Diffuse Part Research Articles

On Ahlfors currents

We answer a basic question in Nevanlinna theory that Ahlfors currents associated to the same entire curve may be nonunique. Indeed, we will construct one exotic entire curve f:C→X which produces infinitely many cohomologically different Ahlfors currents. Moreover, concerning Siu's decomposition, for an arbitrary k∈Z+∪{∞}, some of the obtained Ahlfors currents have singular parts supported on k irreducible curves. In addition, they can have nonzero diffuse parts as well. Lastly, we provide new examples of diffuse Ahlfors currents on the product of two elliptic curves and on P2(C), and we show cohomologically elaborate Ahlfors currents on blow-ups of X.

Revisiting the type of Cespitularia stolonifera/ Gohar, 1938 leads to the description of a new genus and a species of the family Xeniidae (Octocorallia, Alcyonacea).

Because of the problematical identity and status of the type of the xeniid soft coral genus Cespitularia Milne-Edwards Haime, 1850, the species C. stolonifera Gohar, 1938 is revised. Examination of the type colonies has led to the establishment of the new genus Unomia gen. n. which is described and depicted. This genus features a stalk, commonly divided into branches featuring a diffuse polypiferous part consisting of distal clustered polyps and proximal individual ones on the stalk or the basal membranous part of the colonies. The sclerites are ellipsoid platelets composed of dendritic calcite rods whose tips are distinct on the surface of the platelets. Freshly collected material from Venezuelan reefs where the species is invasive was subjected to molecular phylogenetic analysis, the results of which substantiate the taxonomic assignment of the new genus under U. stolonifera comb. n. A new species, U. complanatis, from Japan and Green Island (Taiwan) is described and further illustrates the extent of the interspecific morphological variation within the genus. The results reveal that the biogeographic distribution of Unomia gen. n. includes Pacific Ocean reefs in addition to the previously reported invaded Caribbean reefs.

Electrokinetic Streaming Current Method to Probe Polycrystalline Gold Electrode-Electrolyte Interface Under Applied Potentials

We developed a method, by combining electrochemical and electrokinetic streaming current techniques to study ion distribution and ionic conductivity in the diffuse part of electrochemical double layer (EDL) of a metal-electrolyte interface, when potential is applied on the metal by a potentiostat. We applied this method to an electrochemically clean polycrystalline gold (poly Au)-electrolyte interface and measured zeta potential for various applied potentials, pH, and concentration of the electrolyte. Specific adsorption of chloride ions on poly Au was studied by comparing measurements of zeta potential in KCl and KClO4 electrolytes. In absence of specific adsorption, zeta potential was found to increase linearly with applied potential, having slope of 0.04–0.06. When Cl− adsorption occurs, zeta potential changes the sign from positive to negative value at ∼750 mV vs Ag/AgCl applied potential. Complementary cyclic voltammetry and X-ray photoelectron spectroscopy studies were conducted to determine a degree of chloride ion adsorption on a poly Au. A correlation was observed between the applied potential at which zeta potential is zero and potential of zero charge for poly Au. Ion-distribution and ionic conductivity in the diffuse layer were calculated from the measured zeta potential data using nonlinear Poisson-Boltzmann distribution.

Fractional-order double-ring erbium-doped fiber laser chaotic system and its application on image encryption

Laser chaotic systems have been extensively studied and applied in the past 20 years. However, the fractional form of the chaotic system of erbium-doped fiber laser has not been studied yet. Therefore, this paper proposes a fractional-order double-ring erbium-doped fiber laser chaotic system. The dynamic characteristics of the system are studied by phase diagram, bifurcation diagram, Lyapunov exponent spectrum, Spectral Entropy (SE) complexity, and coexisting attractors. At the same time, the digital circuit of the new system is implemented on the digital signal processing (DSP) platform. Compared with integer-order double-ring erbium-doped fiber laser chaotic systems, this fractional-order chaotic system has more complex dynamics and higher sensitivity and randomness. Finally, the fractional-order double-ring erbium-doped fiber laser chaotic system is applied to the image encryption algorithm with the improved gravitation model. In this encryption algorithm, the diffusion part uses an improved universal gravitation model, and the Zigzag algorithm scrambles the pixels. The security of the algorithm is analyzed. The analyses of the experimental results show that the image encryption scheme proposed in this paper has a good encryption effect and good security performance. The research in this paper provides theoretical guidance and experimental basis for the research of fractional-order laser chaotic secure communication.

