Adaptive State-Dependent Diffusion for Derivative-Free Optimization

This paper develops and analyzes a stochastic derivative-free optimization strategy.A key feature is the state-dependent adaptive variance.We prove global convergence in probability with algebraic rate and give the quantitative results in numerical examples.A striking fact is that convergence is achieved without explicit information of the gradient and even without comparing different objective function values as in established methods such as the simplex method and simulated annealing.It can otherwise be compared to annealing with state-dependent temperature.

Physical mechanism of oxygen diffusion in the formation of Ga_(2)O_(3) Ohmic contacts

The formation of low-resistance Ohmic contacts in Ga_(2)O_(3) is crucial for high-performance electronic devices. Conventionally, a titanium/gold(Ti/Au) electrode is rapidly annealed to achieve Ohmic contacts, resulting in mutual diffusion of atoms at the interface. However, the specific role of diffusing elements in Ohmic contact formation remains unclear.In this work, we investigate the contribution of oxygen atom diffusion to the formation of Ohmic contacts in Ga_(2)O_(3). We prepare a Ti/Au electrode on a single crystal substrate and conduct a series of electrical and structural characterizations.Using density functional theory, we construct a model of the interface and calculate the charge density, partial density of states, planar electrostatic potential energy, and I–V characteristics. Our results demonstrate that the oxygen atom diffusion effectively reduces the interface barrier, leading to low-resistance Ohmic contacts in Ga_(2)O_(3). These findings provide valuable insights into the underlying mechanisms of Ohmic contact formation and highlight the importance of considering the oxygen atom diffusion in the design of Ga_(2)O_(3)-based electronic devices.

Calculation of ion diffusion coefficient related to concrete deterioration based on Debye-Hückel-Onsager theory

This paper applies the Debye-Hückel-Onsager electrolyte solution theory to investigate the diffusivity of ions in concrete pore solutions.First,a model of the diffusion coefficient associated with the ionic species,solution concentration and ambient temperature is proposed in the saturated concrete.Secondly,as an example,the effects of sodium chloride solution concentration,which are associated with influencing factors such as the ionic cloud radius,electrophoresis and relaxation,on the chloride diffusion coefficient are analyzed.It is found that the diffusion coefficient decreases with the increase in solution concentration,and the electrophoresis and ionic cloud radius are two important factors influencing the ionic diffusivity.Finally,the experiments,in which the chloride diffusion coefficients in specimens under different water-cement ratios are measured by the rapid chloride migration（RCM）method,are carried out to validate the effectiveness of the proposed model,and the results indicate that there is a generally reasonable agreement between the experimental and the proposed model results.

'The Theory of Field-Effect Transistors XII.The Bipolar Drift and Diffusion Currents(1-2-MOS-Gates on Thin-Thick Pure-Impure Base)

The previous report （XI） gave the electrochemical-potential theory of the Bipolar Field-Effect Transistors. This report （XII） gives the drift-diffusion theory. Both treat 1-gate and 2-gate, pure-base and impure-base, and thin and thick base. Both utilize the surface and bulk potentials as the parametric variables to couple the voltage and current equations. In the present drift-diffusion theory, the very many current terms are identified by their mobility multiplier for the components of drift current,and the diffusivity multiplier for the components of the diffusion current. Complete analytical driftdiffusion equations are presented to give the DC current-voltage characteristics of four common MOS transistor structures. The drift current consists of four terms： 1-D （One-Dimensional） bulk charge drift term, 1-D carrier space-charge drift term,l-D Ex^2 （transverse electric field） drift term,2-D drift term. The diffusion current consists of three terms： 1-D bulk charge diffusion term,l-D carrier space-charge diffusion term,and 2-D diffusion term. The 1-D Ex^2 drift term was missed by all the existing transistor theories, and contributes significantly, as much as 25 % of the total current when the base layer is nearly pure. The 2-D terms come from longitudinal gradient of the longitudinal electric field,which scales as the square of the Debye to Channel length ratio, at 25nm channel length with nearly pure base, （LD/L）^2 = 10^6 but with impurity concentration of 10^18cm^-3 , （LD/L）^2 = 10^-2 .

