. We do not find support for the extremely red colours found in earlier studies of diffuse halo emission, which we suggest might have been due to residual systematic errors.
We consider the evolution of open planar curves by the steepest descent flow of a geometric functional, under different boundary conditions. We prove that, if any set of stationary solutions with fixed energy is finite, then a solution of the flow converges to a stationary solution as time goes to infinity. We also present a few applications of this result.
For a set $S$ of quadratic polynomials over a finite field, let $C$ be the (infinite) set of arbitrary compositions of elements in $S$. In this paper we show that there are examples with arbitrarily large $S$ such that every polynomial in $C$ is irreducible. As a second result, we give an algorithm to determine whether all the elements in $C$ are irreducible, using only $O( \#S (\log q)^3 q^{1/2} )$ operations.
We report the results of our XMM-Newton monitoring of SN 1987A. The ongoing propagation of the supernova blast wave through the inner circumstellar ring caused a drastic increase in X-ray luminosity during the last years, enabling detailed high resolution X-ray spectroscopy with the Reflection Grating Spectrometer. The observations can be used to follow the detailed evolution of the arising supernova remnant. The fluxes and broadening of the numerous emission lines seen in the dispersed spectra provide information on the evolution of the X-ray emitting plasma and its dynamics. These were analyzed in combination with the EPIC-pn spectra, which allow a precise determination of the higher temperature plasma. We modeled individual emission lines and fitted plasma emission models. Especially from the observations between 2003 and 2007 we can see a significant evolution of the plasma parameters and a deceleration of the radial velocity of the lower temperature plasma regions. We found an indication (3-sigma-level) of an iron K feature in the co-added EPIC-pn spectra. The comparison with Chandra grating observations in 2004 yields a clear temporal coherence of the spectral evolution and the sudden deceleration of the expansion velocity seen in X-ray images ~6100 days after the explosion.
We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We find close quantitative agreement between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In the synchronized state we demonstrate a significant reduction in the phase noise of the oscillators, which is key for sensor and clock applications. Our work establishes that oscillator networks constructed from nanomechanical resonators form an ideal laboratory to study synchronization given their high-quality factors, small footprint, and ease of co-integration with modern electronic signal processing technologies.
In this paper we prove that the 1D Schr\"odinger equation with derivative in the nonlinear term is globally well-posed in $H^{s}$, for $s>\frac12$ for data small in $L^{2}$. To understand the strength of this result one should recall that for $s<\frac12$ the Cauchy problem is ill-posed, in the sense that uniform continuity with respect to the initial data fails. The result follows from the method of almost conserved energies, an evolution of the ``I-method'' used by the same authors to obtain global well-posedness for $s>\frac23$. The same argument can be used to prove that any quintic nonlinear defocusing Schr\"odinger equation on the line is globally well-posed for large data in $H^{s}$, for $s>\frac12$.
Consider a family of $\Delta$-latticed aperiodic random walks $\{S^{(a)},0\le a\le a_0\}$ with increments $X_i^{(a)}$ and non-positive drift $-a$. Suppose that $\sup_{a\le a_0}\mathbf{E}[(X^{(a)})^2]<\infty$ and $\sup_{a\le a_0}\mathbf{E}[\max\{0,X^{(a)}\}^{2+\varepsilon}]<\infty$ for some $\varepsilon>0$. Assume that $X^{(a)}\xrightarrow[]{w} X^{(0)}$ as $a\to 0$ and denote by $M^{(a)}=\max_{k\ge 0} S_k^{(a)}$ the maximum of the random walk $S^{(a)}$. In this paper we provide the asymptotics of $\mathbf{P}(M^{(a)}=y\Delta)$ as $a\to 0$ in the case, when $y\to \infty$ and $ay=O(1)$. This asymptotics follows from a representation of $\mathbf{P}(M^{(a)}=y\Delta)$ via a geometric sum and a uniform renewal theorem, which is also proved in this paper.
A quantum computer is a multi-particle interferometer that comprises beam splitters at both ends and arms, where the n two-level particles undergo the interactions among them. The arms are designed so that relevant functions required to produce a computational result is stored in the phase shifts of the 2^n arms. They can be detected by interferometry that allows us to utilize quantum parallelism. Quantum algorithms are accountable for what interferometers to be constructed to compute particular problems. A standard formalism for constructing the arms has been developed by the extension of classical reversible gate arrays. By its nature of sequential applications of logic operations, the required number of gates increases exponentially as the problem size grows. This may cause a crucial obstacle to perform a quantum computation within a limited decoherence time. We propose a direct and concurrent construction of the interferometer arms by one-time evolution of a physical system with arbitrary multi-particle interactions. It is inherently quantum mechanical and has no classical analogue. Encoding the functions used in Shor's algorithm for prime factoring, Grover's algorithm and Deutsch-Jozsa algorithm requires only one-time evolution of such a system regardless of the problem size n as opposed to its standard sequential counterpart that takes O(n^3), O(n) and O(n2^n).
