On the cardinality of sumsets in torsion-free groups

Let $A, B$ be finite subsets of a torsion-free group $G$. We prove that for every positive integer $k$ there is a $c(k)$ such that if $|B|\ge c(k)$ then the inequality $|AB|\ge |A|+|B|+k$ holds unless a left translate of $A$ is contained in a cyclic subgroup. We obtain $c(k)<c_0k^{6}$ for arbitrary torsion-free groups, and $c(k)<c_0k^{3}$ for groups with the unique product property, where $c_0$ is an absolute constant. We give examples to show that $c(k)$ is at least quadratic in $k$

The Effect of Multiaxial Forging on the Grain Refinement of Low Alloyed Steel

Ultra fine grained low carbon low alloyed steel was formed by multiaxial forging. Altogether five passes of forging were made with decreasing temperature. The first two passes happened in the austenitic state of the steel, the third was made at the austenite-ferrite transition temperature. The fourth occurred in the austenitic-ferritic region, while the last pass was made in pure ferritic state. The intensive plastic deformation caused the austenite-ferrite transition temperature to be lowered, thus the undercooling was larger, and very small ferritic cores were produced. The following deformation made the grain structure even more fine

Heavy Quark Diffusion from the Lattice

We study the diffusion of heavy quarks in the Quark Gluon Plasma using the Langevin equations of motion and estimate the contribution of the transport peak to the Euclidean current-current correlator. We show that the Euclidean correlator is remarkably insensitive to the heavy quark diffusion coefficient and give a simple physical interpretation of this result using the free streaming Boltzmann equation. However if the diffusion coefficient is smaller than $\sim 1/(\pi T)$, as favored by RHIC phenomenology, the transport contribution should be visible in the Euclidean correlator. We outline a procedure to isolate this contribution.Comment: 24 pages, 5 figure

The International Division of Labor in Economists' Field: Academic Subordination in Exchange for Political Prerogatives in Argentina

Since the 1970s, economics has emerged as a global profession, with economists becoming main characters of the intellectual and political life in many countries. Inspired by Bourdieu, several analyses faced the challenge of “theorizing fields beyond the nation-state” (Buchholz 2016). Some scholars emphasized that internationalization entailed a growing asymmetry between dominant and dominated participants: the former acting as “exporters” and the latter as “importers” of ideas (Dezalay and Garth 2002). Others pointed out the process of “creative destruction” that accompanied the globalization of local fields (Fourcade 2006). Finally, still others noted the emergence of a new field of globalized experts and think tanks (Medvetz 2012). Through a socio-historical depiction of economists in Argentina, we problematize the subordinated role of peripheral economists. Rather than a dominant-dominated logic, we identify a new international division of labor. Based on more than 60 interviews with economists, archival research, and statistical analyses, this paper shows that while a dependent position in the global academic field reduced Argentinian economists’ theoretical autonomy, it gave them the scientific authority that in turn paved the road to access very well-paid work as consultants and high-level public servants

Deformation Induced Lattice Misorientation in Lath Martensite

Effect of plastic deformation on the lattice misorientation in lath martensite was investigated by Electron Backscatter Diffraction (EBSD). As-quenched rod-like specimens were plastically deformed until 9000 N, 14000 N, 19000 N and 21000 N of tensile loading. Grain average misorientation maps were collected by EBSD. It was shown that the average misorientation during plastic deformation increased from 0.887 to 1.156 degrees. Results showed that the density of geometrically necessary dislocations, which caused the lattice misorientation, slightly increased during plastic deformation of lath martensite

On infinite-finite duality pairs of directed graphs

The (A,D) duality pairs play crucial role in the theory of general relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both side are infinite seems to be very complex. It is also known that no finite-infinite duality pair is possible if we make the additional restriction that both classes are antichains. In this paper (which is the first one of a series) we start the detailed study of the infinite-finite case. Here we concentrate on directed graphs. We prove some elementary properties of the infinite-finite duality pairs, including lower and upper bounds on the size of D, and show that the elements of A must be equivalent to forests if A is an antichain. Then we construct instructive examples, where the elements of A are paths or trees. Note that the existence of infinite-finite antichain dualities was not previously known

Noncommutative Common Cause Principles in Algebraic Quantum Field Theory

States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set {C, non-C} screens off the correlation between A and B

Nuclear multifragmentation within the framework of different statistical ensembles

The sensitivity of the Statistical Multifragmentation Model to the underlying statistical assumptions is investigated. We concentrate on its micro-canonical, canonical, and isobaric formulations. As far as average values are concerned, our results reveal that all the ensembles make very similar predictions, as long as the relevant macroscopic variables (such as temperature, excitation energy and breakup volume) are the same in all statistical ensembles. It also turns out that the multiplicity dependence of the breakup volume in the micro-canonical version of the model mimics a system at (approximately) constant pressure, at least in the plateau region of the caloric curve. However, in contrast to average values, our results suggest that the distributions of physical observables are quite sensitive to the statistical assumptions. This finding may help deciding which hypothesis corresponds to the best picture for the freeze-out stageComment: 20 pages, 7 figure

Identification of criticality in neuronal avalanches: I. A theoretical investigation of the non-driven case

In this paper, we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a finite-size system. By calculating the exact distribution of avalanche sizes, we are able to show that, over a limited range of avalanche sizes which we precisely identify, the distribution has scale free properties but is not a power law. This suggests that it would be inappropriate to dismiss a system as not being critical purely based on an inability to rigorously fit a power law distribution as has been recently advocated. In assessing whether a system, especially a finite-size one, is critical it is thus important to consider other possible markers. We illustrate one of these by showing the divergence of susceptibility as the critical point of the system is approached. Finally, we provide evidence that power laws may underlie other observables of the system that may be more amenable to robust experimental assessment