Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density

The thermal restoration of chiral symmetry in QCD is known to proceed by an analytic crossover, which is widely expected to turn into a phase transition with a critical endpoint as the baryon density is increased. In the absence of a genuine solution to the sign problem of lattice QCD, simulations at zero and imaginary baryon chemical potential in a parameter space enlarged by a variable number of quark flavours and quark masses constitute a viable way to constrain the location of a possible non-analytic phase transition and its critical endpoint. In this article I review recent progress towards an understanding of the nature of the transition in the massless limit, and its critical temperature at zero density. Combined with increasingly detailed studies of the physical crossover region, current data bound a possible critical point to μB ≳ 3T.

Holographic RG flows and Janus solutions from matter-coupled $$N=4$$ gauged supergravity

We study an $$SO(2)\times SO(2)\times SO(2)\times SO(2)$$ S O ( 2 ) × S O ( 2 ) × S O ( 2 ) × S O ( 2 ) truncation of four-dimensional $$N=4$$ N = 4 gauged supergravity coupled to six vector multiplets with $$SO(4)\times SO(4)$$ S O ( 4 ) × S O ( 4 ) gauge group and find a new class of holographic RG flows and supersymmetric Janus solutions. In this truncation, there is a unique $$N=4$$ N = 4 supersymmetric $$AdS_4$$ A d S 4 vacuum dual to an $$N=4$$ N = 4 SCFT in three dimensions. In the presence of the axion, the RG flows generally preserve $$N=2$$ N = 2 supersymmetry while the supersymmetry is enhanced to $$N=4$$ N = 4 for vanishing axion. We find solutions interpolating between the $$AdS_4$$ A d S 4 vacuum and singular geometries with different residual symmetries. We also show that all the singularities are physically acceptable within the framework of four-dimensional gauged supergravity. Accordingly, the solutions are holographically dual to RG flows from the $$N=4$$ N = 4 SCFT to a number of non-conformal phases in the IR. We also find $$N=4$$ N = 4 and $$N=2$$ N = 2 Janus solutions with $$SO(4)\times SO(4)$$ S O ( 4 ) × S O ( 4 ) and $$SO(2)\times SO(2)\times SO(3)\times SO(2)$$ S O ( 2 ) × S O ( 2 ) × S O ( 3 ) × S O ( 2 ) symmetries, respectively. The former is obtained from a truncation of all scalars from vector multiplets and can be regarded as a solution of pure $$N=4$$ N = 4 gauged supergravity. On the other hand, the latter is a genuine solution of the full matter-coupled theory. These solutions describe conformal interfaces in the $$N=4$$ N = 4 SCFT with $$N=(4,0)$$ N = ( 4 , 0 ) and $$N=(2,0)$$ N = ( 2 , 0 ) supersymmetries.

Σοπενχάουερ περί Θανάτου και Αυτοκτονίας

Schopenhauer is portrayed as the philosopher of pessimism, and for good reason. For him, life is suffering where ‘ultimately death must triumph’ (The World as Will and Representation vol. I, 311). However, his pessimism fades away when he contemplates death. He argues enthusiastically that, far from being an evil, death is in fact a friend we should welcome. Moreover, he believes it is possible for human beings to use their knowledge to fight the fear of death. Interestingly, however, at the point where the reader expects a philosophical defense of suicide, Schopenhauer vehemently argues against it. Suicide to avoid pain and suffering, according to him, is a mistake, a futile, foolish and egoistic act. Not only does suicide not offer a genuine solution to suffering, but also it hinders true salvation, the denial of the will.In this paper, I argue that Schopenhauer’s condemnation of suicide is in fact at odds with his views on death and can weaken his argumentation about why we must not fear death. It is my belief that Schopenhauer’s views on suicide stem - quite ironically - from his being, at times, overly optimistic about the possibility of genuine salvation. When it comes to freeing ourselves from the will, however, we are better off pessimists. This, I explain, will allow us to at least keep our optimism regarding death and find solace in the knowledge that - be it by old age, illness, accident, suicide or any other cause - death is not to be feared.

Introduction

According to George Berkeley, “the doctrine of signs [is] a point of great importance, and general extent, which, if duly considered, would cast no small light upon things, and afford a just and genuine solution to many difficulties” (Alc, §7.16). As has long been recognized (...

Interface layer of a two-component Bose–Einstein condensate

This paper deals with the study of the behavior of the wave functions of a two-component Bose–Einstein condensate near the interface, in the case of strong segregation. This yields a system of two coupled ordinary differential equations for which we want to have estimates on the asymptotic behavior, as the strength of the coupling tends to infinity. As in phase separation models, the leading order profile is a hyperbolic tangent. We construct an approximate solution and use the properties of the associated linearized operator to perturb it into a genuine solution for which we have an asymptotic expansion. We prove that the constructed heteroclinic solutions are linearly nondegenerate, in the natural sense, and that there is a spectral gap, independent of the large interaction parameter, between the zero eigenvalue (due to translations) at the bottom of the spectrum and the rest of the spectrum. Moreover, we prove a uniqueness result which implies that, in fact, the constructed heteroclinic is the unique minimizer (modulo translations) of the associated energy, for which we provide an expansion.

