ShantanuT01/DACTYL-Pretraining huggingface dataset:
Linear perturbation is used to investigate the effect of gravitational softening on the retrieved two-armed spiral eigenmodes of razor-thin stellar discs.   We explore four softening kernels with different degrees of gravity bias, and with/without compact support (compact in the sense that they yield exactly Newtonian forces outside the softening kernel). These kernels are applied to two disc galaxy models with well-known unsoftened unstable modes. We illustrate quantitatively the importance of a vanishing linear gravity bias to yield accurate frequency estimates of the unstable modes. As such, Plummer softening, while very popular amongst simulators, performs poorly in our tests.   The best results, with excellent agreement between the softened and unsoftened mode properties, are obtained with softening kernels that have a reduced gravity bias, obtained by compensating for the sub-Newtonian forces at small interparticle distances with slightly super-Newtonian forces at radii near the softening length. We present examples of such kernels that, moreover, are analytically simple and computationally cheap. Finally, these results light the way to the construction of softening methods with even smaller gravity bias, although at the price of increasingly complex kernels.
We propose a self-consistent scheme for the determination of the ground-state (GS) properties of interacting electrons in a magnetic field, and of systems whose GS's time-reversal-symmetry (TRS) is spontaneously broken. It is based on a newly-developed many-body perturbation theory that is valid, irrespective of the strength of correlation, provided the GS number densities $n_{\uparrow}({\bf r})$, $n_{\downarrow}({\bf r})$, and the {\sl total} paramagnetic particle flux density are pure-state non-interacting $v$-representable. Our approach can in particular be applied to (modulated) two-dimensional electron systems in the fractional quantum-Hall regime.
The recently relased \emph{Planck} data, emphasize that the background geometry of inflation is not pure de Sitter, but from the slow variation of Hubble parameter during the inflationary era, it can be quasi-de Sitter. This motivates us to consider an asymptotic de Sitter mode function for reconstruction of initial mode and primordial power spectrum of curvature perturbation. Using Markov Chain Monte Carlo (MCMC) method together with applying recent observational constraints from the Cosmic Microwave Background (CMB) data for our parametrized asymptotic initial mode shows some deviation from pure de Sitter or Bunch-Davies mode. Based on \emph{Planck 2015} data release the amplitude of scalar perturbations in $ 68 \%$ confidence level is $10^{9} A_s =2.77^{+0.32}_{-0.35}$ and deviation from Bunch-Davies mode is $\sim 0.03-0.04$. In this parametrization, the CMB power spectrum of our model shows more red-tilt in comparison with $\Lambda \rm{CDM}$ model. Furthermore, we found upper limit for tensor-to-scalar ratio with different pivot scales $r_{0.05}< 0.0272$ and $ r_{0.002}< 0.0242$.
The quality and quantity of 6D stellar position-velocity measurements in the second Gaia data release (DR2) allows to study small-scale structure in the orbit distribution of the Galactic disc beyond the immediate Solar neighborhood. We investigate the distribution of orbital actions $(J_R,J_\phi=L_z,J_z)$ of $\sim 3.5$ million stars within $1.5~\text{kpc}$ of the Sun, for which precise actions can be calculated from Gaia DR2 alone. This distribution $n(J_R,L_z)$ reveals a remarkable amount of sub-structure. The known moving groups in the $(U,V)$-plane of the Solar neighborhood correspond to overdensities in $(J_R,L_z)$, as expected. But $n(J_R,L_z)$ also exhibits a wealth of density clumps and ridges that extend towards higher $J_R$. These $n(J_R,L_z)$ features are most prominent among orbits that stay close to the Galactic plane and remain consistently visible out to $\sim1.5~\text{kpc}$, as opposed to the sub-structure in velocity space. Some of these $n(J_R,L_z)$ ridges resemble features expected from rapid orbit diffusion along particular ($J_R,L_z$)-directions in the presence of various resonances. Several of these $n(J_R,L_z)$ structures show a dramatic imbalance of stars moving in or out, suggesting that stars are not phase-mixed along orbits or on resonant orbits. Orbital action and angle space of stars in Gaia DR2 is therefore highly structured over kpc-scales, and appears to be very informative for modeling studies of non-axisymmetric structure and resonances in the Galactic disc.
Lee-Suzuki similarity transformations and Krencigowa-Kuo folded diagrams are two common methods used to derive energy independent model space effective interactions for nuclear many-body systems. We demonstrate that these methods are equivalent to a Renormalization Group (RG) analysis of a separable potential model. The effective low-momentum potentials V_{eff} are shown to give the same scaling equation that RG arguments predict. We find the new result that the different model space techniques considered in this paper yield a unique low-momentum V_{eff} when applied to the toy model problem.
