ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a thorough study on the magnetoanisotropic properties and magnetocaloric effect in the layered ferromagnetic Cr$_4$Te$_5$ single crystals by performing the critical behaviour analysis of magnetization isotherms. The critical exponents $\beta$=0.485(3), $\gamma$=1.202(5), and $\delta$=3.52(3) with a Curie temperature of $T_C \approx 340.73(4)$ K are determined by the modified Arrott plots. We observe a large magnetocrystalline anisotropy K$_u$=330 kJ/$m^3$ at 3 K which gradually decreases with increasing temperature. Maximum entropy change -$\Delta S_{M}^{max}$ and the relative cooling power (RCP) are found to be 2.77 $J/kg-K$ and 88.29 $J/kg$, respectively near $T_C$ when the magnetic field applied parallel to $\it{ab}$-plane. Rescaled -$\Delta S_M (T, H)$ data measured at various temperatures and fields collapse into a single universal curve, confirming the second order magnetic transition in this system. Following the renormalization group theory analysis, we find that the spin-coupling is of 3D Heisenberg-type, $\{d:n\}=\{3:3\}$, with long-range exchange interactions decaying as $J (r) = r^{-(d+\sigma)}= r^{-4.71}$.
We will present a new method, which enables us to find threshold functions for many properties in random intersection graphs. This method will be used to establish sharp threshold functions in random intersection graphs for k-connectivity, perfect matching containment and Hamilton cycle containment.
We give a direct combinatorial proof of a famous identity, $$ \sum_{i+j=n} m{2i}{i} \binom{2j}{j} = 4^n $$ by actually counting pairs of $k$-subsets of $2k$-sets. Then we discuss two different generalizations of the identity, and end the paper by presenting in explicit form the ordinary generating function of the sequence $(\strut\binom{2n+k}{n})_{n\in\mathds{N}_0}$, where $k\in\mathds{R}$.
We prove Zagier's conjecture regarding the 2-adic valuation of the coefficients $\{b_m\}$ that appear in Ewing and Schober's series formula for the area of the Mandelbrot set in the case where $m\equiv 2 \mod 4$.
Ferroelectric domain walls are nm-sized interfaces between sections of different allowed values of the spontaneous polarization, the so-called domains. These walls - neutral or charged - can be created, displaced, deleted, and recreated again in ferroelectric materials. [1-3] Owing to the recent progress in the studies of ferroelectrics, they are expected to be functional active elements of the future nano-electronics.[1,4,5] Metallic-like conductivity of charged domain walls (CDWs) in insulating ferroelectrics, predicted in 1970s6 and detected recently,[7-10] is especially attractive for applications. This important effect is still in its infancy. The electric currents are small, the access to the conductivity is hampered by contact barriers, and stability is low because of sophisticated domain structures and/or proximity of the Curie point. Here, we report on giant and accessible persistent CDW conductivity in lithium niobate (LN) crystals (LiNbO3) - a vital material for photonics. [12] Our results are by far superior to the data known for other materials: Increase of LN conductivity by more than 14 orders of magnitude owing to CDWs, access to the effect via Ohmic and semi-Ohmic contacts, and its high stability for temperatures of up to 70 {\deg}C are demonstrated. It is made clear why this big effect was missed earlier [11,25] in LN. Our results demonstrate that strong conductivity of CDWs is available in simple ferroelectric materials, possessing only two allowed orientations of the spontaneous polarization, far from the Curie point. Also, CDW functionalities can be combined with linear and nonlinear optical phenomena. [14,15] Our findings allow new generations of adaptive-optical elements, of electrically controlled integrated-optical chips for quantum photonics, and of advanced LN-semiconductor hybrid optoelectronic devices.
Let $f(\bfz,\bar\bfz)$ be a mixed polar homogeneous polynomial of $n$ variables $\bfz=(z_1,..., z_n)$. It defines a projective real algebraic variety $V:=\{[\bfz]\in \BC\BP^{n-1} | f(\bfz,\bar\bfz)=0 \}$ in the projective space $\BC\BP^{n-1}$. The behavior is different from that of the projective hypersurface. The topology is not uniquely determined by the degree of the variety even if $V$ is non-singular. We study a basic property of such a variety.