Generic Seebeck effect from spin entropy

How magnetism affects the Seebeck effect is an important issue of wide concern in the thermoelectric community but remains elusive. Based on a thermodynamic analysis of spin degrees of freedom on varied d-electron-based ferromagnets and antiferromagnets, we demonstrate that in itinerant or partially itinerant magnetic compounds there exists a generic spin contribution to the Seebeck effect over an extended temperature range from slightly below to well above the magnetic transition temperature. This contribution is interpreted as resulting from transport spin entropy of (partially) delocalized conducting d electrons with strong thermal spin fluctuations, even semiquantitatively in a single-band case, in addition to the conventional diffusion part arising from their kinetic degrees of freedom. As a highly generic effect, the spin-dependent Seebeck effect might pave a feasible way toward efficient “magnetic thermoelectrics.”

Perturbative analysis of stochastic Hamiltonian problems under time discretizations

In this work we focus on the study of stochastic Hamiltonian problem driven by additive Wiener noise. In particular, we aim to analyse the behaviour of discretizations to these problems, motivated by some results on stochastic Runge–Kutta methods (SRK) developed by Burrage and Burrage (2012). In fact, SRK methods present a remarkable error that increases with the parameter of the diffusive part of the problem. Through a perturbative analysis, we investigate the reason of this behaviour, leading to a negative answer: retaining the main features of stochastic Hamiltonian problems does not happen straightforwardly for any time discretization. This analysis is also numerically confirmed.

Pricing of volatility derivatives in a Heston–CIR model with Markov-modulated jump diffusion

This paper concerns the pricing of volatility and variance swaps with discrete sampling times using a hybrid Heston–CIR model with Markov-modulated jump–diffusion. We extend the regime-switching Heston stochastic volatility model by further considering the Cox–Ingersoll–Ross (CIR) stochastic interest rate with jump diffusion. The market parameters, including the jump–diffusion part, are modulated by a continuous-time Markov chain that represents different market states. The proposed hybrid model can capture the stochastic property of volatility rate, interest rate as well as the short-term and long-term effects on the financial market caused by unexpected events and structural changes of the macroeconomic environment respectively. The fair strike prices of variance swaps and volatility swaps based on four different formulae for the realized variance (volatility) are obtained by utilizing the characteristic function method. The accuracy and efficiency of our method are validated through the semi-Monte-Carlo simulation. Finally, numerical and sensitivity analysis are conducted to show the impact of the change of each market parameter. Overall, pricing results were greatly enhanced with a more realistic financial model, and more driving forces are considered to investigate the formation of the discrete variance and volatility swap prices more comprehensively.

A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance

In this paper, we propose and analyze a positivity-preserving, energy stable numerical scheme for a certain type of reaction-diffusion systems involving the Law of Mass Action with the detailed balance condition. The numerical scheme is constructed based on a recently developed energetic variational formulation, in which the reaction part is reformulated in terms of reaction trajectories. The fact that both the reaction and diffusion parts dissipate the same free energy opens a path of designing an energy stable, operator splitting scheme for these systems. At the reaction stage, we solve equations of reaction trajectories by treating all the logarithmic terms in the reformulated form implicitly due to their convex nature. The positivity-preserving property and unique solvability can be theoretically proved, based on the singular behavior of the logarithmic function around the limiting value. Moreover, the energy stability of this scheme at the reaction stage can be proved by a careful convexity analysis. Similar techniques are used to establish the positivity-preserving property and energy stability for the standard semi-implicit solver at the diffusion stage. As a result, a combination of these two stages leads to a positivity-preserving and energy stable numerical scheme for the original reaction-diffusion system. Several numerical examples are presented to demonstrate the robustness of the proposed operator splitting scheme.

Defaultable sovereign debts with macroeconomic conditions and periodic news

This paper presents a default structural model of sovereign debt under macroeconomic conditions and periodic news. I model the macroeconomic conditions to be a finite state of Markov chain, and the periodic news to be a predictable factor in the drifting and the diffusion parts in the underlying value of the representative firm. The innovation of our model is to characterize the price of sovereign debt and the sovereign credit spread associated with macroeconomic conditions, and to model periodic news with both continuous factors and periodic factors. Both the defaultable yield-to-maturity, the sovereign credit spread and the duration are related to the finite state of Markov chain and periodic news. Furthermore, we obtain a closed-form solution for the two-state Markov chain associated to macroeconomic conditions and periodical information update.

Security Analysis of a Color Image Encryption Algorithm Using a Fractional-Order Chaos.

