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In Sani et al. (Int. J. Numer. Meth. Fluids 2006; 50:673–682), the authors claim to provide a proof of well-posedness for certain formulations of the Navier–Stokes equations for incompressible flow. We consider the proof of their main Theorem 1 incomplete, and point out some inconsistencies in the above paper. Copyright © 2008 John Wiley & Sons, Ltd.

We propose a mathematical model based on probability theory to optimize COVID‐19 testing by a multistep batch testing approach with variable batch sizes. This model and simulation tool dramatically increase the efficiency and efficacy of the tests in a large population at a low cost, particularly when the infection rate is low. The proposed method combines statistical modeling with numerical methods to solve nonlinear equations and obtain optimal batch sizes at each step of tests, with the flexibility to incorporate geographic and demographic information. In theory, this method substantially improves the false positive rate and positive predictive value as well. We also conducted a Monte Carlo simulation to verify this theory. Our simulation results show that our method significantly reduces the false negative rate. More accurate assessment can be made if the dilution effect or other practical factors are taken into consideration. The proposed method will be particularly useful for the early detection of infectious diseases and prevention of future pandemics. The proposed work will have broader impacts on medical testing for contagious diseases in general.

In a recent paper, Dr. Frind has formulated a two-dimensional isoparametric finite element based upon the Hermite bicubic interpolation scheme. The present discussion focuses upon certain simplifications in the derivation which appear to have diminished the accuracy of the resulting element, and suggests a simpler approach to the element formulation. This author agrees strongly with Dr. Frind's recommendation of the Hermite parametric element as an efficient and useful tool for general field problems; the present comments are offered to point out that, in fact, the accuracy comparisons presented by Dr. Frind are biased against the Hermite finite element.

The paper shows a procedure for estimating the shape parameter of a Gamma distribution from a sample. This procedure uses a rapidly converging iteration to solve the maximum-likelihood equation and suggests a simple formula for determing the starting value.

The SARS‐CoV‐2 virus is currently causing a worldwide pandemic with dramatic societal consequences for the humankind. In the past decades, disease outbreaks due to such zoonotic pathogens have appeared with an accelerated rate, which calls for an urgent development of adaptive (smart) therapeutics. Here, a computational strategy is developed to adaptively evolve peptides that could selectively inhibit mutating S protein receptor binding domains (RBDs) of different SARS‐CoV‐2 viral strains from binding to their human host receptor, angiotensin‐converting enzyme 2 (ACE2). Starting from suitable peptide templates, based on selected ACE2 segments (natural RBD binder), the templates are gradually modified by random mutations, while retaining those mutations that maximize their RBD‐binding free energies. In this adaptive evolution, atomistic molecular dynamics simulations of the template‐RBD complexes are iteratively perturbed by the peptide mutations, which are retained under favorable Monte Carlo decisions. The computational search will provide libraries of optimized therapeutics capable of reducing the SARS‐CoV‐2 infection on a global scale., Adaptive evolution of peptides for their strong binding to target proteins is developed computationally. Random mutations are iteratively introduced into peptides, the systems are briefly simulated, and the mutations are accepted or rejected according to their free energy of binding (Metropolis). The strategy is tested in peptide inhibitors of the S protein receptor binding domain in different SARS‐CoV‐2 viral strains.

The COVID‐19 virus has been recently identified as a new species of virus that can cause severe infections such as pneumonia. The sudden outbreak of this disease is being considered a pandemic. Given all this, it is essential to develop smart biosensors that can detect pathogens with minimum time delay. Surface plasmon resonance (SPR) biosensors make use of refractive index (RI) changes as the sensing parameter. In this work, based on actual data taken from previous experimental works done on plasmonic detection of viruses, a detailed simulation of the SPR scheme that can be used to detect the COVID‐19 virus is performed and the results are extrapolated from earlier schemes to predict some outcomes of this SPR model. The results indicate that the conventional Kretschmann configuration can have a limit of detection (LOD) of 2E‐05 in terms of RI change and an average sensitivity of 122.4 degRIU−1 at a wavelength of 780 nm., The entire world is fighting a major public health crisis in the form a unique viral disease, caused by a coronavirus that has been named COVID‐19. In this work, a theoretical study of a plasmonic sensing scheme in the form of simulations that can be used to detect the COVID‐19 virus is presented.

