Phase diagram of fluid phases in 3{}^3He -4{}^4He mixtures

Fluid parts of the phase diagram of ${}^3$He -${}^4$He mixtures are obtained from a mean-field analysis of a suitable lattice gas model for binary liquid mixtures. The proposed model takes into account the continuous rotational symmetry O(2) of the superfluid degrees of freedom associated with ${}^4$He and includes the occurrence of vacancies. This latter degree of freedom allows the model to exhibit a vapor phase and hence can provide the theoretical framework to describe the experimental conditions for measurements of tricritical Casimir forces in ${}^3$He -${}^4$He wetting films

Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation

We consider a class of real random polynomials, indexed by an integer d, of large degree n and focus on the number of real roots of such random polynomials. The probability that such polynomials have no real root in the interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)>0 is the exponent associated to the decay of the persistence probability for the diffusion equation with random initial conditions in space dimension d. For n even, the probability that such polynomials have no root on the full real axis decays as n^{-2(\theta(d) + \theta(2))}. For d=1, this connection allows for a physical realization of real random polynomials. We further show that the probability that such polynomials have exactly k real roots in [0,1] has an unusual scaling form given by n^{-\tilde \phi(k/\log n)} where \tilde \phi(x) is a universal large deviation function.Comment: 4 pages, 3 figures. Minor changes. Accepted version in Phys. Rev. Let

The Simultaneous Impacts of Seasonal Weather and Solar Conditions on PV Panels Electrical Characteristics

Solar energy usage is thriving day by day. These solar panels are installed to absorb solar energy and produce electrical energy. As a result, the efficiency of solar panels depends on different environmental factors, namely, air temperature, dust (aerosols and accumulated dust), and solar incidence, and photovoltaic panel angles. The effects of real conditions factors on power and efficiency of photovoltaic panels are studied in this paper through testing the panel in real environmental tests. To study the mentioned parameters precisely, two panels with different angles are used. The case study is regarding a region of Tehran, Iran, in summer and winter seasons. The results show that panel efficiency during winter is higher than summer due to air temperature decrement. It is discovered that among air pollutants, Al and Fe have the most share in polluting the air that affect the photovoltaic efficiency. Moreover, measuring the accumulated dust on the panels shows more amount in winter in comparison with summer. The important point in studying the effect of tilt angle is that inconformity between solar incidence and photovoltaic panel angles would result in solar radiation absorption and eventually panel efficiency loss and also, photovoltaic panel installation angle would affect the amount of dust deposited on its surface.© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).fi=vertaisarvioitu|en=peerReviewed

Tracking Target Signal Strengths on a Grid using Sparsity

Multi-target tracking is mainly challenged by the nonlinearity present in the measurement equation, and the difficulty in fast and accurate data association. To overcome these challenges, the present paper introduces a grid-based model in which the state captures target signal strengths on a known spatial grid (TSSG). This model leads to \emph{linear} state and measurement equations, which bypass data association and can afford state estimation via sparsity-aware Kalman filtering (KF). Leveraging the grid-induced sparsity of the novel model, two types of sparsity-cognizant TSSG-KF trackers are developed: one effects sparsity through $\ell_1$-norm regularization, and the other invokes sparsity as an extra measurement. Iterative extended KF and Gauss-Newton algorithms are developed for reduced-complexity tracking, along with accurate error covariance updates for assessing performance of the resultant sparsity-aware state estimators. Based on TSSG state estimates, more informative target position and track estimates can be obtained in a follow-up step, ensuring that track association and position estimation errors do not propagate back into TSSG state estimates. The novel TSSG trackers do not require knowing the number of targets or their signal strengths, and exhibit considerably lower complexity than the benchmark hidden Markov model filter, especially for a large number of targets. Numerical simulations demonstrate that sparsity-cognizant trackers enjoy improved root mean-square error performance at reduced complexity when compared to their sparsity-agnostic counterparts.Comment: Submitted to IEEE Trans. on Signal Processin

Hydrothermal Scheduling in the Continuous-Time Framework

Continuous-time optimization models have successfully been used to capture the impact of ramping limitations in power systems. In this paper, the continuous-time framework is adapted to model flexible hydropower resources interacting with slow-ramping thermal generators to minimize the hydrothermal system cost of operation. To accurately represent the non-linear hydropower production function with forbidden production zones, binary variables must be used when linearizing the discharge variables and the continuity constraints on individual hydropower units must be relaxed. To demonstrate the performance of the proposed continuous-time hydrothermal model, a small-scale case study of a hydropower area connected to a thermal area through a controllable high-voltage direct current (HVDC) cable is presented. Results show how the flexibility of the hydropower can reduce the need for ramping by thermal units triggered by intermittent renewable power generation. A reduction of 34% of the structural imbalances in the system is achieved by using the continuous-time model.Comment: Accepted for publication through the Power Systems Computation Conference 202