Equilibrium,pseudoequilibrium and sliding-mode heteroclinic orbit in a Filippov-type plant disease model

Plant diseases have caused tremendous crop losses and have massive impacts on food security and environment. Modeling the spread of plant diseases and understanding the dynamics of the resulting plant disease models may provide practical insights on designing effective control measures. In this paper, by incorporating cultural strategies and economic threshold policy, we present a Filippov-type plant disease model. The resulting model has state dependent discontinuous right-hand side and thus non-smooth analysis and generalized Lyapunov approach are employed for model analysis. We show that the model exhibits the phenomena of stable equilibrium, unstable pseudoequilibrium as well as sliding-mode heteroclinic orbit. Biological implications of our results in implementing control strategies for plant diseases are also discussed.     

Nonlinear vertical accelerations of a floating torus in regular waves

The longitudinal motions and vertical accelerations of a floating torus as well as wave motion inside the torus are studied by model tests in regular deep-water waves. Comparisons are made with linear and partly with second-order potential-flow theory for the smallest examined experimental wave height-to-wave length ratio 1/120. Reasonable agreement is obtained, in particular for the linear problem. The importance of 3D flow, hydroelasticity and strong hydrodynamic frequency dependency is documented. Experimental precision errors and bias errors, for instance, due to tank-wall interference are discussed. Numerical errors due to viscous effects are found to be secondary. Experiments show that the third and fourth harmonic accelerations of the torus matter and cannot be explained by a perturbation method with the wave steepness as a small parameter.     

A generic framework for time-stepping partial differential equations (PDEs): general linear methods,object-oriented implementation and application to fluid problems

Time-stepping algorithms and their implementations are a critical component within the solution of time-dependent partial differential equations (PDEs). In this article, we present a generic framework – both in terms of algorithms and implementations – that allows an almost seamless switch between various explicit, implicit and implicit–explicit (IMEX) time-stepping methods. We put particular emphasis on how to incorporate time-dependent boundary conditions, an issue that goes beyond classical ODE theory but which plays an important role in the time-stepping of the PDEs arising in computational fluid dynamics. Our algorithm is based upon J.C. Butcher's unifying concept of general linear methods that we have extended to accommodate the family of IMEX schemes that are often used in engineering practice. In the article, we discuss design considerations and present an object-oriented implementation. Finally, we illustrate the use of the framework by applications to a model problem as well as to more complex fluid problems.     

Normal Coordinates Analysis for The M(NH3)2+ 4 Complex Ions in D4h and Td Symmetries. Simplified Molecular Models

A normal coordinates analysis for the M(NH₃)²⁺ ₄ complex ions in T_d symmetry (M = Zn, Cd, Co) and in D_4h symmetry (M = Cu, Pd, Pt) has been undertaken on the basis of a General Valence Force Field (GVFF), using simplified molecular models. Throughout the course of the present work, we have relaxed the point mass approximation for the NH₃-ligands in order to investigate, on a quantitative basis, some relevant ligand - framework coupling vibrations. The simplest molecular model able to accomplish this purpose is to treat the ammino group, in a linear ligator approximation. We show that these model calculations provide a satisfactory set of vibrational frequencies as well as consistent sets of force constants.     

Lanthanide Shift Reagents. Paper 18. Equilibrium Binding Constants for Europium Shift Reagent with Nitrogen Heterocycles

Paper 16 in this series^{1, 2, 3} was concerned with the equilibrium binding constants (K) of the shift reagent Europium tris (2, 2, 6, 6-tetramethylheptane-3, 5-dionate), Eu(thd)₃, with primary, secondary and tertiary amines. One nitrogen heterocycle, pyridine, and two of its derivatives (see Table) were included. In the present paper we describe the binding constants for a further 9 nitrogen containing heterocycles and relate these to basicity and steric effects.     

An Inverse Problem in Periodic Diffractive Optics: Reconstruction of Lipschitz Grating Profiles

We consider the problem of recovering a two-dimensional periodic structure from scattered waves measured above the structure. Following an approach by Kirsch and Kress, this inverse problem is reformulated as a nonlinear optimization problem. We develop a theoretical basis for the reconstruction method in the case of an arbitrary Lipschitz grating profile. The convergence analysis is based on new perturbation and stability results for the forward problem.     

Charge generation and electrostatic equilibrium for single granules during sliding

Electrostatic phenomena are commonly observed in the processing of solids. However, the working mechanism of electrostatic charge generation for single granules and particularly, their electrostatic equilibria have not been properly understood. In this work, repeated-sliding charging experiments with single granules were investigated for their electrostatic generation particularly from the perspective of triboelectrification equilibrium. Factors including granule length-ratio, sliding face shape, sliding times, sliding area, sliding velocity, front-facing edge, and sliding-plate inclined-angle were found to have an obvious effect on granule charge generation. Length-ratio and sliding area have significant effects as the granules evolved toward an equilibrium state. Equilibrium charge is suggested as a variable expressing the charging propensity of the material. In addition, under the same working conditions, a semi-cylindrical granule generates greater charge than a rectangular granule.     

Arbitration procedures with multiple arbitrators

We consider two final-offer arbitration procedures in the case where there is more than one arbitrator. Two players, labeled 1 and 2 and interpreted here as Labor and Management, respectively, are in dispute about an increase in the wage rate. They submit final offers to a Referee. There are N arbitrators. Each of the arbitrators has her own assessment and selects the offer which is closest to her assessment. After that each arbitrator informs the Referee about her decision. The Referee counts the votes and declares the player obtaining the most votes to be the winner. Under the second arbitration scheme, the Referee takes into account only the assessments which lie between the players’ offers. The game is modeled as a zero-sum game. The Nash equilibrium in this arbitration game is derived.     

Determination of Formaldehyde Traces in Fabric and in Indoor Air by a Kinetic Fluorimetric Method

A simple and sensitive kinetic fluorimetric method is reported for the determination of trace amount of formaldehyde. The proposed method is based on the catalytic effect of formaldehyde on the oxidation reaction of rhodamine B with potassium chlorate in sulfuric acid solution. Formaldehyde in the range of 0.020-0.340 µg/mL can be determined with a limit of detection of 5.73 ng/mL. The method has been used to determine trace formaldehyde in fabric and in indoor air. The results thus obtained show good agreement with those determined by acetyl acetone method.