The generalized Beverton–Holt equation and the control of populations

This paper is devoted to the investigation of the positivity, stability and control of the solutions of a generalized Beverton–Holt equation arising in population dynamics which is potentially subject to bounded discontinuities at sampling instants due to the harvesting (i.e. fishing/hunting) quota and eventual independent consumption. Other generalizations are that the intrinsic growth rate and the environment carrying capacity gains are allowed to be time-varying sequences. The interpretation of the appearance of discontinuities in the solution is the presence of impulsive terms in the corresponding continuous-time differential equation. The parallel interpretation in ecology is that there are two different recruitment levels at each current sampling time due, firstly, to the evolution of the population driven by its intrinsic growth rate and the environment carrying capacity and, subsequently, a second level arises due to harvesting and independent consumption from the existing spawning stock of the population. The “left” recruitment level occurs immediately before each current sampling time while the “right” one occurs just after related to the sampling period size. By this reason, the mathematical formulation presented distinguishes between “left” and “right” sides of the sampling times. The control actions on the population stock and recruitment might be performed in a direct fashion either through the environment carrying capacity in close habitats gains or the harvesting quota in open air environments. Both actions may be combined in some open air habitats subject to some artificial control.     

Unconditionally Stable Z-Transform ADI-PML Algorithm for Lorentzian Double Negative Meta-Materials

Unconditionally stable formulations of the anisotropic perfectly matched layer (APML) are presented for truncating double negative (DNG) meta-material finite difference time domain (FDTD) grids. In the proposed formulations, the Z-transform theory is employed in the alternating direction implicit FDTD (ADI-FDTD) scheme to obtain update equations for the field components in the DNG meta-material domains. Numerical examples carried out in one dimensional Lorentzian type DNG meta-material domains are included to show the validity of the proposed formulations.     

A new difference scheme with high accuracy and absolute stability for solving convection–diffusion equations

In this paper, we use a semi-discrete and a padé approximation method to propose a new difference scheme for solving convection–diffusion problems. The truncation error of the difference scheme is O(h⁴+τ⁵). It is shown through analysis that the scheme is unconditionally stable. Numerical experiments are conducted to test its high accuracy and to compare it with Crank–Nicolson method.     

Boundary value problems on weighted networks

We present here a systematic study of general boundary value problems on weighted networks that includes the variational formulation of such problems. In particular, we obtain the discrete version of the Dirichlet Principle and we apply it to the analysis of the inverse problem of identifying the conductivities of the network in a very general framework. Our approach is based on the development of an efficient vector calculus on weighted networks which mimetizes the calculus in the smooth case. The key tool is an adequate construction of the tangent space at each vertex. This allows us to consider discrete vector fields, inner products and general metrics. Then, we obtain discrete versions of derivative, gradient, divergence and Laplace-Beltrami operators, satisfying analogous properties to those verified by their continuous counterparts. On the other hand we develop the corresponding integral calculus that includes the discrete versions of the Integration by Parts technique and Green’s Identities. Finally, we apply our discrete vector calculus to analyze the consistency of difference schemes used to solve numerically a Robin boundary value problem in a square.     

A novel frequency encoded all optical CNOT gate exploiting difference frequency generation and implementation of fast binary adders using frequency encoding and nonlinear dielectric films

Optics has an important role in logic implementation and computation is established in two and half decades by many researchers. Recently frequency encoding technique is established. This technique does not suffer from intensity dependent loss problems like other schemes. Amorphous dielectric thin films with reflecting edges can also be used for logic realization and has very fast response speed. It also does not use any semiconductor device and simple to construct. In this communication the authors have proposed all optical CNOT gate using frequency encoded difference frequency generation exploiting nonlinear response of some material and implementation of binary adders by CNOT gate and dielectric thin film AND gate.     

Next‐to‐next‐to‐leading order post‐Newtonian spin(1)‐spin(2) Hamiltonian for self‐gravitating binaries

We present the next‐to‐next‐to‐leading order post‐Newtonian (PN) spin(1)‐spin(2) Hamiltonian for two self‐gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincaré algebra with the center‐of‐mass vector uniquely determined by an ansatz.     

A Poisson–Boltzmann solver on irregular domains with Neumann or Robin boundary conditions on non-graded adaptive grid

We introduce a second-order solver for the Poisson–Boltzmann equation in arbitrary geometry in two and three spatial dimensions. The method differs from existing methods solving the Poisson–Boltzmann equation in the two following ways: first, non-graded Quadtree (in two spatial dimensions) and Octree (in three spatial dimensions) grid structures are used; Second, Neumann or Robin boundary conditions are enforced at the irregular domain’s boundary. The irregular domain is described implicitly and the grid needs not to conform to the domain’s boundary, which makes grid generation straightforward and robust. The linear system is symmetric, positive definite in the case where the grid is uniform, nonsymmetric otherwise. In this case, the resulting matrix is an M-matrix, thus the linear system is invertible. Convergence examples are given in both two and three spatial dimensions and demonstrate that the solution is second-order accurate and that Quadtree/Octree grid structures save a significant amount of computational power at no sacrifice in accuracy.     

Temperature dependent narrow-band terahertz pulse generation in periodically poled crystals via difference frequency generation

Femtosecond optical pulse is used to generate narrow-band terahertz pulses depending on a quasi-phase-matched condition in periodically poled lithium niobate (PPLN) and stoichiometric lithium tantalate (PPSLT) crystals by difference frequency generation. The origin of narrow-band THz generation proved that the two frequency components of the fs pulse contribute to the frequency mixing. By cryogenic cooling, the absorption of THz waves in the crystal is significantly reduced which results in efficient THz generation. Simultaneously generated forward and backward THz pulses were 1.38 and 0.65 THz with as narrow as the bandwidth of 32 GHz in the PPSLT sample. Temperature dependence of the generated THz waveforms had good agreement with the simulation result using one dimensional plane-wave propagation model.     

一类线性差分方程的亚纯解与一个亚纯函数分担3个值的唯一性

主要研究差分方程a_1(z)f(x+1)+a_0(z)f(z)=F(z)的一个有穷级超越亚纯解f(z)与亚纯函数g(z)分担0,1,∞CM时的唯一性问题(其中a_(z),a0(z),F(z)为非零多项式,且满足a_1(z)+a_0(z)■0),得到f(x)≡g(z),或f(z)+g(z)≡f(z)g(z),或存在一个多项式β(z)=az+b_0和一个常数a_0满足e~(a_0)≠e~(b_0),使得f(z)=(1-e~(β(x)))/(e~(β(x))(e~(a_o-b_0)-1))与g(z)=(1-e~(β(x)))/(1-e~(b_o-a_0)),其中a(≠0),b_0为常数.     

Field emission characteristics of screen-printed carbon nanotubes cold cathode by hydrogen plasma treatment

Selective plasma etching and hydrogen plasma treatment were introduced in turn to improve field emission characteristics of screen-printed carbon nanotubes (CNTs) cold cathode, which was prepared by using slurry of mixture of multi-wall CNTs, organic vehicles and inorganic binder, i.e. silicon dioxide sol. The results show that selective plasma etching process could effectively remove parts of surface inorganic vehicle (SiO₂) layer and expose more smooth and clean CNTs on cathode surface, which could significantly decrease the operating field of CNTs cathode. There are some nanoparticles emerging on the out of CNTs wall after hydrogen plasma treatment, which are equivalent to increase field emission point of cathode. At the same time, these nanoparticles can increase the local electric field of CNTs, which can decrease operating voltage of CNTs cathode and improve uniformity field emission.