On the discrete spectrum of quantum layers

Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that the second fundamental form vanishes at infinity, and that the surface is not totally geodesic. This geometric setting is known as a quantum layer. We consider the quantum particle to be governed by the Dirichlet Laplacian as Hamiltonian. Our work concerns the existence of bound states with energy beneath the essential spectrum, which implies the existence of discrete spectrum. We first prove that if the Gauss curvature is integrable, and the surface is weakly $\kappa$-parabolic, then the discrete spectrum is non-empty. This result implies that if the total Gauss curvature is non-positive, then the discrete spectrum is non-empty. We next prove that if the Gauss curvature is non-negative, then the discrete spectrum is non-empty. Finally, we prove that if the surface is parabolic, then the discrete spectrum is non-empty if the layer is sufficiently thin.Comment: Clarifications and corrections to previous version, conjecture from previous version is proven here (Theorem 1.5), additional references include

An Analysis Of The Lyophilization Process Using A Sorption‐sublimation Model And Various Operational Policies

The freeze‐drying process is studied under various operational policies through the use of a sorption‐sublimation model. The operational policy that provides the shortest drying times keeps the pressure at its lowest value. The upper and lower heating plates are independently controlled so that the material constraints are encountered and held throughout the free water removal phase. Under certain conditions, and for the case of samples of small thickness, the sorbed water profiles may have segments whose bound water concentrations are higher than those at the start of the free water removal phase. It is shown that the criterion used in terminating the freeze‐drying process is of extreme importance, since it may lead to an undesirable sorbed water profile which may deteriorate the quality of the dried product. Copyright © 1985 American Institute of Chemical Engineer

Ferromagnetic models for cooperative behavior: Revisiting Universality in complex phenomena

Ferromagnetic models are harmonic oscillators in statistical mechanics. Beyond their original scope in tackling phase transition and symmetry breaking in theoretical physics, they are nowadays experiencing a renewal applicative interest as they capture the main features of disparate complex phenomena, whose quantitative investigation in the past were forbidden due to data lacking. After a streamlined introduction to these models, suitably embedded on random graphs, aim of the present paper is to show their importance in a plethora of widespread research fields, so to highlight the unifying framework reached by using statistical mechanics as a tool for their investigation. Specifically we will deal with examples stemmed from sociology, chemistry, cybernetics (electronics) and biology (immunology).Comment: Contributing to the proceedings of the Conference "Mathematical models and methods for Planet Heart", INdAM, Rome 201

Modeling of droplet generation in a top blowing steelmaking process

Quantification of metal droplets ejected due to impinging gas jet on the surface of liquid metal is an important parameter for the understanding and for the modeling of the refining kinetics of reactions in slag-metal emulsion zone. In the present work, a numerical study has been carried out to critically examine the applicability of droplet generation rate correlation previously proposed by Subagyo et al. on the basis of dimensionless blowing number (N B). The blowing number was re-evaluated at the impingement point of jet with taking into account the temperature effect of change in density and velocity of the gas jet. The result obtained from the work shows that the modified blowing number N B,T at the furnace temperature of 1873 K (1600 °C) is approximately double in magnitude compared to N B calculated by Subagyo and co-workers. When N B,T has been employed to the Subagyo’s empirical correlation for droplet generation, a wide mismatch is observed between the experimental data obtained from cold model and hot model experiments. The reason for this large deviation has been investigated in the current study, and a theoretical approach to estimate the droplet generation rate has been proposed. The suitability of the proposed model has been tested by numerically calculating the amount of metals in slag. The study shows that the weight of metals in emulsion falls in the range of 0 to 21 wt pct of hot metal weight when droplet generation rate has been calculated at ambient furnace temperature of 1873 K (1600 °C)

Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

This review presents an overview of the thermal properties of mesoscopic structures. The discussion is based on the concept of electron energy distribution, and, in particular, on controlling and probing it. The temperature of an electron gas is determined by this distribution: refrigeration is equivalent to narrowing it, and thermometry is probing its convolution with a function characterizing the measuring device. Temperature exists, strictly speaking, only in quasiequilibrium in which the distribution follows the Fermi-Dirac form. Interesting nonequilibrium deviations can occur due to slow relaxation rates of the electrons, e.g., among themselves or with lattice phonons. Observation and applications of nonequilibrium phenomena are also discussed. The focus in this paper is at low temperatures, primarily below 4 K, where physical phenomena on mesoscopic scales and hybrid combinations of various types of materials, e.g., superconductors, normal metals, insulators, and doped semiconductors, open up a rich variety of device concepts. This review starts with an introduction to theoretical concepts and experimental results on thermal properties of mesoscopic structures. Then thermometry and refrigeration are examined with an emphasis on experiments. An immediate application of solid-state refrigeration and thermometry is in ultrasensitive radiation detection, which is discussed in depth. This review concludes with a summary of pertinent fabrication methods of presented devices.Comment: Close to the version published in RMP; 59 pages, 35 figure

Novel sampling method for assessing human-pathogen interactions in the natural environment using boot socks and citizen scientists, with application to Campylobacter seasonality

This paper introduces a novel method for sampling pathogens in natural environments. It uses fabric boot socks worn over walkers' shoes to allow the collection of composite samples over large areas. Wide-area sampling is better suited to studies focusing on human exposure to pathogens (e.g., recreational walking). This sampling method is implemented using a citizen science approach: groups of three walkers wearing boot socks undertook one of six routes, 40 times over 16 months in the North West (NW) and East Anglian (EA) regions of England. To validate this methodology, we report the successful implementation of this citizen science approach, the observation that Campylobacter bacteria were detected on 47% of boot socks, and the observation that multiple boot socks from individual walks produced consistent results. The findings indicate higher Campylobacter levels in the livestock-dominated NW than in EA (55.8% versus 38.6%). Seasonal differences in the presence of Campylobacter bacteria were found between the regions, with indications of winter peaks in both regions but a spring peak in the NW. The presence of Campylobacter bacteria on boot socks was negatively associated with ambient temperature (P = 0.011) and positively associated with precipitation (P < 0.001), results consistent with our understanding of Campylobacter survival and the probability of material adhering to boot socks. Campylobacter jejuni was the predominant species found; Campylobacter coli was largely restricted to the livestock-dominated NW. Source attribution analysis indicated that the potential source of C. jejuni was predominantly sheep in the NW and wild birds in EA but did not differ between peak and nonpeak periods of human incidence

A latent trait look at pretest-posttest validation of criterion-referenced test items

Since Cox and Vargas (1966) introduced their pretest-posttest validity index for criterion-referenced test items, a great number of additions and modifications have followed. All are based on the idea of gain scoring; that is, they are computed from the differences between proportions of pretest and posttest item responses. Although the method is simple and generally considered as the prototype of criterion-referenced item analysis, it has many and serious disadvantages. Some of these go back to the fact that it leads to indices based on a dual test administration- and population-dependent item p values. Others have to do with the global information about the discriminating power that these indices provide, the implicit weighting they suppose, and the meaningless maximization of posttest scores they lead to. Analyzing the pretest-posttest method from a latent trait point of view, it is proposed to replace indices like Cox and Vargas’ Dpp by an evaluation of the item information function for the mastery score. An empirical study was conducted to compare the differences in item selection between both methods

Axial and Radial Forces of Cross-Bridges Depend on Lattice Spacing

Nearly all mechanochemical models of the cross-bridge treat myosin as a simple linear spring arranged parallel to the contractile filaments. These single-spring models cannot account for the radial force that muscle generates (orthogonal to the long axis of the myofilaments) or the effects of changes in filament lattice spacing. We describe a more complex myosin cross-bridge model that uses multiple springs to replicate myosin's force-generating power stroke and account for the effects of lattice spacing and radial force. The four springs which comprise this model (the 4sXB) correspond to the mechanically relevant portions of myosin's structure. As occurs in vivo, the 4sXB's state-transition kinetics and force-production dynamics vary with lattice spacing. Additionally, we describe a simpler two-spring cross-bridge (2sXB) model which produces results similar to those of the 4sXB model. Unlike the 4sXB model, the 2sXB model requires no iterative techniques, making it more computationally efficient. The rate at which both multi-spring cross-bridges bind and generate force decreases as lattice spacing grows. The axial force generated by each cross-bridge as it undergoes a power stroke increases as lattice spacing grows. The radial force that a cross-bridge produces as it undergoes a power stroke varies from expansive to compressive as lattice spacing increases. Importantly, these results mirror those for intact, contracting muscle force production