Reentrant Adhesion Behavior in Nanocluster Deposition

We simulate the collision of atomic clusters with a weakly attractive surface using molecular dynamics in a regime between soft-landing and fragmentation, where the cluster undergoes large deformation but remains intact. As a function of incident kinetic energy, we find a transition from adhesion to reflection at low kinetic energies. We also identify a second adhesive regime at intermediate kinetic energies, where strong deformation of the cluster leads to an increase in contact area and adhesive energy.Comment: 7 pages, 6 figure

Solid-liquid phase coexistence and structural transitions in palladium clusters

We use molecular dynamics with an embedded atom potential to study the behavior of palladium nanoclusters near the melting point in the microcanonical ensemble. We see transitions from both fcc and decahedral ground state structures to icosahedral structures prior to melting over a range of cluster sizes. In all cases this transition occurs during solid-liquid phase coexistence and the mechanism for the transition appears to be fluctuations in the molten fraction of the cluster and subsequent recrystallization into the icosahedral structure.Comment: 8 pages, 6 figure

Molecular dynamics simulations of reflection and adhesion behavior in Lennard-Jones cluster deposition

We conduct molecular dynamics simulations of the collision of atomic clusters with a weakly-attractive surface. We focus on an intermediate regime, between soft-landing and fragmentation, where the cluster undergoes deformation on impact but remains largely intact, and will either adhere to the surface (and possibly slide), or be reflected. We find that the outcome of the collision is determined by the Weber number, We i.e. the ratio of the kinetic energy to the adhesion energy, with a transition between adhesion and reflection occurring as We passes through unity. We also identify two distinct collision regimes: in one regime the collision is largely elastic and deformation of the cluster is relatively small but in the second regime the deformation is large and the adhesion energy starts to depend on the kinetic energy. If the transition between these two regimes occurs at a similar kinetic energy to that of the transition between reflection and adhesion, then we find that the probability of adhesion for a cluster can be bimodal. In addition we investigate the effects of the angle of incidence on adhesion and reflection. Finally we compare our findings both with recent experimental results and with macroscopic theories of particle collisions.Comment: 18 pages, 13 figure

Formulation of Decaffeinated Instant Coffee Effervescent Tablet

Decaffeinated coffee is an alternative for caffeine intollerant consumer as a safe and practical choice. However, since decaffeination process employ high temperature extraction, the coffee produced usually possesses inferior sensory qualities. This research was aimed to get an optimum formulation of effervescent coffee tablet that has good physical and sensory quality. In this research, effervescent coffee tablet was formulated with three different ratios of the decaffeinated instant coffee and effervescent reagent (citric acid and sodium bicarbonate), namely 1.5:1; 1:1; and 1:1.5 (w/w) weighed in 3 g per tablet serving. Sensory evaluation was carried out organoleptically in several criteria such as flavors, aromas, and colors on 40 mL, 80 mL, and 120 mL of the solution. Futher, physical quality evaluation was done by measuring its weight uniformity, hardness, friability, and run time which then calculated by statistic analytical method to decide the best formulation. Based on the result, the best formulation of effervescent coffee tablet was 1:1.5 (w/w) due to its shortest run time (4.2 minutes), good weight uniformity and hardness value, 1.16 ± 0.03 g/cm3 dan 6.7 ± 0.5 kg, respectively, while friability value was the smallest (2%) compared to other formulations. The brewing of this formulation in 40 mL water also had best sensory profiles in term of aroma, color and flavor

Numerical studies for fractional functional differential equations with delay based on BDF-type shifted Chebyshev approximations

Fractional functional differential equations with delay (FDDEs) have recently played a significant role in modeling of many real areas of sciences such as physics, engineering, biology, medicine, and economics. FDDEs often cannot be solved analytically so the approximate and numerical methods should be adapted to solve these types of equations. In this paper we consider a new method of backward differentiation formula-(BDF-) type for solving FDDEs. This approach is based on the interval approximation of the true solution using the Clenshaw and Curtis formula that is based on the truncated shifted Chebyshev polynomials. It is shown that the new approach can be reformulated in an equivalent way as a Runge-Kutta method and the Butcher tableau of this method is given. Estimation of local and global truncating errors is deduced and this leads to the proof of the convergence for the proposed method. Illustrative examples of FDDEs are included to demonstrate the validity and applicability of the proposed approach. © 2015 V. G. Pimenov and A. S. Hendy

A Conservative Scheme with Optimal Error Estimates for a Multidimensional Space-Fractional Gross-Pitaevskii Equation

The present work departs from an extended form of the classical multi-dimensional Gross-Pitaevskii equation, which considers fractional derivatives of the Riesz type in space, a generalized potential function and angular momentum rotation. It is well known that the classical system possesses functionals which are preserved throughout time. It is easy to check that the generalized fractional model considered in this work also possesses conserved quantities, whence the development of conservative and efficient numerical schemes is pragmatically justified. Motivated by these facts, we propose a finite-difference method based on weighted-shifted Grünwald differences to approximate the solutions of the generalized Gross-Pitaevskii system. We provide here a discrete extension of the uniform Sobolev inequality to multiple dimensions, and show that the proposed method is capable of preserving discrete forms of the mass and the energy of the model. Moreover, we establish thoroughly the stability and the convergence of the technique, and provide some illustrative simulations to show that the method is capable of preserving the total mass and the total energy of the generalized system. © 2019 Ahmed S. Hendy et al., published by Sciendo 2019

Discrete monotone method for space-fractional nonlinear reaction–diffusion equations

A discrete monotone iterative method is reported here to solve a space-fractional nonlinear diffusion–reaction equation. More precisely, we propose a Crank–Nicolson discretization of a reaction–diffusion system with fractional spatial derivative of the Riesz type. The finite-difference scheme is based on the use of fractional-order centered differences, and it is solved using a monotone iterative technique. The existence and uniqueness of solutions of the numerical model are analyzed using this approach, along with the technique of upper and lower solutions. This methodology is employed also to prove the main numerical properties of the technique, namely, the consistency, stability, and convergence. As an application, the particular case of the space-fractional Fisher’s equation is theoretically analyzed in full detail. In that case, the monotone iterative method guarantees the preservation of the positivity and the boundedness of the numerical approximations. Various numerical examples are provided to illustrate the validity of the numerical approximations. More precisely, we provide an extensive series of comparisons against other numerical methods available in the literature, we show detailed numerical analyses of convergence in time and in space against fractional and integer-order models, and we provide studies on the robustness and the numerical performance of the discrete monotone method. © 2019, The Author(s).Russian Foundation for Basic Research, RFBR: 19-01-00019Consejo Nacional de Ciencia y Tecnología, CONACYT: A1-S-45928The first author would like to acknowledge the financial support of the National Council for Science and Technology of Mexico (CONACYT). The second (and corresponding) author acknowledges financial support from CONACYT through grant A1-S-45928. ASH is financed by RFBR Grant 19-01-00019