Search

We consider the wave equation in an unbounded domain and are interested in domain truncation methods. Our aim is to develop a numerical scheme that allows calculations for truncated waveguide geometries with periodic coefficient functions. The scheme is constructed with radiation boxes that are attached to the artificially introduced boundaries. A Dirichlet-to-Neumann operator |$N$| is calculated in these radiation boxes. Efficiency of the scheme is obtained by calculating |$N$| not with an iteration, but with a single run through the time interval. We observe speed-up factors of up to |$20$| in comparison to calculations without domain truncation. [ABSTRACT FROM AUTHOR]

Brown algae are considered promising crops for the production of sustainable biofuels. However, the commercial application has been limited by lack of efficient methods for converting alginate into fermentable sugars. Herein, we cloned and characterized a novel alginate lyase AlyPL17 from Pedobacter hainanensis NJ-02. It possessed outstanding catalytic efficiency toward polymannuronic acid (polyM), polyguluronic acid (polyG), and alginate sodium, with kcat of 39.42 ± 1.9 s−1, 32.53 ± 0.88 s−1, and 38.30 ± 2.12 s−1, respectively. AlyPL17 showed maximum activity at 45 °C and pH 9.0. The domain truncation did not change the optimal temperature and optimal pH, but greatly reduced the activity. In addition, AlyPL17 degrades alginate through the cooperative action of two structural domains in an exolytic mode. The minimal degradation substrate of AlyPL17 is a disaccharide. Furthermore, AlyPL17 and AlyPL6 can synergistically degrade alginate to prepare unsaturated monosaccharides that can be converted to 4-deoxy-l-erythron-5-hexoseuloseuronate acid (DEH). DEH is reduced to KDG by DEH reductase (Sdr), which enters the Entner-Doudoroff (ED) pathway as a common metabolite and is converted to bioethanol. Key points: • Biochemical characterization of alginate lyase from Pedobacter hainanensis NJ-02 and its truncated form. • Degradation patterns of AlyPL17 and the role of its domains in product distribution and mode of action. • Potential of synergistic degradation system for efficient preparation of unsaturated monosaccharides. [ABSTRACT FROM AUTHOR]

We analyse how the spectrum of the anisotropic Maxwell system with bounded conductivity σ on a Lipschitz domain Ω is approximated by domain truncation. First we prove a new non-convex enclosure for the spectrum of the Maxwell system, with weak assumptions on the geometry of Ω and none on the behaviour of the coefficients at infinity. We also establish a simple criterion for non-accumulation of eigenvalues at i R as well as resolvent estimates. For asymptotically constant coefficients, we describe the essential spectrum and show that spectral pollution may occur only in the essential numerical range W e (L ∞) ⊂ R of the quadratic pencil L ∞ (ω) = μ ∞ − 1 curl 2 − ω 2 ε ∞ , acting on divergence-free vector fields. Further, every isolated spectral point of the Maxwell system lying outside W e (L ∞) and outside the part of the essential spectrum on i R is approximated by spectral points of the Maxwell system on the truncated domains. Our analysis is based on two new abstract results on the (limiting) essential spectrum of polynomial pencils and triangular block operator matrices, which are of general interest. We believe our strategy of proof could be used to establish domain truncation spectral exactness for more general classes of non-self-adjoint differential operators and systems with non-constant coefficients. [ABSTRACT FROM AUTHOR]

We consider the wave equation ∂ t 2 v ϵ − ∇ ⋅ (a ϵ ∇) v ϵ = f on an unbounded domain Ω ∞ for highly oscillatory coefficients a ϵ with the scaling a ϵ (x) = a (x / ϵ). We consider settings in which the homogenization process for this equation is well understood, which means that v ϵ → v ¯ holds for the solution v ¯ of the homogenized problem ∂ t 2 v ¯ − ∇ ⋅ (a ∗ ∇) v ¯ = f. In this context, domain truncation methods are studied. The goal is to calculate an approximate solution u ϵ on a subdomain, say Ω − ⊂ Ω ∞ . We are ready to solve the ε-problem on Ω − , but we want to solve only homogenized problems on the unbounded domains Ω ∞ or Ω ∞ ∖ Ω ¯ − . The main task is to define transmission conditions at the interface to have small differences u ϵ − v ϵ . We present different methods and corresponding O (ϵ) error estimates. [ABSTRACT FROM AUTHOR]

Diverging eigenvalues in domain truncations of Schrödinger operators with complex potentials are analyzed and their asymptotic formulas are obtained. Our approach also yields asymptotic formulas for diverging eigenvalues in the strong coupling regime for the imaginary part of the potential. [ABSTRACT FROM AUTHOR]

