Nekrasov Functions and Exact Bohr-Sommerfeld Integrals

In the case of SU(2), associated by the AGT relation to the 2d Liouville theory, the Seiberg-Witten prepotential is constructed from the Bohr-Sommerfeld periods of 1d sine-Gordon model. If the same construction is literally applied to monodromies of exact wave functions, the prepotential turns into the one-parametric Nekrasov prepotential F(a,\epsilon_1) with the other epsilon parameter vanishing, \epsilon_2=0, and \epsilon_1 playing the role of the Planck constant in the sine-Gordon Shroedinger equation, \hbar=\epsilon_1. This seems to be in accordance with the recent claim in arXiv:0908.4052 and poses a problem of describing the full Nekrasov function as a seemingly straightforward double-parametric quantization of sine-Gordon model. This also provides a new link between the Liouville and sine-Gordon theories.Comment: 10 page

Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals

The AGT relation identifies the Nekrasov functions for various N=2 SUSY gauge theories with the 2d conformal blocks, which possess explicit Dotsenko-Fateev matrix model (beta-ensemble) representations the latter being polylinear combinations of Selberg integrals. The "pure gauge" limit of these matrix models is, however, a non-trivial multiscaling large-N limit, which requires a separate investigation. We show that in this pure gauge limit the Selberg integrals turn into averages in a Brezin-Gross-Witten (BGW) model. Thus, the Nekrasov function for pure SU(2) theory acquires a form very much reminiscent of the AMM decomposition formula for some model X into a pair of the BGW models. At the same time, X, which still has to be found, is the pure gauge limit of the elliptic Selberg integral. Presumably, it is again a BGW model, only in the Dijkgraaf-Vafa double cut phase.Comment: 21 page

Metastable de Sitter vacua in N=2 to N=1 truncated supergravity

We study the possibility of achieving metastable de Sitter vacua in general N=2 to N=1 truncated supergravities without vector multiplets, and compare with the situations arising in N=2 theories with only hypermultiplets and N=1 theories with only chiral multiplets. In N=2 theories based on a quaternionic manifold and a graviphoton gauging, de Sitter vacua are necessarily unstable, as a result of the peculiar properties of the geometry. In N=1 theories based on a Kahler manifold and a superpotential, de Sitter vacua can instead be metastable provided the geometry satisfies some constraint and the superpotential can be freely adjusted. In N=2 to N=1 truncations, the crucial requirement is then that the tachyon of the mother theory be projected out from the daughter theory, so that the original unstable vacuum is projected to a metastable vacuum. We study the circumstances under which this may happen and derive general constraints for metastability on the geometry and the gauging. We then study in full detail the simplest case of quaternionic manifolds of dimension four with at least one isometry, for which there exists a general parametrization, and study two types of truncations defining Kahler submanifolds of dimension two. As an application, we finally discuss the case of the universal hypermultiplet of N=2 superstrings and its truncations to the dilaton chiral multiplet of N=1 superstrings. We argue that de Sitter vacua in such theories are necessarily unstable in weakly coupled situations, while they can in principle be metastable in strongly coupled regimes.Comment: 40 pages, no figure

The matrix model version of AGT conjecture and CIV-DV prepotential

Recently exact formulas were provided for partition function of conformal (multi-Penner) beta-ensemble in the Dijkgraaf-Vafa phase, which, if interpreted as Dotsenko-Fateev correlator of screenings and analytically continued in the number of screening insertions, represents generic Virasoro conformal blocks. Actually these formulas describe the lowest terms of the q_a-expansion, where q_a parameterize the shape of the Penner potential, and are exact in the filling numbers N_a. At the same time, the older theory of CIV-DV prepotential, straightforwardly extended to arbitrary beta and to non-polynomial potentials, provides an alternative expansion: in powers of N_a and exact in q_a. We check that the two expansions coincide in the overlapping region, i.e. for the lowest terms of expansions in both q_a and N_a. This coincidence is somewhat non-trivial, since the two methods use different integration contours: integrals in one case are of the B-function (Euler-Selberg) type, while in the other case they are Gaussian integrals.Comment: 27 pages, 1 figur

Anomalous kinetics, patterns formation in recalescence, and final microstructure of rapidly solidified Al-rich Al-Ni alloys

Copyright © 2022 The Authors. From thermodynamical consideration, rather a monotonically increasing crystal growth velocity with increasing undercooling is expected in the crystallization of liquids, mixtures, and alloys [P.K. Galenko and D. Jou, Physics Reports 818 (2019) 1]. By contrast to this general theoretical statement, Al-rich Al-Ni alloys show an anomalous solidification behavior: the solid-liquid interface velocity slows down as the undercooling increases [R. Lengsdorf, D. Holland-Moritz, D. M. Herlach, Scripta Materialia 62 (2010) 365]. It is also found that besides the anomalous growth behaviour, changes in the shape of the recalescence front as the growth front morphology occur. In the light of recent measurements in microgravity with an Al-25at.% Ni alloy sample onboard the International Space Station (ISS) results confirming this anomalous behavior as an unexpected trend in solidification kinetics are presented. The measurements show multiple nucleation events forming the growth front, a mechanism that has been observed for the first time in Al-Ni alloys [D. Herlach et al., Physical Review Materials 3 (2019) 073402; M. Reinartz et al. JOM 74 (2022) 2420] and summarized with detailed analysis in the present publication over a wider range of concentrations. Particularly, the experimental measurements and obtained data directly demonstrate that the growth front does thus not consist of dendrite tips (as in usual rapid solidifying samples), but of newly forming nuclei propagating along the sample surface in a coordinated manner. Theoretical analysis on intensive nucleation ahead of crystal growth front is made using the previously developed model [D.V. Alexandrov, Journal of Physics A: Mathematical and Theoretical 50 (2017) 345101]. Using equations of this model, quantitative calculations confirm the interpretation of experimentally observed propagation of the recalescence front and obtained data on the microstructure of droplets solidified in electromagnetic levitation facility (EML) on the Ground, under reduced gravity during parabolic flights, and in microgravity conditions onboard the ISS.European Space Agency (ESA) within the project NEQUISOL under contract No. 15236/02/NL/SH for experimental measurements under reduced gravity and by RSF under project No. 21-19-00279 for theoretical modeling; German Space Center - Space Administration under contract No. 50WM1941; German Science Foundation (DFG) under the Project GA 1142/11-1 for experimental measurements on the Ground