The notion of the orbifold Euler characteristic came from physics at the end of 80's. There were defined higher order versions of the orbifold Euler characteristic and generalized ("motivic") versions of them. In a previous paper the authors defined a notion of the Grothendieck ring $K_0^{\rm fGr}(Var)$ of varieties with actions of finite groups on which the orbifold Euler characteristic and its higher order versions are homomorphisms to the ring of integers. Here we define the generalized orbifold Euler characteristic and higher order versions of it as ring homomorphisms from $K_0^{\rm fGr}(Var)$ to the Grothendieck ring $K_0(Var)$ of complex quasi-projective varieties and give some analogues of the classical Macdonald equations for the generating series of the Euler characteristics of the symmetric products of a space.
We propose a simple conjecture for the functional form of the asymptotic behavior of work distributions for driven overdamped Brownian motion of a particle in confining potentials. This conjecture is motivated by the fact that these functional forms are independent of the velocity of the driving for all potentials and protocols, where explicit analytical solutions for the work distributions have been derived in the literature. To test the conjecture, we use Brownian dynamics simulations and a recent theory developed by Engel and Nickelsen (EN theory), which is based on the contraction principle of large deviation theory. Our tests suggest that the conjecture is valid for potentials with a confinement equal to or weaker than the parabolic one, both for equilibrium and for nonequilibrium distributions of the initial particle position. In addition we obtain a new analytical solution for the asymptotic behavior of the work distribution for the V-potential by application of the EN theory, and we extend this theory to nonequilibrated initial particle positions.
We present a comprehensive multi-wavelength analysis of the young cluster NGC 1624 associated with the H II region Sh2-212 using optical UBVRI photometry, optical spectroscopy and GMRT radio continuum mapping along with the near-infrared (NIR) JHK archival data. Reddening E(B-V) and distance to the cluster are estimated to be 0.76 - 1.00 mag and 6.0 +/- 0.8 kpc, respectively. Present analysis yields a spectral class of O6.5V for the main ionizing source of the region. The distribution of YSOs in (J-H)/ (H-K) NIR colour-colour diagram shows that a majority of them have A_V $\le$ 4 mag. Based on the NIR excess characteristics, we identified 120 probable candidate YSOs in this region which yield a disk frequency of ~ 20%. These YSOs are found to have an age spread of ~ 5 Myr with a median age of ~ 2-3 Myr and a mass range of ~ 0.1 - 3.0 $M_\odot$. A significant number of YSOs are located close to the cluster centre and we detect an enhanced density of reddened YSOs located/projected close to the molecular clumps at the periphery of NGC 1624. This indicates that the YSOs located within the cluster core are relatively older in comparison to those located/projected near the clumps. From the radio continuum flux, spectral class of the ionizing source of the ultra-compact H II region at the periphery of Sh2-212 is estimated to be ~ B0.5V. From optical data, slope of the mass function (MF) $\Gamma$, in the mass range $1.2 \le M/M_{\odot}<27$ can be represented by a single power law with a slope -1.18 +/- 0.10, whereas the NIR data in the mass range $0.65 \le M/M_{\odot}<27$ yields $\Gamma$ = -1.31 +/- 0.15. The slope of the K-band luminosity function (KLF) for the cluster is found to be 0.30 +/- 0.06 which is in agreement with the values obtained for other young clusters.
Within the microscopic transport, systematic investigation of the many facets of hyperons and hypernuclei up to strangeness $S = -2$ are carried out for $^{197}$Au + $^{197}$Au and $^{40}$Ca + $^{40}$Ca at the incident energy of $3A$ GeV. The spatial, temporal and density distributions of hyperon production, absorption and freeze-out are thoroughly investigated. The rapidity and kinetic energy spectra of $\Xi$ hyperons and double $\Lambda$ hypernuclei are analyzed. It is revealed that the chemical balance of hyperon production is established in baryon-baryon channels while the opposite is found in baryon-meson channels. It turns out that the rapidity spectra of $^{4,5}_{\Lambda\Lambda}$X are single-peak and more than two orders of magnitude lower than that of $^{3}_{\Lambda}$H. Formation of double $\Lambda$ hypernuclei through $\Xi$ hypernuclei as intermediate states is also discussed in kinematics.