Hyaluronidases are a group of glycosidases catalyzing the degradation of hyaluronic acid (HA). Because of the advantages of effectively hydrolyzing the HA-rich matrix and low immunogenicity, human hyaluronidase PH20 (hPH20) is widely used in the medical field. Here, we realized the active expression of recombinant hPH20 by Pichia pastoris under a methanol-induced promoter PAOX1. By optimizing the composition of the C-terminal domain and fusing protein tags, we constructed a fusion mutant AP2-△491C with the extracellular hyaluronidase activity of 258.1 U·L−1 in a 3-L bioreactor, the highest expression level of recombinant hPH20 produced by microbes. Furthermore, we found recombinant hPH20 hydrolyzed the β-1,4 glycosidic bonds sequentially from the reducing end of o-HAs, with HA6NA as the smallest substrate. The result will provide important theoretical guidance for the directed evolution of the enzyme to prepare multifunctional o-HAs with specific molecular weights.

We study spectral approximations of Schrödinger operatorsT = −Δ+Qwith complex potentials on Ω = ℝd, or exterior domains Ω⊂ℝd, by domain truncation. Our weak assumptions cover wide classes of potentialsQfor whichThas discrete spectrum, of approximating domains Ωn, and of boundary conditions on∂Ωnsuch as mixed Dirichlet/Robin type. In particular,Re Qneed not be bounded from below andQmay be singular. We prove generalized norm resolvent convergence and spectral exactness,i.e.approximation ofalleigenvalues ofTby those of the truncated operatorsTnwithoutspectral pollution. Moreover, we estimate the eigenvalue convergence rate and prove convergence of pseudospectra. Numerical computations for several examples, such as complex harmonic and cubic oscillators ford = 1,2,3, illustrate our results. [ABSTRACT FROM AUTHOR]

One of the challenges in electromagnetics is to solve electromagnetic fields originated from a radiating source or a scattering object in distances that largely exceed the dimensions of the source or scatterer. In this paper, domain decomposition based on the application reasoning of the perfectly matched layer (PML) is studied by the spectral element method (SEM) for the first time in order to solve near and far electromagnetic fields without requiring substantially computational resources. Scattering from a loss-free dielectric cylinder and radiated fields from a line source are the problems utilized for the purpose of numerical demonstration in two dimensions in order to verify the successful application of SEM and its accuracy under domain decomposition. It is demonstrated that it is possible to accurately solve for near-field and far-field zones where millions of unknowns are encountered by using a typical personal computer. [ABSTRACT FROM AUTHOR]

A semianalytical solution to the eddy-current induction problem in a conducting, nonmagnetic plate near a cylindrical through-hole is derived by means of the second-order vector potential and the domain truncation technique. The construction of a solution, which simultaneously satisfies the field continuity across the cylindrical surface of the hole and the planar interfaces of the plate, proves to be a very challenging problem, and thus, a special superposition of partial subsolutions is proposed. The presented solution is part of a more general development aiming at the calculation of the probe interaction with material flaws located in the vicinity of the hole by means of the integral equation formalism. These tasks will be the subject of a future paper. The comparison of the semianalytical results against both finite-element simulations as well as experimental data demonstrates excellent agreement. [ABSTRACT FROM AUTHOR]

• A novel and more efficient bifunctional xylanase/feruloyl esterase XynII-Fae was constructed. • Synergistic action of XynII-Fae with cellulase could dramatically improve the hydrolysis efficiency of lignocellulose. • Replacement with XynII-Fae increased glucan and xylan conversion by 54.3% and 125.1%. • XynII-Fae enhanced cellulase hydrolysis against different agricultural residues. Herein, the xylanase and feruloyl esterase domains of the xylanase/feruloyl esterase bifunctional enzyme (Xyn-Fae) from Prevotella ruminicola 23 were identified using N- and C-terminal truncation mutagenesis. In addition, a novel and more efficient xylanase/feruloyl esterase bifunctional enzyme XynII-Fae was constructed, and its synergistic action with a commercial cellulase for lignocellulose hydrolysis was studied. When 40% cellulase was replaced by XynII-Fae, the production of reducing sugars increased by 65% than that with the cellulase alone, and the conversions of xylan and glucan were increased by 125.1% and 54.3%, respectively. When 80% cellulase was substituted by XynII-Fae, up to 43.5 μg/mL ferulic acid and 418.7 μg/mL acetic acid were obtained. The XynII-Fae could also accelerate the hydrolysis of wheat straw and sugarcane bagasse with commercial cellulase. These results indicated that the synergistic action of XynII-Fae with cellulase could dramatically improve the hydrolysis efficiency of lignocellulose, showing the great potential for industrial applications. [ABSTRACT FROM AUTHOR]

