Metastates in Finite-type Mean-field Models: Visibility,Invisibility, and Random Restoration of Symmetry

We consider a general class of disordered mean-field models where both the spin variables and disorder variables η take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate describing the probabilities to find a large system close to a particular convex combination of the pure infinite-volume states. We show that, under a non-degeneracy assumption, only pure states j are seen, with non-random probability weights w _j for which we derive explicit expressions in terms of interactions and distributions of the disorder variables. We provide a geometric construction distinguishing invisible states (having w _j =0) from visible ones. As a further consequence we show that, in the case where precisely two pure states are available, these must necessarily occur with the same weight, even if the model has no obvious symmetry relating the two.     

Heat and moisture transfer in sol–gel treated cotton fabrics

Cotton fabrics have been treated by sol–gel processes in order to produce an inorganic coating on fibres, able to modify their thermal conductivity under an irradiating flow. To this aim, fabric specimens with different silica content have been tested following the ISO 6942 standard in order to establish the effect of the coating on coupled heat and moisture transfer through the cotton fibres. The collected results have been compared with those obtained by an optimized method using a cone calorimeter as the heating source. By this latter approach, it has been demonstrated that sol–gel cotton treated fabrics with high moisture uptake possess a significantly lower thermal conductivity with respect to cotton alone.     

Combining Different Docking Engines and Consensus Strategies to Design and Validate Optimized Virtual Screening Protocols for the SARS-CoV-2 3CL Protease

The 3CL-Protease appears to be a very promising medicinal target to develop anti-SARS-CoV-2 agents. The availability of resolved structures allows structure-based computational approaches to be carried out even though the lack of known inhibitors prevents a proper validation of the performed simulations. The innovative idea of the study is to exploit known inhibitors of SARS-CoV 3CL-Pro as a training set to perform and validate multiple virtual screening campaigns. Docking simulations using four different programs (Fred, Glide, LiGen, and PLANTS) were performed investigating the role of both multiple binding modes (by binding space) and multiple isomers/states (by developing the corresponding isomeric space). The computed docking scores were used to develop consensus models, which allow an in-depth comparison of the resulting performances. On average, the reached performances revealed the different sensitivity to isomeric differences and multiple binding modes between the four docking engines. In detail, Glide and LiGen are the tools that best benefit from isomeric and binding space, respectively, while Fred is the most insensitive program. The obtained results emphasize the fruitful role of combining various docking tools to optimize the predictive performances. Taken together, the performed simulations allowed the rational development of highly performing virtual screening workflows, which could be further optimized by considering different 3CL-Pro structures and, more importantly, by including true SARS-CoV-2 3CL-Pro inhibitors (as learning set) when available.     

Tight-binding models for ultracold atoms in optical lattices: general formulation and applications

Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.     

On the establishment of thermal diffusion in binary Lennard-Jones liquids

The establishment of thermal diffusion in an Ar-Kr Lennard-Jones mixture is investigated via dynamical non equilibrium molecular dynamics [G. Ciccotti, G. Jacucci, Phys. Rev. Lett. 35, 789 (1975)]. We observe, in particular, the evolution of the density and temperature fields of the system following the onset of the thermal gradient. In stationary conditions, we also compute the Soret coefficient of the mixture. This study confirms that dynamical non equilibrium molecular dynamics is an effective tool to gather information on transient phenomena, even though the full evolution of the mass and energy fluxes associated to the temperature and density fields requires, in this case, a more substantial numerical effort than the one employed here.     

Energy,Exergy, Exergoeconomic and Emergy-Based Exergoeconomic (Emergoeconomic) Analyses of a Biomass Combustion Waste Heat Recovery Organic Rankine Cycle

In recent decades, there has been an increasing trend toward the technical development of efficient energy system assessment tools owing to the growing energy demand and subsequent greenhouse gas emissions. Accordingly, in this paper, a comprehensive emergy-based exergoeconomic (emergoeconomic) method has been developed to study the biomass combustion waste heat recovery organic Rankine cycle (BCWHR-ORC), taking into account thermodynamics, economics, and sustainability aspects. To this end, the system was formulated in Engineering Equation Solver (EES) software, and then the exergy, exergoeconomic, and emergoeconomic analyses were conducted accordingly. The exergy analysis results revealed that the evaporator unit with 55.05 kilowatts and the turbine with 89.57% had the highest exergy destruction rate and exergy efficiency, respectively. Based on the exergoeconomic analysis, the cost per exergy unit (c), and the cost rate (C˙) of the output power of the system were calculated to be 24.13 USD/GJ and 14.19 USD/h, respectively. Next, by applying the emergoeconomic approach, the monetary emergy content of the system components and the flows were calculated to evaluate the system’s sustainability. Accordingly, the turbine was found to have the highest monetary emergy rate of capital investment, equal to 5.43×1012 sej/h, and an output power monetary emergy of 4.77×104 sej/J. Finally, a sensitivity analysis was performed to investigate the system’s overall performance characteristics from an exergoeconomic perspective, regarding the changes in the transformation coefficients (specific monetary emergy).     

Long Time Behavior of the Cahn-Hilliard Equation with Irregular Potentials and Dynamic Boundary Conditions

The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered.The existence of the global attractor is proved and the long time behavior of the trajectories,namely,the convergence to steady states,is studied.     

Existence of Indecomposable Rank Two Vector Bundles on Higher Dimensional Toric Varieties

In the mid 1970s, Hartshorne conjectured that, for all n > 7, any rank 2 vector bundles on ? ⁿ is a direct sum of line bundles. This conjecture remains still open. In this paper, we construct indecomposable rank two vector bundles on a large class of Fano toric varieties. Unfortunately, this class does not contain ? ⁿ .