Auxiliary Diffusion Research Articles

A New Chaotic Image Encryption Algorithm Based on Transversals in a Latin Square

In this paper, a new combinatorial structure is introduced for image encryption, which has an excellent encryption effect on security and efficiency. An n-transversal in a Latin square has the function of classifying all the matrix's positions, and it can provide a pair of orthogonal Latin squares. Employing an n-transversal of a Latin square, we can permutate all the pixels of an image group by group for the first time, then use two Latin squares for auxiliary diffusion based on a chaotic sequence, and finally, make use of a pair of orthogonal Latin squares to perform the second scrambling. The whole encryption process is "scrambling-diffusion-scrambling". The experimental results indicated that this algorithm passed various tests and achieved a secure and fast encryption effect, which outperformed many of the latest papers. The final information entropy was very close to 8, and the correlation coefficient was approximately 0. All these tests verified the robustness and practicability of the proposed algorithm.

Corrigendum to ‘Simulation of Multivariate Diffusion Bridges’

Abstract We correct an error in Theorem 1 in Bladt et al. (2016) Journal of the Royal Statistical Society: Series B, 78, 343–369 by changing the initial distribution of an auxiliary diffusion process, which is used to describe the distribution of the proposed approximate diffusion bridges. As a consequence, we correct two algorithms for simulating exact diffusion bridges by changing the initial distribution of auxiliary diffusion processes in the same way. Simulation studies affected by the error are redone.

Corrigendum to “Simple simulation of diffusion bridges with application to likelihood inference for diffusions”

We correct an error in Theorem 2.1 in Bladt and Sørensen (Bernoulli 20 (2014) 645–675), where the initial distribution of an auxiliary diffusion process that is used to describe the distribution of the proposed approximate diffusion bridge is wrong. As a consequence, we also correct the pseudo marginal Metropolis-Hastings algorithm that has an exact diffusion bridge as its target distribution. The same auxiliary diffusion plays a central role in the algorithm.

On absolute continuity and singularity of multidimensional diffusions

Consider two laws $P$ and $Q$ of multidimensional possibly explosive diffusions with common diffusion coefficient $\mathfrak {a}$ and drift coefficients $\mathfrak {b}$ and $\mathfrak {b}+ \mathfrak {a}\mathfrak {c}$, respectively, and the law $P^{\circ }$ of an auxiliary diffusion with diffusion coefficient $\langle \mathfrak {c}, \mathfrak {a}\mathfrak {c}\rangle ^{-1}\mathfrak {a}$ and drift coefficient $\langle \mathfrak {c}, \mathfrak {a}\mathfrak {c}\rangle ^{-1}\mathfrak {b}$. We show that $P \ll Q$ if and only if the auxiliary diffusion $P^{\circ }$ explodes almost surely and that $P\perp Q$ if and only if the auxiliary diffusion $P^{\circ }$ almost surely does not explode. As applications we derive a Khasminskii-type integral test for absolute continuity and singularity, an integral test for explosion of time-changed Brownian motion, and we discuss applications to mathematical finance.

Reconstruction of unknown storativity and transmissivity functions in 2D groundwater equations

ABSTRACT The paper deals with the identification from some pumping tests of unknown storativity and transmissivity functions defining a confined aquifer. We introduce an appropriate change of variables that transforms the groundwater equation into a diffusion-reaction one wherein the diffusion term is defined by the fraction transmissivity/storativity and the reaction term yields the right hand side of a second-order nonlinear elliptic partial differential equation satisfied by the unknown storativity function. Using time records of the drawdown taken at some measuring wells within the monitored aquifer, we establish identifiability results on the involved unknown variables. We develop an identification approach that starts by determining the two auxiliary diffusion and reaction variables. Afterwards, the developed approach proposes local and global procedures to reconstruct the unknown storativity function. That leads to deduce the sought transmissivity function from the product of the two identified storativity and diffusion functions. Some numerical experiments on a variant of groundwater equations are presented.