We propose chiral analogues of some infinite complexes appearing in the description of the coherent derived categories for projective spaces.
It appears to follow from the Reissner-Nordstrom solution of Einstein's equations that the charge of a body reduces its gravitational field. In a recent note Hushwater offered an explanation of this apparent paradox. His explanation, however, raises more questions than solves since it implies that the active gravitational mass of a charged body is distance-dependent and therefore is not equal to its inertial mass.
We analyze a class of spatial random spanning trees built on a realization of a homogeneous Poisson point process of the plane. This tree has a simple radial structure with the origin as its root. We first use stochastic geometry arguments to analyze local functionals of the random tree such as the distribution of the length of the edges or the mean degree of the vertices. Far away from the origin, these local properties are shown to be close to those of a variant of the directed spanning tree introduced by Bhatt and Roy. We then use the theory of continuous state space Markov chains to analyze some nonlocal properties of the tree, such as the shape and structure of its semi-infinite paths or the shape of the set of its vertices less than $k$ generations away from the origin. This class of spanning trees has applications in many fields and, in particular, in communications.
We establish the relationship between volumes of flow polytopes associated to signed graphs and the Kostant partition function. A special case of this relationship, namely, when the graphs are signless, has been studied in detail by Baldoni and Vergne using techniques of residues. In contrast with their approach, we provide entirely combinatorial proofs inspired by the work of Postnikov and Stanley on flow polytopes. As a fascinating special family of flow polytopes, we study the Chan-Robbins-Yuen polytopes. Motivated by the beautiful volume formula $\prod_{k=1}^{n-2} Cat(k)$ for the type $A_n$ version, where $Cat(k)$ is the $k$th Catalan number, we introduce type $C_{n+1}$ and $D_{n+1}$ Chan-Robbins-Yuen polytopes along with intriguing conjectures pertaining to their properties.
We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix . A nonultralocal quantum algebras on the lattices for these systems are constructed.For some class of such algebras an ultralocalization procedure is proposed.The technique of the modified Bethe-Anzatz for these algebras is developed.This technique is applied to the nonlinear sigma model problem.
We present a theory of magnetic anisotropy in ${\rm III}_{1-x}{\rm Mn}_{x}{\rm V}$ diluted magnetic semiconductors with carrier-induced ferromagnetism. The theory is based on four and six band envelope functions models for the valence band holes and a mean-field treatment of their exchange interactions with ${\rm Mn}^{++}$ ions. We find that easy-axis reorientations can occur as a function of temperature, carrier density $p$, and strain. The magnetic anisotropy in strain-free samples is predicted to have a $p^{5/3}$ hole-density dependence at small $p$, a $p^{-1}$ dependence at large $p$, and remarkably large values at intermediate densities. An explicit expression, valid at small $p$, is given for the uniaxial contribution to the magnetic anisotropy due to unrelaxed epitaxial growth lattice-matching strains. Results of our numerical simulations are in agreement with magnetic anisotropy measurements on samples with both compressive and tensile strains. We predict that decreasing the hole density in current samples will lower the ferromagnetic transition temperature, but will increase the magnetic anisotropy energy and the coercivity.
In this article, we provide a review of the current state of the research of the black hole shadow, focusing on analytical (as opposed to numerical and observational) studies. We start with particular attention to the definition of the shadow and its relation to the often used concepts of escape cone, critical impact parameter and particle cross-section. For methodological purposes, we present the derivation of the angular size of the shadow for an arbitrary spherically symmetric and static space-time, which allows one to calculate the shadow for an observer at arbitrary distance from the center. Then we discuss the calculation of the shadow of a Kerr black hole, for an observer anywhere outside of the black hole. For observers at large distances we present and compare two methods used in the literature. Special attention is given to calculating the shadow in space-times which are not asymptotically flat. Shadows of wormholes and other black-hole impostors are reviewed. Then we discuss the calculation of the black hole shadow in an expanding universe as seen by a comoving observer. The influence of a plasma on the shadow of a black hole is also considered.
It is crucial that magnetic memory devices formed from magnetic heterostructures possess sizable spin-orbit torque (SOT) efficiency and high thermal stability to realize both efficient SOT control and robust storage of such memory devices. However, most previous studies on various types of magnetic heterostructures have focused on only their SOT efficiencies, whereas the thermal stabilities therein have been largely ignored. In this work, we study the temperature-dependent SOT and stability properties of two types of W-based heterostructures, namely W/CoFeB/MgO (standard) and CoFeB/W/CoFeB/MgO (field-free), from 25 ^{\circ}C (298 K) to 80 ^{\circ}C (353 K). Via temperature-dependent SOT characterization, the SOT efficacies for both systems are found to be invariant within the range of studied temperatures. Temperature-dependent current-induced SOT switching measurements further show that the critical switching current densities decrease with respect to the ambient temperature; thermal stability factors ({\Delta}) are also found to degrade as temperature increases for both standard and field-free systems. The memristive SOT switching behaviors in both systems with various pulse-widths and temperatures are also examined. Our results suggest that although the SOT efficacy is robust against thermal effects, the reduction of {\Delta} at elevated temperatures could be detrimental to standard memory as well as neuromorphic (memristive) device applications.