The analytical solution for the eddy-current induction in a conducting half-space containing an infinitely long cylindrical hole parallel to the interface is derived by means of the second-order vector potential and the domain truncation technique. The eddy currents are induced by a cylindrical coil which can be placed either in the nonconductive region above the half-space or inside the hole or in both locations simultaneously. Analytical expressions for the coil impedance are derived in both cases. The problem is treated as a coupled scattering problem and the derived analytical expressions permit a clear physical interpretation of the different terms, thus enhancing the understanding of underlying physics. The validity of the solution is demonstrated by comparisons to results obtained with the finite element method. [ABSTRACT FROM PUBLISHER]

Abstract: This paper presents an analysis and a semi-analytical study of the boundary value problem resulting from a self-similar transformation of the partial differential equations governing the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet with suction. Existence of a solution is shown using the fixed point argument and the boundary value problem is solved. Galerkin–Legendre spectral method with domain truncation is used to obtain approximate analytical solutions. The approximate solutions computed confirm the theoretical analysis. [Copyright &y& Elsevier]

Abstract: Recombinant expression of the large alternansucrase (2057 amino acids) was hindered in E. coli due to poor enzyme solubility and protein degradation. The effects of deletions of the alternansucrase C-terminal CW-like and APY repeated motifs on enzyme solubility and specificity were investigated. A truncated variant deleted of the APY repeats but harboring four C-terminal CW-like repeats displayed a high specific activity and the same specificity of product synthesis as the native enzyme. It is more soluble and suffers less degradation than full length alternansucrase. Hence this truncated variant is a promising tool for the further structural and kinetic study of this interesting enzyme. [Copyright &y& Elsevier]

The effects of the reaction terms, diffusion coefficients and size of the computational domain on the dynamics of the two-equation Oregonator model in two-dimensional reactive–diffusive media is studied numerically, and it is shown that spiral waves are robust under truncation or expansion of the computational domain. It is also shown that large diffusion coefficients for the inhibitor may result on either annihilation of the wave or unbounded growth, whereas large diffusion coefficients for the activator concentration may result in unbounded decay of both the activator’s and inhibitor’s concentrations. Small diffusion coefficients of the inhibitor may result in stationary tongue-like shapes, whereas small diffusion coefficients of the activator may result in narrow ring shapes where the activator’s concentration is high. A decrease in the parameter which controls the stiffness of the activator’s reaction rate is found to result in unbounded growth of the activator’s concentration, whereas an increase in the parameter that couples the activator and inhibitor is found to result in either annihilation of the spiral wave or unbounded growth of the concentrations of both the activator and the inhibitor. [Copyright &y& Elsevier]

Hyaluronidases are a group of glycosidases catalyzing the degradation of hyaluronic acid (HA). Because of the advantages of effectively hydrolyzing the HA-rich matrix and low immunogenicity, human hyaluronidase PH20 (hPH20) is widely used in the medical field. Here, we realized the active expression of recombinant hPH20 by Pichia pastoris under a methanol-induced promoter P AOX1 . By optimizing the composition of the C-terminal domain and fusing protein tags, we constructed a fusion mutant AP 2 -△491C with the extracellular hyaluronidase activity of 258.1 U·L -1 in a 3-L bioreactor, the highest expression level of recombinant hPH20 produced by microbes. Furthermore, we found recombinant hPH20 hydrolyzed the β-1,4 glycosidic bonds sequentially from the reducing end of o-HAs, with HA 6 NA as the smallest substrate. The result will provide important theoretical guidance for the directed evolution of the enzyme to prepare multifunctional o-HAs with specific molecular weights., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Pang, He, Zhang, Huang, Wang, Wang, Du and Kang.)

Pullulanase is a commonly used debranching enzyme in the starch processing industry. Because the starch liquefaction process requires high temperature, a thermostable pullulanase is desired. Here, a novel hyperthermostable type II pullulanase gene ( pul PY ) was cloned from Pyrococcus yayanosii CH1, isolated from a deep-sea hydrothermal site. Pul PY was optimally active at pH 6.6 and 95 °C, retaining more than 50% activity after incubation at 95 °C for 10 h. The thermostability was significantly higher than those of most pullulanases reported previously. To further improve its activity and thermostability, the N-terminal and C-terminal domains of Pul PY were truncated. The optimum temperature of the combined truncation mutant Δ28N + Δ791C increased to 100 °C with a specific activity of 32.18 U/mg, which was six times higher than that of wild-type Pul PY . Pul PY and the truncation mutant enzyme could realize the combined use of pullulanase with α-amylase during the starch liquefaction process to improve hydrolysis efficiency.

The low-frequency electromagnetic scattering problem of a near-surface hollow spherical inclusion is solved by means of a modal approach. The primary field is excited using a current-carrying coil. The presented solution addresses the full coupling between the two interfaces of the geometry in a rigorous way. There is a direct physical interpretation of the different occurring terms in the formal solution, which provides a deeper understanding of the underlying phenomena. The calculation is very fast, which makes the proposed model suitable for use with parametric inversion algorithms. [ABSTRACT FROM AUTHOR]