SXP 15.3 and SXP 305 are two Be X-ray binaries in the Small Magellanic Cloud that are spatially separated by ~7 arcsec. The small separation between these sources has, in the past, resulted in confusion about the origin of the emission from the combined region. We present long-term optical and X-ray monitoring results of both sources, where we study the historic and recent behaviour. In particular, from data collected as part of the S-CUBED project we see repeating X-ray outbursts from the combined region of the two sources in the recent lightcurve from the Neil Gehrels Swift Observatory, and we investigate the origin of this emission. Using the H-alpha emission line from the Southern African Large Telescope (SALT) and photometric flux from the Optical Gravitational Lensing Experiment (OGLE) to study the changes in the size and structure of the Be disc, we demonstrate that the X-ray emission likely originates from SXP 15.3. Timing analysis reveals unusual behaviour, where the optical outburst profile shows modulation at twice the frequency of the X-ray outbursts. We consider either of these periodicities being the true orbital period in SXP 15.3 and propose models based on the geometric orientations of the Be disc and neutron star to explain the physical origin of the outbursts.
This paper studies the curvatures of amoebas and real amoebas (i.e. essentially logarithmic curvatures of the complex and real parts of a real algebraic hypersurface) and of tropical and real tropical hypersurfaces.   If V is a tropical hypersurface defined over the field of real Puiseux series, it has a real part RV which is a polyhedral complex. We define the total curvature of V (resp. RV) by using the total curvature of Amoebas and passing to the limit.   We also define the "polyhedral total curvature" of the real part RV of a generic tropical hypersurface.   The main results we prove about these notions are the following:   - The fact that the total curvature and the polyhedral total curvature coincide for real non-singular tropical hypersurfaces.   - A universal inequality between the total curvatures of V and RV and another between the logarithmic curvatures of the real and complex parts of a real algebraic hypersurface.   -The fact that this inequality is sharp in the non-singular case.
We construct the canonical structure of an irreducible projective variety on the set of connected curves of degree $d$ in $\Bbb P^n$ with rational components (some components can be multiple). The set of rational curves is open subset in the Zariski topology under this structure.
Recent experiments demonstrated generation of spin currents by ultrasound. We can understand this acoustically induced spin pumping in terms of the coupling between magnetization and lattice waves. Here we study the parametric excitation of magnetization by longitudinal acoustic waves and calculate the acoustic threshold power. The induced magnetization dynamics can be detected by the spin pumping into an adjacent normal metal that displays the inverse spin Hall effect.
We study the fourth order normalized cumulant of height fluctuations governed by $1+1$ dimensional Kardar-Parisi-Zhang (KPZ) equation for a growing surface. Following a diagrammatic renormalization scheme, we evaluate the kurtosis $Q$ from the connected diagrams leading to the value $Q=0.1523$ in the large-scale long-time limit.
The new generation of solar instruments provides better spectral, spatial, and temporal resolution for a better understanding of the physical processes that take place on the Sun. Multiple-component profiles are more commonly observed with these instruments. Particularly, the He I 10830 \r{A} triplet presents such peculiar spectral profiles, which give information on the velocity and magnetic fine structure of the upper chromosphere. The purpose of this investigation is to describe a technique to efficiently fit the two blended components of the He I 10830 \r{A} triplet, which are commonly observed when two atmospheric components are located within the same resolution element. The observations used in this study were taken on 2015 April 17 with the very fast spectroscopic mode of the GREGOR Infrared Spectrograph (GRIS) attached to the 1.5-meter GREGOR solar telescope, located at the Observatorio del Teide, Tenerife, Spain. We apply a double-Lorentzian fitting technique using Levenberg-Marquardt least-squares minimization. This technique is very simple and much faster than inversion codes. Line-of-sight Doppler velocities can be inferred for a whole map of pixels within just a few minutes. Our results show sub- and supersonic downflow velocities of up to 32 km/s for the fast component in the vicinity of footpoints of filamentary structures. The slow component presents velocities close to rest.
The purpose of this note is to study the number of elements in Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone.
Given a random matrix A with eigenvalues between -1 and 1, we analyze the number of iterations needed to solve the linear equation (I-A)x=b with the Neumann series iteration. We give sufficient conditions for convergence of an upper bound of the iteration count in distribution. Specifically, our results show that when the scaled extreme eigenvalues of A converge in distribution, this scaled upper bound on the number of iterations will converge to the reciprocal of the limiting distribution of the largest eigenvalue.
