Entanglement in fermionic chains with finite range coupling and broken symmetries

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of $X$ contiguous sites in the limit of large $X$. The present work generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size of $X$. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyse the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long range pairing.Comment: 27 pages, 5 figure

On the M\"obius transformation in the entanglement entropy of fermionic chains

There is an intimate relation between entanglement entropy and Riemann surfaces. This fact is explicitly noticed for the case of quadratic fermionic Hamiltonians with finite range couplings. After recollecting this fact, we make a comprehensive analysis of the action of the M\"obius transformations on the Riemann surface. We are then able to uncover the origin of some symmetries and dualities of the entanglement entropy already noticed recently in the literature. These results give further support for the use of entanglement entropy to analyse phase transition.Comment: 29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos correcte

Million frames per second infrared imaging system

An infrared imaging system has been developed for measuring the temperature increase during the dynamic deformation of materials. The system consists of an 8×8 HgCdTe focal plane array, each with its own preamplifier. Outputs from the 64 detector/preamplifiers are digitized using a row-parallel scheme. In this approach, all 64 signals are simultaneously acquired and held using a bank of track and hold amplifiers. An array of eight 8:1 multiplexers then routes the signals to eight 10 MHz digitizers, acquiring data from each row of detectors in parallel. The maximum rate is one million frames per second. A fully reflective lens system was developed, consisting of two Schwarszchild objectives operating at infinite conjugation ratio. The ratio of the focal lengths of the objectives determines the lens magnification. The system has been used to image the distribution of temperature rise near the tip of a notch in a high strength steel sample (C-300) subjected to impact loading by a drop weight testing machine. The results show temperature rises at the crack tip up to around 70 K. Localization of temperature, and hence, of deformation into "U" shaped zones emanating from the notch tip is clearly seen, as is the onset of crack propagation

Theory of Bubble Nucleation and Cooperativity in DNA Melting

The onset of intermediate states (denaturation bubbles) and their role during the melting transition of DNA are studied using the Peyrard-Bishop-Daxuois model by Monte Carlo simulations with no adjustable parameters. Comparison is made with previously published experimental results finding excellent agreement. Melting curves, critical DNA segment length for stability of bubbles and the possibility of a two states transition are studied.Comment: 4 figures. Accepted for publication in Physical Review Letter

Second order equation of motion for electromagnetic radiation back-reaction

We take the viewpoint that the physically acceptable solutions of the Lorentz--Dirac equation for radiation back-reaction are actually determined by a second order equation of motion, the self-force being given as a function of spacetime location and velocity. We propose three different methods to obtain this self-force function. For two example systems, we determine the second order equation of motion exactly in the nonrelativistic regime via each of these three methods, the three methods leading to the same result. We reveal that, for both systems considered, back-reaction induces a damping proportional to velocity and, in addition, it decreases the effect of the external force.Comment: 13 page

Super-roughening as a disorder-dominated flat phase

We study the phenomenon of super-roughening found on surfaces growing on disordered substrates. We consider a one-dimensional version of the problem for which the pure, ordered model exhibits a roughening phase transition. Extensive numerical simulations combined with analytical approximations indicate that super-roughening is a regime of asymptotically flat surfaces with non-trivial, rough short-scale features arising from the competition between surface tension and disorder. Based on this evidence and on previous simulations of the two-dimensional Random sine-Gordon model [Sanchez et al., Phys. Rev. E 62, 3219 (2000)], we argue that this scenario is general and explains equally well the hitherto poorly understood two-dimensional case.Comment: 7 pages, 4 figures. Accepted for publication in Europhysics Letter

Microhardness study in aluminum and copper base alloys

En el presente trabajo se realiza un estudio de la variación de la microdureza con las diferentes estructuras formadas, columnar, equiaxial y con transición de estructura columnar a equiaxial, TCE, en aleaciones Al - Cu, Al - Si, Al - Li, Al - Mg, Al-Zn y Cu - Zn, solidificadas direccionalmente empleando diferentes cargas. Las medidas de microdureza fueron realizadas a temperatura ambiente con un microdurómetro Buehler, con cargas entre 10 y 1000 gf. Se analizaron las variaciones de la microdureza en función de la longitud y el ancho de las probetas y, además, en función de la concentración. Se observó que los valores de microdureza tienden a disminuir con el aumento de la carga, por lo tanto, tienen una tendencia a permanecer constantes con cargas más elevadas.También se observó que las aleaciones en el estado bruto de fusión exhiben una mayor microdureza que cuando se las solidifica direccionalmente. Se analizan y discuten los resultados obtenidos.In the present work we analyze the variations in microhardness as a function of both microstructure and load applied in Al-Cu, Al-Si, Al-Li, Al-Mg, Al-Zn and Cu-Zn alloys directionally solidified. The microstructures analyzed were columnar, equiaxed and columnar to equiaxed (CET) transition zones. Microhardness measurements were made at room temperature using a Buehler microdurometer and loads between 10 and 1000 gf were used. Furthermore, variations in microhardness as a function of concentration and as a function of both sample length and width are reported. We noticed that the microhardness values decrease when the load increase reaching almost constant values at higher loads. We observed that bulk alloys have greater microhardness values than those directionally solidified. The experimental results are analyzed and discussed.Fil: Ares, Alicia Esther. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; Argentina. Universidad Nacional de Misiones. Facultad de Ciencias Exactas, Químicas y Naturales; ArgentinaFil: Caram, R.. Universidade Estadual de Campinas; BrasilFil: Schvezov, Carlos Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

CECM: A continuous empirical cubature method with application to the dimensional hyperreduction of parameterized finite element models

We present the Continuous Empirical Cubature Method (CECM), a novel algorithm for empirically devising efficient integration rules. The CECM aims to improve existing cubature methods by producing rules that are close to the optimal, featuring far less points than the number of functions to integrate. The CECM consists on a two-stage strategy. First, a point selection strategy is applied for obtaining an initial approximation to the cubature rule, featuring as many points as functions to integrate. The second stage consists in a sparsification strategy in which, alongside the indexes and corresponding weights, the spatial coordinates of the points are also considered as design variables. The positions of the initially selected points are changed to render their associated weights to zero, and in this way, the minimum number of points is achieved. Although originally conceived within the framework of hyper-reduced order models (HROMs), we present the method's formulation in terms of generic vector-valued functions, thereby accentuating its versatility across various problem domains. To demonstrate the extensive applicability of the method, we conduct numerical validations using univariate and multivariate Lagrange polynomials. In these cases, we show the method's capacity to retrieve the optimal Gaussian rule. We also asses the method for an arbitrary exponential-sinusoidal function in a 3D domain, and finally consider an example of the application of the method to the hyperreduction of a multiscale finite element model, showcasing notable computational performance gains. A secondary contribution of the current paper is the Sequential Randomized SVD (SRSVD) approach for computing the Singular Value Decomposition (SVD) in a column-partitioned format. The SRSVD is particularly advantageous when matrix sizes approach memory limitations