Diffusion mechanism simulation of cloud manufacturing complex network based on cooperative game theory

Cloud manufacturing is a specific implementation form of the "Internet + manufacturing" strategy. Why and how to develop cloud manufacturing platform(CMP), however, remains the key concern of both platform operators and users. A microscopic model is proposed to investigate advantages and diffusion forces of CMP through exploration of its diffusion process and mechanism. Specifically, a three-stage basic evolution process of CMP is innovatively proposed. Then, based on this basic process, a more complex CMP evolution model has been established in virtue of complex network theory, with five diffusion forces identified. Thereafter, simulations on CMP diffusion have been conducted. The results indicate that, CMP possesses better resource utilization,user satisfaction, and enterprise utility. Results of simulation on impacts of different diffusion forces show that both the time required for CMP to reach an equilibrium state and the final network size are affected simultaneously by the five diffusion forces. All these analyses indicate that CMP could create an open online cooperation environment and turns out to be an effective implementation of the "Internet + manufacturing" strategy.

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa- tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode- coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.

Mechanisms of ultrasonic modulation of multiply scattered incoherent light based on diffusion theory

An analytic equation interpreting the intensity of ultrasound-modulated scattering light is derived, based on diffusion theory and previous explanations of the intensity modulation mechanism. Furthermore, an experiment of ultrasonic modulation of incoherent light in a scattering medium is developed. This analytical model agrees well with experimental results,which confirms the validity of the proposed intensity modulation mechanism. The model supplements the existing research on the ultrasonic modulation mechanism of scattering light.

3D Model Encryption Algorithm by Parallel Bidirectional Diffusion and 1D Map with Sin and Logistic Coupling

3D models are essential in virtual reality,game development,architecture design,engineering drawing,medicine,and more.Compared to digital images,3D models can provide more realistic visual effects.In recent years,significant progress has been made in the field of digital image encryption,and researchers have developed new algorithms that are more secure and efficient.However,there needs to be more research on 3D model encryption.This paper proposes a new 3D model encryption algorithm,called the 1D map with sin and logistic coupling(1D-MWSLC),because existing digital image encryption algorithms cannot be directly applied to 3D models.Firstly,this paper introduce 1D-MWSLC,which has a wider range of parameters compared to traditional 1D chaotic systems.When the parameter exceeds a specific range,the chaotic phenomenon does not weaken.Additionally,1D-MWSLC has two control parameters,which increases the cryptosystem’s parameter space.Next,1D-MWSLC generates keystreams for confusion and diffusion.In the confusion stage,this paper use random confusion,and the keystream generates an index matrix that confuses the integer and decimal parts of the 3D model simultaneously.In the diffusion stage,this paper use parallel bidirectional diffusion to simultaneously diffuse the integer parts of the three coordinates of the 3D model.Finally,this paper verify the proposed algorithm through statistical analysis,and experimental results demonstrate that the proposed 3D model encryption algorithm has robust security.

Density Functional Theory Study of Water Diffusion and Clustering on Pd(111)

The internal structures as well as adsorption and hopping energies of monomers, dimers, trimers, tetramers, pentamers and hexamers of water on Pd（111） have been studied by density functional theory （DFT） plane-wave pseudopotential method which performs the firstprinciples quantum-mechanical calculations to explore the properties of crystals and surfaces in materials. Based on the calculations, we suppose that their absorption is via one water molecule for monomers, dimmers and trimers, but three water molecules for pentamers and hexamers. Moreover, there is one water molecule bonding with Pd atom by O atom in pentamers and hexamers, which explains why pentamers and hexamers are stable. The binding energies of polymers may be used to explain why the trimer comes close to two nearby monomers to form a stable pentamer instead of tetramer. And the difference of mobility of small water clusters is due to their different hopping energies.

Some New Features of Linear Theory for Describing Non-linear Diffusion

The non-linear flux equation, the non-linear Fokker-Planck equation （or Smoluchowski equation）, and the non-linear Langiven equation are the basic equations for describing particle diffusion in non-ideal system subjected to time-dependent external fields. Nevertheless, the exact solution of those equations is still a challenge because of their inherent complexity of the non-linear mathematics. Li et al. found that, based on the defined apparent variables, the nonlinear Fokker-Planck equation and the non-linear flux equation could be transformed to linear forms under the condition of strong friction limit or loeal equilibrium assumption. In this paper, some new features of the theory were found： （i） The linear flux equation for describing non-linear diffusion can be obtained from the irreversible thermodynamic theory; （ii） The linear non-steady state diffusion equation for describing non-linear diffusion of the non-steady state, which was described by the non-linear Fokker-Planek equation, can be derived more consistently from the microscopic molecular statistical theory; （iii） In the theory, the non-linear Langiven equation also bears a linear form; （iv） For some special cases, e.g. diffusion in a periodic total potential system, the local equilibrium assumption or the strong friction limit is not required in establishing the linear theory for describing non-linear diffusion, so the linear theory may be important in the study of Brown motor.

Computation of Diffusion Activation Energies of C, N in γFe

A structure relaxation model based on the empirical electron theory of solids and molecules is developed to compute the diffusion active energies of C, N in γFe. First, adding a restriction, the lattice maintains rigidity when solute atom migrates to the saddle point. In this step, the hybridization classes of every atom do not change. Then, the restriction is loosed and the atoms are relaxed under the coulomb repulsive forces. It is supposed that the energy needed in the first step would be compensated partly by the second step. In this way, the diffusion active energies of C, N in γFe are computed. Compared with the experiment data, the relative errors are less than 5%, which are good results in the computation of activation energy of diffusion.

Equilibrium Swelling and Solute Diffusion Characteristics of Poly (Methacrylic Acid co-Poloxamer) Hydrogels

Poly(methacrylic acid co-poloxamer) hydrogel networks were synthesized by free radical solution polymerization and their equilibrium swelling and solute permeation properties were characterized. These gels exhibited pH dependant swelling and solute diffusivity due to the formation or disruption of hydrogen bonded complexation between methacrylic acid (MAA) and etheric (EO). In neutral and basic conditions (above the swelling transition pH), the copolymer swelling was greatly higher than acid condition. In complexed hydrogels, the diffusion coefficients of vitamin B12 (VB12) were in the range of 10-10 to 10-7 cm2s-1; While in uncomplexed hydrogels, the values were about 210-6 cm2s-1. The comonomer composition and synthesis conditions have great effect on the structure, and thereby, swelling and solute diffusion characteristics of the resultant hydrogels. For the copolymers with composition of less than or more than 1:1 MAA/EO molar ratio, the plot of lnD vs 1/H-1 followed two different linear equations of 慺ree volume theory? respectively.

A New Method to Estimate Nonlinear Diffusions Based on Discretely Observed Data

The paper proposes a new method to estimate nonlinear diffusions based on discretely observed data, and gives some properties of the corresponding parameters estimation.

First principles calculations of alloying element diffusion coefficients in Ni using the five-frequency model

The diffusion coefficients of several alloying elements（Al,Mo,Co,Ta,Ru,W,Cr,Re） in Ni are directly calculated using the five-frequency model and the first principles density functional theory.The correlation factors provided by the five-frequency model are explicitly calculated.The calculated diffusion coefficients show their excellent agreement with the available experimental data.Both the diffusion pre-factor（D 0） and the activation energy（Q） of impurity diffusion are obtained.The diffusion coefficients above 700 K are sorted in the following order：DAl〉DCr〉DCo〉DTa〉DMo〉DRu〉DW〉D Re.It is found that there is a positive correlation between the atomic radius of the solute and the jump energy of Ni that results in the rotation of the solute-vacancy pair（E 1）.The value of E 2-E 1（E 2 is the solute diffusion energy） and the correlation factor each also show a positive correlation.The larger atoms in the same series have lower diffusion activation energies and faster diffusion coefficients.

Simulation research on monomer agglomeration of nonmetallic inclusions in steel with a diffusion limited aggregation model

The monomer agglomeration of nonmetallic inclusions was simulated with a diffusion limited aggregation （DLA） model of the fractal theory. The simulation study with a random two-dimensional diffusion was carried out. The results indicate that the DLA model can be used for the simulation of agglomeration behavior of the cluster-type inclusions. The morphology of clusters was observed with SEM and compared with the simulated agglomerates. The modelling procedure of the DLA model is applicable for the agglomeration process. The uncertainty of agglomeration process and the persuasive average agglomerative ratio was analyzed. The factors about the agglomerative ratio with the collision path distance and the size of particles or seed were discussed. The adherence of the nonmetallic inclusions on the dam, the weir and the walls of a tundish, and the absorption of inclusions by stopper or nozzle were also discussed.

Multi-scale Modeling of the Effective Chloride Ion Diffusion Coefficient in Cement-based Composite Materials

N-layered spherical inclusions model was used to calculate the effective diffusion coefficient of chloride ion in cement-based materials by using multi-scale method and then to investigate the relationship between the diffusivity and the microstructure of cement-basted materials where the microstructure included the interfacial transition zone （ITZ） between the aggregates and the bulk cement pastes as well as the microstructure of the bulk cement paste itself. For the convenience of applications, the mortar and concrete were considered as a four-phase spherical model, consisting of cement continuous phase, dispersed aggregates phase, interface transition zone and their homogenized effective medium phase. A general effective medium equation was established to calculate the diffusion coefficient of the hardened cement paste by considering the microstructure. During calculation, the tortuosity （n） and constrictivity factors （Ds/Do） of pore in the hardened pastes are n^3.2, Ds/Do=l.Ox 10-4 respectively from the test data. The calculated results using the n-layered spherical inclusions model are in good agreement with the experimental results; The effective diffusion coefficient of ITZ is 12 times that of the bulk cement for mortar and 17 times for concrete due to the difference between particle size distribution and the volume fraction of aggregates in mortar and concrete.

STABILITY AND BIFURCATION ANALYSIS OF A DELAYED INNOVATION DIFFUSION MODEL

In this article, a nonlinear mathematical model for innovation diffusion with stage structure which incorporates the evaluation stage （time delay） is proposed. The model is analyzed by considering the effects of external as well as internal influences and other demographic processes such as emigration, intrinsic growth rate, death rate, etc. The asymptotical stability of the various equilibria is investigated. By analyzing the exponential characteristic equation with delay-dependent coefficients obtained through the variational matrix, it is found that Hopf bifurcation occurs when the evaluation period （time delay, T） passes through a critical value. Applying the normal form theory and the center manifold argument, we de- rive the explicit formulas determining the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.

First-principles computational studies on Na^(+) diffusion in Li-doped P3-type NaMnO_(2) as cathode material for Na-ion batteries

Na-ion diffusion kinetics is a key factor that decided the charge/discharge rate of the electrode materials in Na-ion batteries.In this work,two extreme concentrations of NaMnO_(2) and Na_(2/3)Li_(1/6)Mn_(5/6)O_(2) are considered,namely,the vacancy migration of Na ions in the fully intercalated and the migration of Na ions in the fully de-intercalated.The Na-vacancy and Na^(+)distribution in NaMnO_(2) migrated along oxygen dumbbell hop(ODH)and tetrahedral site hop(TSH),and the migration energy barriers were 0.374 and 0.296 eV,respectively.In NaLi_(1/6)Mn_(5/6)O_(2),the inhomogeneity of Li doping leads to the narrowing of the interlayer spacing by 0.9%and the increase of the energy barrier by 53.8%.On the other hand,due to the alleviation of Jahn-Teller effect of neighboring Mn,the bonding strength of Mn-O was enhanced,so that the energy barrier of path 2-3 in Mn-L1 and Mn-L2 was the lowest,which was 0.234 and 0.424 eV,respectively.In Na_(1/6)Li_(1/6)Mn_(5/6)O_(2),the migration energy barriers of Na-L2 and Na-L3 are 1.233 and 0.779 eV,respectively,because Li+migrates from the transition(TM)layer to the alkali metal(AM)layer with Na^(+)migration,which requires additional energy.

Study of Diffusion Instability in Some Ternary Gas Mixtures at Various Temperatures

Within the linear theory of stability, the process of isothermal mixing of three-component gas mixtures in a channel of final dimensions in the absence of mass-transfer through its walls is considered. The comparison of experimental data with the results of theoretical calculations for the mixtures He+Ar-N2 and H2+N2-CH4 is shown, that a stable diffusion process as the temperature increased will remain the same and be described by the ordinary diffusion laws, but unstable one lost its intensity and tend to the stable diffusion.

ELECTROLYTE-DIFFUSION OF CoSO_4 IN AQUEOUS SOLUTIONS

Electrolyte-diffusion of CoSO4 in pure aqueous solution is studied at 25 ℃ over a concentration range of 10-5-0.25 mol/l. The measurement of diffusion coefficients are done by improved capillary technique without stirring. These values are compared with the theoretical values computed on the basis of Onsager-Fuoss theory.