Amid the ongoing COVID-19 pandemic, public health authorities and the general population are striving to achieve a balance between safety and normalcy. Ever changing conditions call for the development of theory and simulation tools to finely describe multiple strata of society while supporting the evaluation of "what-if" scenarios. Particularly important is to assess the effectiveness of potential testing approaches and vaccination strategies. Here, an agent-based modeling platform is proposed to simulate the spreading of COVID-19 in small towns and cities, with a single-individual resolution. The platform is validated on real data from New Rochelle, NY -- one of the first outbreaks registered in the United States. Supported by expert knowledge and informed by reported data, the model incorporates detailed elements of the spreading within a statistically realistic population. Along with pertinent functionality such as testing, treatment, and vaccination options, the model accounts for the burden of other illnesses with symptoms similar to COVID-19. Unique to the model is the possibility to explore different testing approaches -- in hospitals or drive-through facilities -- and vaccination strategies that could prioritize vulnerable groups. Decision making by public authorities could benefit from the model, for its fine-grain resolution, open-source nature, and wide range of features., 44 pages (including 16 of Supplementary Information). Published online in Advanced Theory and Simulations

Over the past two decades, the use of fragment‐based lead generation has become a common, mature approach to identify tractable starting points in chemical space for the drug discovery process. This approach naturally involves the study of the binding properties of highly heterogeneous ligands. Such datasets challenge computational techniques to provide comparable binding free energy estimates from different binding modes. The performance of a range of statistically robust ensemble‐based binding free energy calculation protocols, called ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent), is evaluated. Ligands designed to target two binding pockets in the lactate dehydogenase, a target protein, which vary in size, charge, and binding mode, are studied. When compared to experimental results, excellent statistical rankings are obtained across this highly diverse set of ligands. In addition, three approaches to account for entropic contributions are investigated: 1) normal mode analysis, 2) weighted solvent accessible surface area (WSAS), and 3) variational entropy. Normal mode analysis and WSAS correlate strongly with each other—although the latter is computationally far cheaper—but do not improve rankings. Variational entropy corrects exaggerated discrimination of ligands bound in different pockets but creates three outliers which reduce the quality of the overall ranking., A challenging application of ensemble‐based binding free energy calculations is reported in which the dataset exhibits substantial chemical diversity in ligands and their binding modes. Excellent correlation is obtained between predictions and experimental results, notwithstanding that the ligands vary in size, charge, and binding pockets targeted. Entropic contributions are evaluated and compared using three different methods, none of which improve the overall ranking.

Closed form solutions for the evaluation of the wave and natural parameters of inhomogeneous cable configurations where skin- and proximity-effects are present rarely exist. In most cases such parameters can only be retrieved from measurement experiments or by resorting to numerical methods. In this short paper we present the theoretical foundations of a novel measurement principle, as well as specific formulae for the determination of the parameters of a shielded bifilar line, avoiding the end-effects that usually arise when cables are tested using short- and open-circuit terminations. Copyright © 2010 John Wiley & Sons, Ltd.

A refined non-conforming triangular plate/shell element for geometric non-linear analysis of plates/shells using the total Lagrangian/updated Lagrangian approach is constructed in this paper based on the refined non-conforming element method for geometric non-linear analysis. The Allman's triangular plane element with vertex degrees of freedom and the refined triangular plate-bending element RT9 are used to construct the present element. Numerical examples demonstrate that the accuracy of the new element is quite high in the geometric non-linear analysis of plates/shells. Copyright © 2003 John Wiley & Sons, Ltd.

A finite difference numerical method to predict temperatures and destruction of a thermally labile species in cylindrical cans of conduction heating food was applied to compute final microbial load in an inoculated 18°Brix canned tomato concentrate at pH = 4.5 processed under conditions simulating industrial practice. Predictions of product temperature and final microbial load in three can sizes compared well with experimental heat penetration data and estimation of surviving species of Bacillus coagulans ATC 8038 spores inoculated into the cans. The application of the model as an aid to establishing process schedules is illustrated for a can with a required IS 14 100 = 11.44 min. The model predicts that a 29.5 min heating time at 105.6°C would provide an IS 14 100 = 11.77 min.

A long established approximation, normally invoked in the development of classical rolling theory, is that the work roll-strip interface assumes a circular profile. Although valid for a wide range of practical rolling conditions, the approximation is definitely suspect for instance in the last and penultimate stand of a thin sheet tandem mill, and algorithms based on classical theory may fail to converge. This paper computing solutions. In deriving the algorithm it is convenient to employ the formalism of functional One notable feature is that the gradients have to be carefully defined with respect to the correct ‘space’, in order that physically inadmissible discontinuties are not introduced during the hill-climbing. Computed roll gap solutions sometimes display elastic deformation regions embedded within the normal plastic deformation zone. It is thought that this is the first time this possibility has been allowed for in the formulation, or solutions obtained exhibiting this feature.