Piecewise B-Spline Tool Paths With the Arc-Length Parameter and Their Application on High Feed, Accurate CNC Milling of Free-Form Profiles

To conduct B-spline curve machining, first, B-spline tool paths with feed rates are planned; and second, the B-spline interpolator generates tool trajectories in real-time based on the paths fed into the computer numerically controlled (CNC) controller. Currently, the paths are often planned geometrically with a nonarc-length parameter. Literally, the interpolator can process B-spline paths with the arc-length parameter well, while it sometimes is challenged to work with the nonarc-length parameterized B-spline paths. As a consequence, it is difficult to ensure high accuracy of the tool trajectories in B-spline machining in terms of their corresponding paths; especially, if the feed is very high, smooth tool kinematics cannot be well maintained. To root out these problems, a new type of tool path—piecewise B-spline tool paths with the arc-length parameter—is first proposed in this work. Given a B-spline path with a nonarc-length parameter, it is accurately converted into a B-spline path with an arc-length parameter before sending it into the CNC controller. Furthermore, if the prescribed feed rate is very high and the arc-length parameterized B-spline path is disqualified, it is split into pieces represented with distinct arc-length parameterized B-spline paths in different feed rates. The main advantage of these piecewise paths is that they can eliminate the problems encountered by the existing B-spline interpolator with input of nonarc-length parameterized B-spline paths. Therefore, the piecewise arc-length parameterized B-spline paths are a genuine solution to high feed-and-accuracy B-spline machining.

Generalized Limit Equilibrium Method for Slope Stability Analysis

On the basis of the limit equilibrium method and the physical significance of Coulomb’s yield criteria, extremum conditions of yield functions is established, which will be the fundamental equations for the limit analysis of soil mass. Once the stress equation along a sliding surface is available, the normal stress on the sliding surface can be obtained, a new limit analysis method, generalized limit equilibrium method (GLEM), can be established. With the generalized limit equilibrium method, an analysis method to solve the problem of slope stability can be obtained without introducing any other assumptions or simplified conditions but the sliding surface. With this algorithm, any discretionally possible sliding surface can be trial calculated and the least value of the calculated results of different sliding surfaces is taken as the safety factor. As long as a selected sliding surface is close to the true sliding surface, the derived safety factor will be approximate to the genuine solution to a problem of slope stability.

Hyperbolization of cocycles by isometries of the Euclidean space

We study hyperbolized versions of cohomological equations that appear with cocycles by isometries of the Euclidean space. These (hyperbolized versions of) equations have a unique continuous solution. We concentrate on the question whether or not these solutions converge to a genuine solution to the original equation, and in what sense we can use them as good approximative solutions. The main advantage of considering solutions to hyperbolized cohomological equations is that they can be easily described, since they are global attractors of a naturally defined skew-product dynamics. We also include some technical results about twisted Birkhoff sums and exponential averaging.

Semantics-Based Compiling: A Case Study in Type-Directed Partial Evaluation

<p>We illustrate a simple and effective solution to semantics-based<br />compiling. Our solution is based on type-directed partial evaluation, where</p><p><br />- our compiler generator is expressed in a few lines, and is efficient; <p> - its input is a well-typed, purely functional definitional interpreter in the manner of denotational semantics;</p>- the output of the generated compiler is three-address code, in the fashion and efficiency of the Dragon Book;</p><p>- the generated compiler processes several hundred lines of source code per second.</p><p><br />The source language considered in this case study is imperative, block-structured,<br />higher-order, call-by-value, allows subtyping, and obeys<br />stack discipline. It is bigger than what is usually reported in the literature on semantics-based compiling and partial evaluation.<br />Our compiling technique uses the first Futamura projection, i.e., we compile programs by specializing a definitional interpreter with respect to this program. Our denitional interpreter is completely straightforward, stack-based, and in direct style. In particular, it requires no clever staging technique (currying, continuations, binding-time improvements, etc.), nor does it rely on any other framework (attribute grammars, annotations, etc.) than the typed lambda-calculus. In particular, it uses no other program analysis than traditional type inference. The overall simplicity and effectiveness of the approach has encouraged us to write this paper, to illustrate this genuine solution to denotational semantics-directed compilation, in the spirit of Scott and Strachey.</p>

HOW TO IMPROVE PUBLIC HEALTH

Doctors and other health workers are even less able to assure happiness than they are to assure health. If work is unsatisfying to many in modern society, psychopharmacology is a toxic and inappropriate remedy for correcting the resulting tension and alienation. if unemployed workers are depressed, mental-health counseling may be a temporary source of comfort, but the only genuine solution is full employment. If children fail to thrive, child-guidance workers may diminish their misery, but they cannot guarantee their flowering in the midst of social disaster. As physicians, our daily practice with human ailments makes us aware of the extent to which problems of ill health flow from failures in our political, economic, and social institutions. The redesign of these institutions is the central challenge for the coming century, and gives the greatest promise for improving public health.