After a brief historical survey that emphasizes the role of the algebra obeyed by the Dirac operator, we examine an algebraic Dirac operator associated with Lie algebras and Lie algebra cosets. For symmetric cosets, its ``massless'' solutions display non-relativistic supersymmetry, and can be identified with the massless degrees of freedom of some supersymmetric theories: N=1 supergravity in eleven dimensions (M-theory), type IIB string theory in ten and four dimensions, and in four dimensions, N=8 supergravity, N=4 super-Yang-Mills, and the N=1 Wess-Zumino multiplet. By generalizing this Dirac operator to the affine case, we generate superconformal algebras associated with cosets ${\bf g}/\bf h$, where $\bf h$ contains the {\it space} little group. Only for eleven dimensional supergravity is $\bf h$ simple. This suggests, albeit in a non-relativistic setting, that these may be the limit of theories with underlying two-dimensional superconformal structure.
For decades cataclysmic variables (CVs) were thought to be one of the few classes of accreting compact objects to not launch jets, and have consequently been used to constrain jet launching models. However, recent theoretical and observational advances indicate that CVs do in fact launch jets. Specifically, it was demonstrated that their accretion-outflow cycle is analogous to that of their higher mass cousins -- the X-ray Binaries (XRBs). Subsequent observations of the CV SS Cygni confirmed this and have consistently shown radio flaring equivalent to that in the XRBs that marks a transient jet. Based on this finding and the emission properties, several studies have concluded that the radio emission is most likely from a transient jet. Observations of other CVs, while not conclusive, are consistent with this interpretation. However, the issue is not yet settled. Later observations have raised a number of questions about this model, as well as about potential alternative radio emission mechanisms. CVs are non-relativistic and many have well-determined distances; these properties would make them ideal candidates with which to address many of our outstanding questions about fundamental jet physics. Here we review the case for jets in CVs, discuss the outstanding questions and issues, and outline the future work necessary to conclusively answer the question of whether CVs launch jets.
We perform global linear stability analysis and idealized numerical simulations in global thermal balance to understand the condensation of cold gas from hot/virial atmospheres (coronae), in particular the intracluster medium (ICM). We pay particular attention to geometry (e.g., spherical versus plane-parallel) and the nature of the gravitational potential. Global linear analysis gives a similar value for the fastest growing thermal instability modes in spherical and Cartesian geometries. Simulations and observations suggest that cooling in halos critically depends on the ratio of the cooling time to the free-fall time ($t_{cool}/t_{ff}$). Extended cold gas condenses out of the ICM only if this ratio is smaller than a threshold value close to 10. Previous works highlighted the difference between the nature of cold gas condensation in spherical and plane-parallel atmospheres; namely, cold gas condensation appeared easier in spherical atmospheres. This apparent difference due to geometry arises because the previous plane-parallel simulations focussed on {\em in situ} condensation of multiphase gas but spherical simulations studied condensation {\em anywhere} in the box. Unlike previous claims, our nonlinear simulations show that there are only minor differences in cold gas condensation, either in situ or anywhere, for different geometries. The amount of cold gas condensing depends on the shape of the gravitational potential well; gas has more time to condense if gravitational acceleration decreases toward the center. In our idealized simulations with heating balancing cooling in each layer, there can be significant mass/energy/momentum transfer across layers that can trigger condensation and drive $t_{cool}/t_{ff}$ far beyond the critical value close to 10. Triggered condensation is very prominent in plane-parallel simulations, in which a large amount of cold gas condenses out.
Suppose $X$ and $Y$ are $p\times n$ matrices each with mean $0$, variance $1$ and where all moments of any order are uniformly bounded as $p,n \to \infty$. Moreover, the entries $(X_{ij}, Y_{ij})$ are independent across $i,j$ with a common correlation $\rho$. Let $C=n^{-1}XY^*$ be the sample cross-covariance matrix. We show that if $n, p\to \infty, p/n\to y\neq 0$, then $C$ converges in the algebraic sense and the limit moments depend only on $\rho$. Independent copies of such matrices with same $p$ but different $n$, say $\{n_l\}$, different correlations $\{\rho_l\}$, and different non-zero $y$'s, say $\{y_l\}$ also converge jointly and are asymptotically free. When $y=0$, the matrix $\sqrt{np^{-1}}(C-\rho I_p)$ converges to an elliptic variable with parameter $\rho^2$. In particular, this elliptic variable is circular when $\rho=0$ and is semi-circular when $\rho=1$. If we take independent $C_l$, then the matrices $\{\sqrt{n_lp^{-1}}(C_l-\rho_l I_p)\}$ converge jointly and are also asymptotically free. As a consequence, the limiting spectral distribution of any symmetric matrix polynomial exists and has compact support.