Fractional-order chaos has complex dynamic behavior characteristics, so its application in secure communication has attracted much attention. Compared with the design of fractional-order chaos-based cipher, there are fewer researches on security analysis. This paper conducts a comprehensive security analysis of a color image encryption algorithm using a fractional-order hyperchaotic system (CIEA-FOHS). Experimental simulation based on excellent numerical statistical results supported that CIEA-FOHS is cryptographically secure. Yet, from the perspective of cryptanalysis, this paper found that CIEA-FOHS can be broken by a chosen-plaintext attack method owing to its some inherent security defects. Firstly, the diffusion part can be eliminated by choosing some special images with all the same pixel values. Secondly, the permutation-only part can be deciphered by some chosen plain images and the corresponding cipher images. Finally, using the equivalent diffusion and permutation keys obtained in the previous two steps, the original plain image can be recovered from a target cipher image. Theoretical analysis and experimental simulations show that the attack method is both effective and efficient. To enhance the security, some suggestions for improvement are given. The reported results would help the designers of chaotic cryptography pay more attention to the gap of complex chaotic system and secure cryptosystem.

El aprendizaje de la escritura

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Combined effect of thermal anisotropy and shrinkage on growth of binary alloy equiaxed crystal

A numerical model for microscale binary alloy solidification is proposed taking the effect of both thermal anisotropy and shrinkage into consideration. The model couples an enthalpy based solidification model with a SIMPLER algorithm based flow solver. The effect of shrinkage is implemented in an incompressible framework with the addition of transient source terms in continuity and pressure correction equations. Shrinkage leads to the generation of shrinkage induced flow which affects the growth of the equiaxed crystal. Thermal anisotropy is modelled by considering anisotropic conductivity within the solid crystal and implemented by splitting the diffusive part of the energy equation into its equivalent isotropic and anisotropic parts. The presence of thermal anisotropy leads to non-uniform temperature distribution within the solid crystal resulting in the unequal growth rate of dendrite arms. Simulations have been performed to investigate the combined effects of shrinkage and thermal anisotropy on growth and morphology of equiaxed dendrites for different sets of thermal anisotropy ratio (AR) and density ratio (ρs/ρl). Subsequently, based on parametric analysis, 3D contour diagrams have been developed to summarize the combined effect of thermal anisotropy and density ratio for different undercooling and Lewis number.

EM algorithm for stochastic hybrid systems

A stochastic hybrid system, also known as a switching diffusion, is a continuous-time Markov process with state space consisting of discrete and continuous parts. We consider parametric estimation of the Q matrix for the discrete state transitions and of the drift coefficient for the diffusion part. First, we derive the likelihood function under the complete observation of a sample path in continuous-time. Then, extending a finite-dimensional filter for hidden Markov models developed by Elliott et al. (Hidden Markov Models, Springer, 1995) to stochastic hybrid systems, we derive the likelihood function and the EM algorithm under a partial observation where the continuous state is monitored continuously in time, while the discrete state is unobserved.

Analysis of swirling and choking in diffuser using CFD analysis

Effect of swirl on static pressure evolution, total pressure, velocity component recirculation zones and wall shear stress such parameters in conical diffuser flow is studied. Higher pressure recovery is attained with swirl addition at the exit of the diffuser without addition tailpipe. Generally, swirling may not prevent boundary layer separation due to an intermediary recirculation zone appears hence tailpipe is suitable to allow a large-scale mixing for enhancing pressure recovery process. The present study involves the CFD analysis to predict swirl effect in the diffuser which is use in subsonic wind tunnel. 1/8th part of diffuser uses for CFD analysis. Also, it has 50swirl angle, area ratio 2 and length 1.5 m. Reynolds Average Navierstoke’s [RANS] and Shear Stress Transport [SST] use to solve closing problem and turbulence modeling respectively. For solving these numerical simulations, CFX5 Ansys based solver use. Governing equation may solved by finite volume method using Software. Turbulence effect is taken into account employing the k-ε model with an enhanced wall treatment. Mass flow (0.3445) i.e. 25 m/s velocity take as initial boundary condition for steady, incompressible as well as density based flow. Reynolds number kept constant as 30*105. Result show that swirl velocity component develops into a Rankine-vortex type or a Forced-vortex type. Input swirl intensity provides minimum energy loss and leading pressure recovery to an optimum level. Total pressure, static pressure and Mach number verses mass flow graphic result shows swirl uniformity at exit ofdiffuser.

Effect of Radiative Filling Gas in Compound Parabolic Solar Energy Collectors

In the present paper, the use of radiating gas instead of air inside the cavity of compound parabolic collectors (CPSs) is suggested and verified by numerical analysis. The collector under study has a simple cone shape with flat absorber which is filled with a participating gas such as carbon dioxide instead of air for the purpose of increasing the thermal performance. In numerical simulation, the continuity, momentum and energy equations for the steady natural convection laminar gas flow in the CPC’s cavity and the conduction equation for glass cover and absorber plate were solved by the finite element method (FEM) using the COMSOL multi-physics. Because of the radiative term in the gas energy equation, the intensity of radiation in participating gas flow should be computed. Toward this end, the radiative transfer equation (RTE) was solved by the discrete ordinate method (DOM), considering both diffuse and collimated radiations. The approximation was employed in calculation of the diffuse part of radiation. It was observed that the gas radiation causes high temperature with more uniform distribution inside the cavity of collector. Also, numerical results reveal more than 3% increase in the rate of heat transfer from absorber surface into working fluid and hence a desired performance for the collector because of the gas radiation effect. Comparison between the present numerical results with theoretical and experimental data reported in the literature showed good consistency.

Mathematical model of electromigration allowing the deviation from electroneutrality.

The structure of the double layer on the boundary between solid and liquid phases is described by various models, of which the Stern-Gouy-Chapman model is still commonly accepted. Generally, the solid phase is charged, which also causes the distribution of the electric charge in the adjacent diffuse layer in the liquid phase. We propose a new mathematical model of electromigrationconsidering the high deviation from electroneutrality in the diffuse layer of the double layer when the liquid phase is composed of solution of weak multivalent electrolytes of any valence and of any complexity. The mathematical model joins together the Poisson equation, the continuity equation for electric charge, the mass continuity equations, and the modified G-function. The model is able to calculate the volume charge density, electric potential, and concentration profiles of all ionic forms of all electrolytes in the diffuse part of the double layer, which consequently enables to calculate conductivity, pH, and deviation from electroneutrality. The model can easily be implemented into the numerical simulation software such as Comsol. Its outcome is demonstrated by the numerical simulation of the double layer composed of a charged silica surface and an adjacent liquid solution composed of weak multivalent electrolytes. The validity of the model is not limited only to the diffuse part of the double layer but is valid for electromigration of electrolytes in general.

Combined diffusion approximation–simulation model of AQM’s transient behavior

The article introduces an approach combining diffusion approximation and simulation ones. Furthermore, it describes how it can be used to evaluate active queue management (AQM) mechanisms. Based on the obtained queue distributions, the simulation part of the model decides on package losses and modifies the flow intensity sent by the transmitter. The diffusion is used to estimate queue distributions and the goal of the simulation part of the model is to represent the AQM mechanism. On the one hand, the use of the diffusion part considerably accelerates the performance of the whole model. On the other hand, the simulation increases the accuracy of the diffusion part. We apply the model to compare the performance of fractional order PIη controller used in AQM with the performance of RED, a well known active queue management mechanism.

Two Dimension Vertically Integrated Numerical Suspended Sediment Transport Model (Dept.C)

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The Height Process of a Continuous-State Branching Process with Interaction

For a generalized continuous-state branching process with non-vanishing diffusion part, finite expectation and a directed (“left-to-right”) interaction, we construct the height process of its forest of genealogical trees. The connection between this height process and the population size process is given by an extension of the second Ray–Knight theorem. This paper generalizes earlier work of the two last authors which was restricted to the case of continuous branching mechanisms. Our approach is different from that of Berestycki et al. (Probab Theory Relat Fields 172:725–788, 2018). There the diffusion part of the population process was allowed to vanish, but the class of interactions was more restricted.

On the Effect of Vaccination, Screening and Treatment in Controlling Typhoid Fever Spread Dynamics: Deterministic and Stochastic Applications

This work concerns a deterministic and stochastic model describing the transmission of typhoid fever infection in human host community, where the vaccination of susceptible births and immigrants as well as screening and treatment of carriers and infected individuals are considered in the model build - up. The well-posedness and computation of the basic reproduction number R_typ of the deterministic model are obtained and analysed. The deterministic model is further transformed into a stochastic model, where the drift and diffusion parts of the model are obtained, and the existence and uniqueness of the stochastic model are discussed. Numerical simulations involving the model parameters of R_typ showed that vaccination of susceptible births and influx of immigrants as well as screening and treatment of carriers and infected humans are effective in bringing the threshold R_typ(R_typ)≈0.7944) below 1, and the results of other simulations suggest more health policies are to be implemented, as low R_typ may not be guaranteed because vaccination wanes over time. In addition, the numerical simulations of the stochastic model equations describing the sub - population of human individuals in the total human host community are carried out using the computational software MATLAB.