Solid state dewetting of Ag/Pt bilayers for the stronger localized surface plasmon resonance (LSPR) properties: The dynamic control of surface morphology and elemental composition of AgPt and Pt nanostructures by the auxiliary Ag layer

The modification and control of localized surface plasmon resonance (LSPR) properties of metallic nanoparticles (NPs) has become a vigorous research focus in various fields due to its wide range of applicability in various applications, which can be achieved by the control of surface morphology and elemental composition. In this paper, various configurations and compositions of AgPt and Pt NPs are demonstrated by the solid state dewetting using an auxiliary Ag layer on sapphire (0001) along with their strong dynamic LSPR properties. By the systematic control of Ag/Pt bilayer thickness and temperature, the interconnected AgPt nanoclusters at low temperature (<600 °C) and well-isolated pure Pt NPs at higher temperature (>650 °C) are obtained based on the enhanced diffusion, alloying, surface energy minimization and Ag sublimation. A strong LSPR response in the UV and VIS region is exhibited by the AgPt and Pt NPs depending on the alteration of size, shape, uniformity and elemental compositions. In particular, the AgPt NPs show the stronger plasmonic responses and it gradually attenuates with the sublimation of Ag atoms which results in the development of Pt NPs. In comparison with the previous study on the pure Pt NPs on sapphire, the Pt NPs in this study are significantly improved in terms of shape, size and spacing, whose LSPR responses are much stronger and dynamic. The auxiliary diffusion enhancement by Ag atoms leads to the rapid dewetting of AgPt NPs while the Ag sublimation assists the evolution of well-developed Pt NPs due to the vacancy creation and removal of material during mass transport. The tunability of surface morphologies and LSPR properties of AgPt and Pt NPs are systematically demonstrated by the methodical control of Ag/Pt bilayer thickness.

Fabrication of Various Plasmonic Pt Nanostructures via Indium Assisted Solid-State Dewetting: From Small Nanoparticles to Widely Connected Networks.

In this paper, the modified solid-state dewetting (MSSD) of well-defined and various uniform Pt nanostructures is demonstrated by the auxiliary diffusion enhancement. The MSSD utilizes the introduction of metallic indium (In) layers with high diffusivity in between sapphire and platinum (Pt) layer, through which the global diffusion and dewetting of metallic atoms can be significantly enhanced. Subsequently, the In atoms can be sublimated from the NP matrix, resulting in the formation of pure Pt NPs. By the systematic control of In and Pt bi-layer thickness, various areal density, size and configuration of Pt NPs are demonstrated. The In2 nm/Pt2 nm bilayers establish very small and highly dense NPs throughout the temperature range due to the early maturation of growth. Intermediate size of NPs is demonstrated with the In45 nm/Pt15 nm bilayers with the much improved interparticle spacings by annealing between 650 and 900 °C for 450 s. Finally, the In30 nm/Pt30 nm bilayers demonstrate the widely connected network-like nanostructures. In addition, the finite difference time domain (FDTD) simulation is employed to exploit the local electric field distributions at resonance wavelengths. The dewetting characteristics of In/Pt bilayers is systematically controlled by the modifications of layer thickness and annealing temperature and is systematically described based on the diffusion of atoms, Rayleigh instability and surface energy minimization mechanism. The optical properties demonstrate dynamic and widely tunable localized surface plasmon resonance (LSPR) responses depending upon the various surface morphologies of Pt nanostructures.

Modification based on internal refinement and external decoration: A powerful strategy for superior thermodynamics and hysteresis of Mg-Ni hydrogen energy storage alloys

The as-cast Mg-Ni alloy with nominal component Mg-10 wt%Ni (Mg10Ni) is successively modified based on the internal refinement by melt-spinning and external decoration through surface catalysis. The isothermal hydrogenation kinetics, absorption/desorption thermodynamics, hysteresis and non-isothermal desorption of modified Mg-rich alloys are investigated in this work. The results of modification indicate that the alloying and refinement microstructure are the foundation for high capacity and rapid kinetics. The active surface is the precondition to achieve the above-mentioned process. MWCNTs especially MWCNTs coupling with TiF3 can easily activate the Mg-10 wt%Ni alloy and promote rapid absorption/desorption kinetics by H2 dissociation and H-atoms auxiliary diffusion. Mg-rich Mg-Ni alloy after internal refinement and external decoration with MWCNTs and TiF3 possesses superior thermodynamics and hysteresis. As high as 5.5 wt% hydrogen can be rapidly absorbed within 60 s and the endothermic peak is around 374 °C, which shifts toward low temperature as high as ∼75 °C than that of Mg-10 wt%Ni alloy without any catalysts. It is the synergistic catalytic effect originated from the assisted diffusion of MWCNTs and the surface spillover special effects of TiF3 that promote the outstanding thermodynamics and hysteresis for Mg10Ni-MWCNTs-TiF3.

Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor Model

This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The criterion, following earlier work by Bielecki, Pliska, Nagai, and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance). By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps. The main result of this paper is to show that the risk-sensitive jump-diffusion problem can be fully characterized in terms of a parabolic Hamilton–Jacobi–Bellman PDE rather than a partial integro-differential equation, and that this PDE admits a classical $(C^{1,2})$ solution.

The effect of hyperbaric pressure on catalytic and electrochemical gas sensors

Sensors commonly used in workplace multi-gas monitors, and normally operating at atmospheric pressure, have been evaluated under the pressurized (hyperbaric) atmospheres typically found in tunnelling operations, i.e., 1–4.5 bar (100–450 kPa) static pressure and pulses of up to 0.3 bar (30 kPa) above ambient pressure and of less than 30 s duration. Three types of sensor have been tested: catalytic sensors (pellistors) for methane, electrochemical fuel cells for carbon monoxide and electrochemical metal-air batteries for oxygen. All the sensors are affected by pressure to some degree. Pellistors show a positive pressure effect (response increases by up to 50% at 3 bar), while pulses up to 0.3 bar produce transient responses equivalent to 0.2% methane. The electrochemical carbon monoxide sensors are unaffected by pressure in clean air but there is a positive effect in carbon monoxide/air (the sensor reads approximately 11% high at 3 bar). During compression and pulsing in carbon monoxide/air larger effects are observed. The electrochemical oxygen sensor behaves similarly to the carbon monoxide sensor: at 3 bar the sensor reads 12% high, while pulses of the order of 0.1 bar above ambient induce a 25% increase in response. The effects of static hyperbaric pressure can be overcome by recalibration of the sensors at the working pressure. Transient effects on electrochemical sensors can be reduced by careful siting of the sensor away from pressure-pulse sources or possibly by the incorporation of auxiliary diffusion barriers into the sensor. The effects of pressure on the sensor characteristics are compared with theoretical models.

Functionals of paths of a diffusion process and the Onsager-Machlup function

The Onsager-Machlup function for a one-dimensional diffusion processXt is obtained by means of the Radon-Nikodym derivative of the measure in function space induced byXt with respect to the measure corresponding to an auxiliary diffusion processYt.

Rate equation approaches to thin film nucleation kinetics

Abstract The nucleation and growth of crystals on a substrate are discussed in terms of rate equations for the atom cluster concentrations as a function of time. Simple approximations allow this general set of equations to be reduced to three coupled equations. Many physical processes can be incorporated into these rate equations, including coalescence of clusters, and cluster mobility. The problem of increasing correlation between single atoms and stable clusters as growth proceeds is studied. It is shown that the problem can be solved self-consistently using an auxiliary diffusion equation and that approximations may be obtained which give upper and lower bounds for the cluster growth rates. These diffusion equations also give expressions which enable the cluster-cluster correlations and cluster size distributions to be discussed. With these approximations, expressions are derived for observable quantities and the expressions are compared with one experimental example. In this case, that of gold on alka...

Flash-type Getter Pump for Evacuation of the Large Volume Apparatus

Utilization of the flash-type titanium getter pump for evacation of the large volume apparatus was studied. The testing appratus consists of the getter pump chamber, an auxiliary diffusion pump and a mass-spectrometer used to analyze the residual gases. The pumping speed for air is 1000 l/sec to 1200 l/sec at 7×10-7mm Hg, the end vacuum is 8×10-7mm Hg to 2×10-8mm Hg, and these performances are maintained for about 5 hours. The peak heights of the oil fragments other than methane in the getter pump are lower than those in the oil diffusion pump and the rotary pump. The pump system of this type will be used for evacuation of the Hitachi nuclear fusion testing device.