We study the low energy behavior of the one dimensional Hubbard model across the Mott metal-insulator phase transition in an external magnetic field. In particular we calculate elements of the dressed charge matrix at the critical point of the Mott transition for arbitrary Hubbard repulsion and magnetization numerically and, in certain limiting cases, analytically. These results are combined with a non-perturbative effective field theory approach to reveal how the breaking of time reversal symmetry influences the Mott transition.
The generating functionals of Green's functions with composite and external fields are considered in the framework of BV and BLT quantization methods for general gauge theories. The corresponding Ward identities are derived and the gauge dependence is investigated
Analyses of multi-epoch, high-resolution (R ~ 50.000) optical spectra of the O-type star HD 152246 (O9 IV according to the most recent classification), complemented by a limited number of earlier published radial velocities, led to the finding that the object is a hierarchical triple system, where a close inner pair (Ba-Bb) with a slightly eccentric orbit (e = 0.11) and a period of 6.0049 days revolves in a 470-day highly eccentric orbit (e = 0.865) with another massive and brighter component A. The mass ratio of the inner system must be low since we were unable to find any traces of the secondary spectrum. The mass ratio A/(Ba+Bb) is 0.89. The outer system has recently been resolved using long-baseline interferometry on three occasions. The interferometry confirms the spectroscopic results and specifies elements of the system. Our orbital solutions, including the combined radial-velocity and interferometric solution indicate an orbital inclination of the outer orbit of 112{\deg} and stellar masses of 20.4 and 22.8 solar masses. We also disentangled the spectra of components A and Ba and compare them to synthetic spectra from two independent programmes, TLUSTY and FASTWIND. In either case, the fit was not satisfactory and we postpone a better determination of the system properties for a future study, after obtaining observations during the periastron passage of the outer orbit (the nearest chance being March 2015). For the moment, we can only conclude that component A is an O9 IV star with v*sin(i) = 210 +\- 10 km/s and effective temperature of 33000 +\- 500 K, while component Ba is an O9 V object with v*sin(i) = 65 +/- 3 km/s and T_eff = 33600 +\- 600 K.
Introduction A business plan can be an essential aspect in directing the processes, aims, and objectives of a venture. It sets up the procedural and management tactics that each achievement in a proposed firm can be made. Essentially, these plans allow investors gain confidence to issue funding and buy shares for the promising businesses. Therefore, it is neither surprising nor obvious that while some businesspeople try to collect information in a bid to validate the businesses, other perform minimal assessment and quick survey to start them stringently. This paper presents the different ideologies as depicted from experiences of businesspersons. Short Cycle Who is the decision maker? In each of the descriptions made, the person possessing the idea is a decision maker. He or she determines how and when the plan is performed. In fact, the person owning the idea for the business plan, also termed as the founder, chooses its stringency and process. In this respect, this case has such founders of business plan like Jeff Hyman and Mandy Williams. What is the main issue/problem/opportunity? The main issue discussed by the case involves handling business plans. It involves managing time for planning and implementing the plans. The case informs on the various distinct and somewhat contradicting problems. However, there are recommendations given in order to exclude the faults made by the planners. In this regard, they offer opportunities to carry out reliable plans for business implementation. Why has the issue arisen? The issue has been introduced by the fact that a strict planner compiles a document of 150 pages to get a funding of $500000 whereas another makes 2 pages to get $2.7 million. The issue also addresses the differences put forward by the steps of planning business which depict many debatable issues. When must a decision be made urgency? Decisions for implementing ideas should be made once the market and progress of a business are set. The case argues that the time given to the evaluation of the plan should not take long as it may seem hesitant. Urgent decisions may be made prior to stringent changes in the market orientation or delivery of better opportunities during the implementation process than in the plan. Long Cycle Issues The planner must set a schedule for his or her planning study as well as estimate its length and funding expectations. In this respect, length of document occupies a medium strategic importance to the firm. However, the funding demands a topmost or high strategic significance since it is core to the implementation and progress. Finally, the plan should take a medium-term which is not too little to allow presence of errors and not too long to bypass the significance of prevailing markets and strategies being used. Basic Issues The basic issues include business implementation and sustainability. In essence, a business must be directed towards attaining viable idea. This part should verify th