We simulate antiferromagnetic thin films. Dipole-dipole and antiferromagnetic exchange interactions as well as uniaxial and quadrupolar anisotropies are taken into account. Various phases unfold as the corresponding parameters, J, D and C, as well as the temperature T and the number n of film layers vary. We find (1) how the strength Delta_m of the anisotropy arising from dipole-dipole interactions varies with the number of layers m away from the film's surface, with J and with n; (2) a unified phase diagram for all n-layer films and bulk systems; (3) a layer dependent spin reorientation (SR) phase in which spins rotate continuously as T, D, C and n vary; (4) that the ratio of the SR to the ordering temperature depends (approximately) on n only through (D+Delta/n)/C, and hardly on J; (5) a phase transformation between two different magnetic orderings, in which spin orientations may or may not change, for some values of J, by varying n.
We construct ferroelectric (LuFeO3)m/(LuFe2O4) superlattices with varying index m to study the effect of confinement on topological defects. We observe a thickness-dependent transition from neutral to charged domain walls and the emergence of fractional vortices. In thin LuFeO3 layers, the volume fraction of domain walls grows, lowering the symmetry from P63cm to P3c1 before reaching the non-polar P63/mmc state, analogous to the high-temperature ferroelectric to paraelectric transition. Our study shows how dimensional confinement stabilizes textures beyond those in bulk ferroelectric systems.
Two-branes RS-I 5-dimensional model is generalized in higher dimensional string-induced theory with dilaton and $n$-form field. It is supposed that "hidden" and "visible" Randall-Sundrum branes are located at the boundaries of region of space-time where low-energy supergravity description is valid. This permits to determine mass scale hierarchy which calculated value proves to be strongly dependent on dimensionalities of subspaces.
We study the regularity properties of the solutions to the nonlinear equation with fractional diffusion $$ \partial_tu+(-\Delta)^{\sigma/2}\varphi(u)=0, $$ posed for $x\in \mathbb{R}^N$, $t>0$, with $0<\sigma<2$, $N\ge1$. If the nonlinearity satisfies some not very restrictive conditions: $\varphi\in C^{1,\gamma}(\mathbb{R})$, $1+\gamma>\sigma$, and $\varphi'(u)>0$ for every $u\in\mathbb{R}$, we prove that bounded weak solutions are classical solutions for all positive times. We also explore sufficient conditions on the non-linearity to obtain higher regularity for the solutions, even $C^\infty$ regularity. Degenerate and singular cases, including the power nonlinearity $\varphi(u)=|u|^{m-1}u$, $m>0$, are also considered, and the existence of classical solutions in the power case is proved.
We study the birational self-maps of the projective plane over finite fields that induce permutations on the set of rational points. As a main result, we prove that no odd permutation arises over a non-prime finite field of characteristic two, which completes the investigation initiated by Cantat about which permutations can be realized this way. Main ingredients in our proof include the invariance of parity under groupoid conjugations by birational maps, and a list of generators for the group of such maps.
The running of the $\rho\bar N N$ couplings in presence of nuclear matter is studied, and the relevant $\beta$-functions are shown to be different for $\rho^0$ and $\rho^+$, when the nuclear medium is asymmetric.
We present Euler-type recurrence relations for some partition functions. Some of our results provide new recurrences for the number of unrestricted partitions of $n$, denote by $p(n)$. Others establish recurrences for partition functions not yet considered.
R-parity and L violation in the MSSM would be the origin of the neutrino oscillation observed in Super-Kamiokande. A distinctive feature of this framework is that it can be tested in colliders by observing decay products of the destabilized LSP. We examine all the possible decay processes of the neutralino LSP assuming the bilinear contribution to neutrino masses dominates over the trilinear one which gives rise to the solar neutrino mass. We find that it is possible to probe neutrino oscillations through colliders in most of the R-parity conserving MSSM parameter space.