Introduction of a new model for time-continuous and non-contact investigations of in-vitro thrombolysis under physiological flow conditions

<p>Abstract</p> <p>Background</p> <p>Thrombolysis is a dynamic and time-dependent process influenced by the haemodynamic conditions. Currently there is no model that allows for time-continuous, non-contact measurements under physiological flow conditions. The aim of this work was to introduce such a model.</p> <p>Methods</p> <p>The model is based on a computer-controlled pump providing variable constant or pulsatile flows in a tube system filled with blood substitute. Clots can be fixed in a custom-built clot carrier within the tube system. The pressure decline at the clot carrier is measured as a novel way to measure lysis of the clot. With different experiments the hydrodynamic properties and reliability of the model were analyzed. Finally, the lysis rate of clots generated from human platelet rich plasma (PRP) was measured during a one hour combined application of diagnostic ultrasound (2 MHz, 0.179 W/cm²) and a thrombolytic agent (rt-PA) as it is commonly used for clinical sonothrombolysis treatments.</p> <p>Results</p> <p>All hydrodynamic parameters can be adjusted and measured with high accuracy. First experiments with sonothrombolysis demonstrated the feasibility of the model despite low lysis rates.</p> <p>Conclusions</p> <p>The model allows to adjust accurately all hydrodynamic parameters affecting thrombolysis under physiological flow conditions and for non-contact, time-continuous measurements. Low lysis rates of first sonothrombolysis experiments are primarily attributable to the high stability of the used PRP-clots.</p

Can pulsed ultrasound increase tissue damage during ischemia? A study of the effects of ultrasound on infarcted and non-infarcted myocardium in anesthetized pigs

BACKGROUND: The same mechanisms by which ultrasound enhances thrombolysis are described in connection with non-beneficial effects of ultrasound. The present safety study was therefore designed to explore effects of beneficial ultrasound characteristics on the infarcted and non-infarcted myocardium. METHODS: In an open chest porcine model (n = 17), myocardial infarction was induced by ligating a coronary diagonal branch. Pulsed ultrasound of frequency 1 MHz and intensity 0.1 W/cm(2 )(I(SATA)) was applied during one hour to both infarcted and non-infarcted myocardial tissue. These ultrasound characteristics are similar to those used in studies of ultrasound enhanced thrombolysis. Using blinded assessment technique, myocardial damage was rated according to histopathological criteria. RESULTS: Infarcted myocardium exhibited a significant increase in damage score compared to non-infarcted myocardium: 6.2 ± 2.0 vs. 4.3 ± 1.5 (mean ± standard deviation), (p = 0.004). In the infarcted myocardium, ultrasound exposure yielded a further significant increase of damage scores: 8.1 ± 1.7 vs. 6.2 ± 2.0 (p = 0.027). CONCLUSION: Our results suggest an instantaneous additive effect on the ischemic damage in myocardial tissue when exposed to ultrasound of stated characteristics. The ultimate damage degree remains to be clarified

Observation of a J^PC = 1-+ exotic resonance in diffractive dissociation of 190 GeV/c pi- into pi- pi- pi+

The COMPASS experiment at the CERN SPS has studied the diffractive dissociation of negative pions into the pi- pi- pi+ final state using a 190 GeV/c pion beam hitting a lead target. A partial wave analysis has been performed on a sample of 420000 events taken at values of the squared 4-momentum transfer t' between 0.1 and 1 GeV^2/c^2. The well-known resonances a1(1260), a2(1320), and pi2(1670) are clearly observed. In addition, the data show a significant natural parity exchange production of a resonance with spin-exotic quantum numbers J^PC = 1-+ at 1.66 GeV/c^2 decaying to rho pi. The resonant nature of this wave is evident from the mass-dependent phase differences to the J^PC = 2-+ and 1++ waves. From a mass-dependent fit a resonance mass of 1660 +- 10+0-64 MeV/c^2 and a width of 269+-21+42-64 MeV/c^2 is deduced.Comment: 7 page, 3 figures; version 2 gives some more details, data unchanged; version 3 updated authors, text shortened, data unchange

The Spin Foam Approach to Quantum Gravity

This article reviews the present status of the spin foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently introduced new models for four dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of the 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.Comment: To appear in Living Reviews in Relativit

The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference