Comparison of Entropy Production Rates in Two Different Types of Self-organized Flows: B\'{e}nard Convection and Zonal flow

Entropy production rate (EPR) is often effective to describe how a structure is self-organized in a nonequilibrium thermodynamic system. The "minimum EPR principle" is widely applicable to characterizing self-organized structures, but is sometimes disproved by observations of "maximum EPR states." Here we delineate a dual relation between the minimum and maximum principles; the mathematical representation of the duality is given by a Legendre transformation. For explicit formulation, we consider heat transport in the boundary layer of fusion plasma [Phys. Plasmas {\bf 15}, 032307 (2008)]. The mechanism of bifurcation and hysteresis (which are the determining characteristics of the so-called H-mode, a self-organized state of reduced thermal conduction) is explained by multiple tangent lines to a pleated graph of an appropriate thermodynamic potential. In the nonlinear regime, we have to generalize Onsager's dissipation function. The generalized function is no longer equivalent to EPR; then EPR ceases to be the determinant of the operating point, and may take either minimum or maximum values depending on how the system is driven

A superadditivity and submultiplicativity property for cardinalities of sumsets

For finite sets of integers A1, . . . ,An we study the cardinality of the n-fold sumset A1 + · · · + An compared to those of (n − 1)-fold sumsets A1 + · · · + Ai−1 + Ai+1 + · · · + An. We prove a superadditivity and a submultiplicativity property for these quantities. We also examine the case when the addition of elements is restricted to an addition graph between the sets

Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states

If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Green's operator in Coulomb-Sturmian basis representation. Based on this representation, a quantum mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $\alpha$ particles.Comment: 7 pages, 4 ps figures, revised versio

Decoherence time in self-induced decoherence

A general method for obtaining the decoherence time in self-induced decoherence is presented. In particular, it is shown that such a time can be computed from the poles of the resolvent or of the initial conditions in the complex extension of the Hamiltonian's spectrum. Several decoherence times are estimated: $10^{-13}-$ $10^{-15}s$ for microscopic systems, and $10^{-37}-10^{-39}s$ for macroscopic bodies. For the particular case of a thermal bath, our results agree with those obtained by the einselection (environment-induced decoherence) approach.Comment: 11 page

The role of TRPC6 calcium channels and P2 purinergic receptors in podocyte mechanical and metabolic sensing

Podocyte calcium (Ca2+) signaling plays important roles in the (patho)physiology of the glomerular filtration barrier. Overactivation of podocyte transient receptor potential canonical (TRPC) channels including TRPC6 and purinergic signaling via P2 receptors that are known mechanosensors can increase podocyte intracellular Ca2+ levels ([Ca2+]i) and cause cell injury, proteinuria and glomerular disease including in diabetes. However, important mechanistic details of the trigger and activation of these pathways in vivo in the intact glomerular environment are lacking. Here we show direct visual evidence that podocytes can sense mechanical overload (increased glomerular capillary pressure) and metabolic alterations (increased plasma glucose) via TRPC6 and purinergic receptors including P2Y2. Multiphoton microscopy of podocyte [Ca2+]i was performed in vivo using wild-type and TRPC6 or P2Y2 knockout (KO) mice expressing the calcium reporter GCaMP3/5 only in podocytes and in vitro using freshly dissected microperfused glomeruli. Single-nephron intra-glomerular capillary pressure elevations induced by obstructing the efferent arteriole lumen with laser-induced microthrombus in vivo and by a micropipette in vitro triggered >2-fold increases in podocyte [Ca2+]i. These responses were blocked in TRPC6 and P2Y2 KO mice. Acute elevations of plasma glucose caused >4-fold increases in podocyte [Ca2+]i that were abolished by pharmacological inhibition of TRPC6 or P2 receptors using SAR7334 or suramin treatment, respectively. This study established the role of Ca2+ signaling via TRPC6 channels and P2 receptors in mechanical and metabolic sensing of podocytes in vivo, which are promising therapeutic targets in conditions with high intra-glomerular capillary pressure and plasma glucose, such as diabetic and hypertensive nephropathy. © 2021 The Author(s)

Thermodynamic Field Theory with the Iso-Entropic Formalism

A new formulation of the thermodynamic field theory (TFT) is presented. In this new version, one of the basic restriction in the old theory, namely a closed-form solution for the thermodynamic field strength, has been removed. In addition, the general covariance principle is replaced by Prigogine's thermodynamic covariance principle (TCP). The introduction of TCP required the application of an appropriate mathematical formalism, which has been referred to as the iso-entropic formalism. The validity of the Glansdorff-Prigogine Universal Criterion of Evolution, via geometrical arguments, is proven. A new set of thermodynamic field equations, able to determine the nonlinear corrections to the linear ("Onsager") transport coefficients, is also derived. The geometry of the thermodynamic space is non-Riemannian tending to be Riemannian for hight values of the entropy production. In this limit, we obtain again the same thermodynamic field equations found by the old theory. Applications of the theory, such as transport in magnetically confined plasmas, materials submitted to temperature and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein.Comment: 35 page

Shell model in the complex energy plane and two-particle resonances

An implementation of the shell-model to the complex energy plane is presented. The representation used in the method consists of bound single-particle states, Gamow resonances and scattering waves on the complex energy plane. Two-particle resonances are evaluated and their structure in terms of the single-particle degreees of freedom are analysed. It is found that two-particle resonances are mainly built upon bound states and Gamow resonances, but the contribution of the scattering states is also important.Comment: 20 pages, 9 figures, submitted to Phys.Rev.

Gamow Shell Model Description of Weakly Bound Nuclei and Unbound Nuclear States

We present the study of weakly bound, neutron-rich nuclei using the nuclear shell model employing the complex Berggren ensemble representing the bound single-particle states, unbound Gamow states, and the non-resonant continuum. In the proposed Gamow Shell Model, the Hamiltonian consists of a one-body finite depth (Woods-Saxon) potential and a residual two-body interaction. We discuss the basic ingredients of the Gamow Shell Model. The formalism is illustrated by calculations involving {\it several} valence neutrons outside the double-magic core: $^{6-10}$He and $^{18-22}$O.Comment: 19 pages, 20 encapsulated PostScript figure