Ochiai has previously proved that the Beilinson-Kato Euler systems for modular forms interpolate in nearly-ordinary $p$-adic families (Howard has obtained a similar result for Heegner points), based on which he was able to prove a half of the two-variable main conjectures. The principal goal of this article is to generalize Ochiai's work in the level of Kolyvagin systems so as to prove that Kolyvagin systems associated to Beilinson-Kato elements interpolate in the full deformation space (in particular, beyond the nearly-ordinary locus) and use what we call universal Kolyvagin systems to attempt a main conjecture over the eigencurve. Along the way, we utilize these objects in order to define a quasicoherent sheaf on the eigencurve that behaves like a $p$-adic $L$-function (in a certain sense of the word, in $3$-variables).
The electroweak unification group $G\equiv SU(2)_L\times U(1)_e\times U(1)_\mu\times U(1)_\tau$ in which each fermion multiplet has its own $U(1)$ factor was proposed in 1986 to get the neutrino mass matrix. In this paper, the gauge group G is restricted to lepton section only, leaving quark multiplets as in the standard model. In addition to lepton multiplets $L_e$, $L_\mu$ and $L_\tau$, there are three $SU(2)$singlet right handed neutrinos $N_{R}^{(i)}$'s. WIth the breaking of G to $SU(2)_L\times U(1)$, the right handed neutrinos acquire heavy Majorana masses. Three heavy right handed neutrinos $N_{R}^{(i)}$'s are available to generate a $3\times 3$ non-diagonal neutrino mass matrix in terms of three Yukawa couplings $h^{(2)}_{1}$, $h^{(3)}_{2}$, $h^{(1)}_{3}$ of the Higgs scalar doublet to $L_e$, $L_\mu$, $L_\tau$ with $N_{R}^{(1)}$, $N_{R}^{(2)}$ and $N_{R}^{(3)}$ respectively. Three Yukawa couplings can be arranged and expressed in terms of masses $m_e$, $m_\mu$, $m_\tau$ in three different ways to obtain the results of interest for Case 1: ($\nu_e \rightarrow \nu_\tau$); Case 2: ($\nu_e \rightarrow \nu_\mu$); Case 3: ($\nu_\mu \rightarrow \nu_\tau$). The results obtained for the three cases are compared with the experimental data from neutrino oscillations. Cases 1 and 2 are relevant for solar neutrino oscillations whereas Case 3 is relevant for atmospheric neutrino oscillations.
It has been shown observationally that star formation (SF) correlates tightly with the presence of molecular hydrogen (H$_2$). Therefore it would be important to investigate its implication on galaxy formation in a cosmological context. In the present work, we track the H$_2$ mass fraction within our cosmological smoothed particle hydrodynamics (SPH) code GADGET-3 using an equilibrium analytic model by Krumholz et al. This model allows us to regulate the star formation in our simulation by the local abundance of H$_2$ rather than the total cold gas density, and naturally introduce the dependence of star formation on metallicity. We investigate implications of the equilibrium H$_2$-based SF model on galaxy population properties, such as the stellar-to-halo mass ratio (SHMR), baryon fraction, cosmic star formation rate density (SFRD), galaxy specific SFR, galaxy stellar mass functions (GSMF), and Kennicutt-Schmidt (KS) relationship. The advantage of our work over the previous ones is having a large sample of simulated galaxies in a cosmological volume from high-redshift to $z=0$. We find that low-mass halos with M$_{DM}<10^{10.5}$ M$_\odot$ are less efficient in producing stars in the H$_2$-based SF model at $z\geq6$, which brings the simulations to a better agreement with observational estimates of SHMR and GSMF at the low-mass end. This is particularly evident by a reduction in the number of low-mass galaxies at M$_\star\leq10^{8}$ M$_\odot$ in the GSMF. The overall SFRD is also reduced at high-$z$ in the H$_2$ run, which results in slightly higher SFRD at low-redshift due to more abundant gas available for star formation at later times. This new H$_2$ model is able to reproduce the empirical KS relationship at $z=0$ naturally without the need for setting its normalization by hand, and overall it seems to have more advantages than the previous pressure-based SF model.
A graphical representation based on duplication is developed that is suitable for the study of Ising systems in external fields. Two independent replicas of the Ising system in the same field are treated as a single four-state (Ashkin-Teller) model. Bonds in the graphical representation connect the Ashkin-Teller spins. For ferromagnetic systems it is proved that ordering is characterized by percolation in this representation. The representation leads immediately to cluster algorithms; some applications along these lines are discussed.
Photodisintegration of the deuteron above pi-threshold is studied in a coupled channel approach including N Delta- and pi d-channels with pion retardation in potentials and exchange currents. A much improved description of total and differential cross sections in the energy region between pi-threshold and 400-450 MeV is achieved.
A diversity of spin Hall effects in metallic systems is known to rely on Mott skew scattering. In this work its high-temperature counterpart, phonon skew scattering, which is expected to be of foremost experimental relevance, is investigated. In particular, the phonon skew scattering spin Hall conductivity is found to be practically $T$-independent for temperatures above the Debye temperature $T_D$. As a consequence, in Rashba-like systems a high-$T$ linear behavior of the spin Hall angle demonstrates the dominance of extrinsic spin-orbit scattering only if the intrinsic spin splitting is smaller than the temperature.
We construct the Hamiltonian of the super five brane in terms of its physical degrees of freedom. It does not depend on the inverse of the induced metric. Consequently, some singular configurations are physically admissible, implying an interpretation of the theory as a multiparticle one. The symmetries of the theory are analyzed from the canonical point of view in terms of the first and second class constraints. In particular it is shown how the chiral sector may be canonically reduced to its physical degrees of freedom.
We show that there is a perverse sheaf on a fine moduli space of stable sheaves on a smooth projective Calabi-Yau 3-fold, which is locally the perverse sheaf of vanishing cycles for a local Chern-Simons functional, possibly after taking an etale Galois cover. This perverse sheaf lifts to a mixed Hodge module and gives us a cohomology theory which enables us to define the Gopakumar-Vafa invariants mathematically.
We extend the eV seesaw scenario to four lepton generations. The LSND anomaly is taken as the right-handed seesaw scale, i.e. m_R ~ eV. The fourth generation then gives a heavy pseudo-Dirac neutrino which largely decouples from other generations, and is relatively stable. One effectively has a 3+3 solution to the LSND anomaly, where we illustrate with numerical solutions. Our study indicates that the third mixing angle sin^2(theta13) is likely less than 0.01.
Nagao's conjecture relates the rank of an elliptic surface to a limit formula arising from a weighted average of fibral Frobenius traces, and it is further generalized for smooth irreducible projective surfaces by M. Hindry and A. Pacheco. We show that the Sato-Tate conjecture based on the random matrix model implies Nagao's conjecture for certain twist families of elliptic curves and hyperelliptic curves.
In this survey we explore the salient connections made between Brownian motion, symmetrization and complex analysis in the last 60 years starting with Kakutani's paper (1944) equating harmonic measure and exit probability. To exemplify these connections we will survey the techniques used in the literature to prove isoperimetric results for exit probabilities and Riesz capacities.
Nanoscale layered ferromagnets have demonstrated fascinating two-dimensional magnetism down to atomic layers, providing a peculiar playground of spin orders for investigating fundamental physics and spintronic applications. However, strategy for growing films with designed magnetic properties is not well established yet. Herein, we present a versatile method to control the Curie temperature (T_{C}) and magnetic anisotropy during growth of ultrathin Cr_{2}Te_{3} films. We demonstrate increase of the TC from 165 K to 310 K in sync with magnetic anisotropy switching from an out-of-plane orientation to an in-plane one, respectively, via controlling the Te source flux during film growth, leading to different c-lattice parameters while preserving the stoichiometries and thicknesses of the films. We attributed this modulation of magnetic anisotropy to the switching of the orbital magnetic moment, using X-ray magnetic circular dichroism analysis. We also inferred that different c-lattice constants might be responsible for the magnetic anisotropy change, supported by theoretical calculations. These findings emphasize the potential of ultrathin Cr_{2}Te_{3} films as candidates for developing room-temperature spintronics applications and similar growth strategies could be applicable to fabricate other nanoscale layered magnetic compounds.
The structural motifs of a Zr$_{50}$Cu$_{45}$Al$_{5}$ metallic glass were learned from atomistic models using a new structure analysis method called motif extraction that employs point-pattern matching and machine learning clustering techniques. The motifs are the nearest-neighbor building blocks of the glass and reveal a well-defined hierarchy of structures as a function of coordination number. Some of the motifs are icosahedral or quasi-icosahedral in structure, while others take on the structure of the most close-packed geometries for each coordination number. These results set the stage for developing clearer structure-property connections in metallic glasses. Motif extraction can be applied to any disordered material to identify its structural motifs without the need for human input.
In this contribution we study the birefringence and the quasinormal modes (QNM) in the eikonal approximation, of the Einstein-Euler-Heisenberg black hole (EEH-BH) . The EEH-BH is an exact solution of the Einstein equations coupled to the Euler-Heisenberg nonlinear electrodynamics. It is well known that in the presence of strong electromagnetic fields light rays modify their trajectories and do follow the null geodesics of an effective metric as a result of the nonlinear interaction between light and the intense magnetic or electric background. In the Euler-Heisenberg theory the phenomenon of birefringence arises and then exist two possible light trajectories for polarized light in the vicinity of the EEH-BH. On the other hand, using the correspondence between the parameters of the null unstable geodesics and the quasinormal modes in the eikonal approximation. We determine these QNM for both, the electric and the magnetic EEH-BH and compare them with its linear counterpart, the Reissner-Nordstr\"{o}m black hole, since there are two effective metrics, to each one corresponds one null geodesic that renders two possible QNM from the same compact object.