Global mass-preserving solutions to a chemotaxis-fluid model involving Dirichlet boundary conditions for the signal

The chemotaxis-Stokes system [Formula: see text] is considered subject to the boundary condition [Formula: see text] with [Formula: see text] and a given nonnegative function [Formula: see text]. In contrast to the well-studied case when the second requirement herein is replaced by a homogeneous Neumann boundary condition for [Formula: see text], the Dirichlet condition imposed here seems to destroy a natural energy-like property that has formed a core ingredient in the literature by providing comprehensive regularity features of the latter problem. This paper attempts to suitably cope with accordingly poor regularity information in order to nevertheless derive a statement on global existence within a generalized framework of solvability which involves appropriately mild requirements on regularity, but which maintains mass conservation in the first component as a key solution property.

Comparison of Huggins Coefficients and Osmotic Second Virial Coefficients of Buffered Solutions of Monoclonal Antibodies

The Huggins coefficient kH is a well-known metric for quantifying the increase in solution viscosity arising from intermolecular interactions in relatively dilute macromolecular solutions, and there has been much interest in this solution property in connection with developing improved antibody therapeutics. While numerous kH measurements have been reported for select monoclonal antibodies (mAbs) solutions, there has been limited study of kH in terms of the fundamental molecular interactions that determine this property. In this paper, we compare measurements of the osmotic second virial coefficient B22, a common metric of intermolecular and interparticle interaction strength, to measurements of kH for model antibody solutions. This comparison is motivated by the seminal work of Russel for hard sphere particles having a short-range “sticky” interparticle interaction, and we also compare our data with known results for uncharged flexible polymers having variable excluded volume interactions because proteins are polypeptide chains. Our observations indicate that neither the adhesive hard sphere model, a common colloidal model of globular proteins, nor the familiar uncharged flexible polymer model, an excellent model of intrinsically disordered proteins, describes the dependence of kH of these antibodies on B22. Clearly, an improved understanding of protein and ion solvation by water as well as dipole–dipole and charge–dipole effects is required to understand the significance of kH from the standpoint of fundamental protein–protein interactions. Despite shortcomings in our theoretical understanding of kH for antibody solutions, this quantity provides a useful practical measure of the strength of interprotein interactions at elevated protein concentrations that is of direct significance for the development of antibody formulations that minimize the solution viscosity.

A fractal Langmuir kinetic equation and its solution structure

The Langmuir kinetic equation is analyzed by the variational iteration method, its solution property is revealed analytically. The effects of desorption time and adsorption coefficient on the solution properties are also discussed, and a fractal modification of Langmuir kinetic equation is suggested.

Approximate solutions for a fractional hybrid initial value problem via the Caputo conformable derivative

Our main purpose in this work is to derive an existence criterion for a Caputo conformable hybrid multi-term integro-differential equation equipped with initial conditions. In this way, we consider a partially ordered Banach space, and, by applying the lower solution property, the existence and successive approximations of solutions for the mentioned hybrid initial problem are investigated. Eventually, we formulate an illustrative example for this hybrid IVP to support our findings from a numerical point of view. Moreover, we plot the sequence of the obtained approximate solutions for different values of noninteger orders.

Computing the Assembly Guidance for Maximizing Product Quality in the Virtual Assembly

Assembly is the final process of manufacturing, and a good assembly plan reduces the effect of the tolerance generated in the early stages by the tolerance elimination. In the current assembly lines, the assemblers pick up the workpieces and install them together by the assembly instructions. When the workpieces are oversize or undersize, the product can not be installed correctly. Therefore, the assembler considers the secondary processing to fix the tolerance and then installs them together again. The product could be installed, but the product quality may be reduced by the secondary process. So, we formulate the assembly process as a combinatorial optimization problem, named by the dimensional chain assembly (DCA) problem. Given some workpieces with the corresponding actual size, computing the assembly guidance is the goal of the DCA problem, and the product quality is applied to represent the solution quality. The assemblers follow the assembly guidance to install the products. We firstly prove that the DCA problem is NP-complete and collect the requirements of solving the DCA problem from the implementation perspective: the sustainability, the minimization of computation time, and the guarantee of product quality. We consider solution refinement and the solution property inheritance of the single-solution evolution approach to discover and refine the quality of the assembly guidance. Based on the above strategies, we propose the assembly guidance optimizer (AGO) based on the simulated annealing algorithm to compute the assembly guidance. From the simulation results, the AGO reaches all requirements of the DCA problem. The variance of the computation time and the solution quality is related to the problem scale linearly, so the computation time and the solution quality can be estimated by the problem scale. Moreover, increasing the search breadth is unnecessary for improving the solution quality. In summary, the proposed AGO satisfies with the necessaries of the sustainability, the minimization of computation time, and the guarantee of product quality for the requirements of the DCA, and it can be considered in the real-world applications.