It is essential to remember that gender equality is supported in modern society when discussing women’s right to work in law enforcement agencies. My point of view also coincides with the public one. I think there are many advantages to having women working in law enforcement. Cox et al. (2020) consider that for many women, working in law enforcement serves “to wield power in the African American community and to work to alter an organization often viewed as oppressive.” (p.316). For women, this will be a vast field of research on their strengths and talents, which they can show in their work. I consider that women should have the right to work in law enforcement not only because of the gender equality idea but also because women open up new perspectives in solving public issues, they are good at solving problems related to logic and do not lag behind men in their desire to be beneficial to society. Firstly, female candidates are much less likely to receive complaints about using excessive force. At the same time, women candidates are a tremendous force that can change the world for the better through their efforts (Cox et al., 2020). Despite the low level of support that women working in the police sometimes give to each other, their work has an undeniable impact on the public and changes many people’s views about a uniform women. Since more and more women join the police ranks, the level of trust in it increases. Moreover, due to the police’s increased confidence, there was a decrease in the rate of intimate partner murders (Miller & Segal, 2018). More and more people turn to the police in advance because they believe in its effectiveness. A sad statistic is the turnover of female staff in various departments, caused by discrimination and pressure from the desire to assert themselves on male employees. Moreover, sometimes women who do not belong to the police force suspect female police officers of their motives for joining the law enforcement agencies. For example, African American female police officers are likely to feel lonely and isolated in a group of white women or black men (Cox et al., 2020). It is important to note that women working in law enforcement agencies are genuinely unique, and the time will only reveal their potential. For the time being, only men are still welcome among the police since masculinity is still considered a necessary quality for working in the police (Cox et al., 2020). That is why women are so rarely recruited into the police force, even though many of them deserve to be accepted into law enforcement officers’ ranks. In modern society, it is necessary to break down stereotypes properly, and the employment of women in law enforcement agencies is one of the right ways. Due to the stereotypes strengthening, people have believed that working in the police is only a man’s job since a man’s image of fighting crime has been formed because of greater physical strength and aggression. Ho
Every person’s life should be filled with meaning and should be structured by his or her calling, aims, wishes and ambitions. The person who does something he or she does not like for a living just because it is necessary to, will never be happy and will never achieve anything worthy in life. Life requires spiritual filling as well as satisfaction with certain material needs and wishes. The sense of life is to do a bit more than others wait for you, more than you yourself have expected – here comes the genuine satisfaction and success in life. However, all these elevated words are nothing more than words, as the true meaning of life built up according to a set of firm, integral principles have been left on the pages of classical literature, in the words of outstanding people who despite any challenges managed to achieve this and left their experience as an example for others. It is a pity to realize that such people are a rare species being born once in quite a long period of time and still being not understood by their peers and dying forgotten. The humanity is rusted by excessive pleasures, by duality of moral principles being fitted to some particular situations, thus degrading and losing the true thirst for life, for the truth and for achievement. Many writers and great thinkers of old times and modernity have been devoting their works to considerations of why this happened and what reasons lie within the degradation of the world population. They call people to be genuine, explaining that only this way they will achieve eternity – they should not betray their ethical standards, they should pursue one common goal for their whole life and should become
The question of the Negro people in the American society has always been a real problem. People, especially black one, have always asked themselves questions about their place in the world and why they are treated differently. The problem of the attitude to black people is solved now, they are considered to be the same members of the society, but the problem still exists. Du Bois and Booker T. Washington tried to examine the question from their points of view and their considerations are going to be discussed in the current paper. Du Bois in the work “The Soul of Black Folk” asks the question, why black people are considered to be different, why they are treated differently as they are the same members of the society, they are the same people, created by God, but at the same time they are thought to be strangers even in their own houses. “The history of the American Negro is the history of this strife, — this longing to attain self-conscious manhood, to merge his double-self into a better and truer self” (Du Bois ) says Du Bois and he is right. The life of black people is known as the life of straggle, black people were fighting for their freedom for many centuries and now they have got that freedom, they have reached their aim. Du Bois in his work dwells upon the difficulties in Negro lives, when they were rejected by the society, when they had no one to rely on – the whole world was against them. Booker T. Washington in his work “Up from slavery” tells his story, his life, when he managed to become the respected person, in spite of the fact that he had come out of slaves. Being black, he managed to cope with lots of difficulties and reach the level, where he was at. The chapter, which is discussed, is “The Atlanta Exposition Address”, where the author tried to show the President and Directors that black people are not the minority in the South. Moreover, telling about black people, Washington says with assurance that South America is inhabited with the Negros on one third, and it is unjust not to pay attention to their problems. The terrible conditions of black people are discussed and Washington just wants to ask, how long will black people be ignored. The hope for better fills in the heart of black people and they hope that some time later, they will be considered similar, black and white (Washington ). These two works, by Washington and Du Bois raise the similar problems, the pla