Bounds for the generalized Marcum function of the second kind

The Ramanujan Journal - This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use...     

An off-lattice, self-learning kinetic Monte Carlo method using local environments

We present a method called local environment kinetic Monte Carlo (LE-KMC) method for efficiently performing off-lattice, self-learning kinetic Monte Carlo (KMC) simulations of activated processes in material systems. Like other off-lattice KMC schemes, new atomic processes can be found on-the-fly in LE-KMC. However, a unique feature of LE-KMC is that as long as the assumption that all processes and rates depend only on the local environment is satisfied, LE-KMC provides a general algorithm for (i) unambiguously describing a process in terms of its local atomic environments, (ii) storing new processes and environments in a catalog for later use with standard KMC, and (iii) updating the system based on the local information once a process has been selected for a KMC move. Search, classification, storage and retrieval steps needed while employing local environments and processes in the LE-KMC method are discussed. The advantages and computational cost of LE-KMC are discussed. We assess the performance of the LE-KMC algorithm by considering test systems involving diffusion in a submonolayer Ag and Ag-Cu alloy films on Ag(001) surface.     

An alternative technique for solving a coupled PDE system in interphase heat transfer

Recently an accelerated iterative procedure was studied for solving a coupled partial differential equation system in interphase heat transfer to improve some existing iterative procedures in the literature. In that procedure, at each step of the iteration one has to evaluate the derivative of a well-known function at a new point. In this paper, an alternative approach is proposed in which one has to evaluate the derivative only once throughout the procedure. The proposed new iterative scheme also has the same order of convergence and takes lesser number of iterations for certain benchmark problems. An interesting theoretical study on the monotone convergence as well as error estimate of the proposed iterative procedure are provided for continuous as well as discretized problems. The proposed iterative procedure also supplements the existence and uniqueness of the solution in both the cases. A comparative numerical study is also done to demonstrate the efficacy of the proposed scheme.     

A Short Note on the Quasilinearization Method for Fractional Differential Equations

Recent literature shows that for certain classes of fractional differential equations the monotone iterative technique fails to guarantee the quadratic convergence of the quasilinearization method. The present work proves the quadratic convergence of the quasilinearization method and the existence and uniqueness of the solution of such a class of fractional differential equations. Our analysis depends upon the classical Kantorovich theorem on Newton's method. Various examples are discussed in order to illustrate our approach.     

Legendre wavelet – quasilinearization technique for solving q-difference equations

Recently, various fixed point theorems have been used to prove the existence and uniqueness of the solutions for q-difference equations. In this paper, we obtain the existence and uniqueness theorems for a q-initial and a q-boundary value problem using the classical Newton’s method. Making use of the main theorems, a Legendre wavelet technique has been proposed to solve the q-difference equations numerically. The numerical simulation shows that the proposed scheme produces higher accuracy and is very straightforward to apply.     

Onset of nonlinearity and yield strain of a model soft solid

For soft solids with their low modulus, small stress already results in large strain, which may cause nonlinearity and yielding. These potentially competing effects were studied on a clay/polybutadiene (clay/sPB) composite, which is a soft physical gel. Structural changes were introduced by oscillatory shear using large amplitude (LAOS). LAOS beyond a critical limit reduced the internal connectivity. This softened the already soft solid even further, thereby moving it closer to its physical gel point. For clay/sPB, the shear-induced changes were irreversible so that they could get probed using small amplitude shear (SAOS) frequency sweeps. Sequences of SAOS-LAOS-SAOS (SLS) where repeated with increasing LAOS amplitude and increasing duration. The flow-induced structural changes in the soft solid were attributed to yielding, which began to occur at about the same stress/strain values as found for the onset of nonlinearity in traditional SAOS to LAOS (StL) stress amplitude sweeps. The onset of nonlinearity and the yielding seem to be a strain activated process since the characteristic strain amplitude is independent of frequency and temperature, but not so for the characteristic stress amplitude. The duration of LAOS in a SLS experiment beyond yielding is an important parameter since flow-induced structural changes require time to grow.     

Molecular docking studies of some new imidazole derivatives for antimicrobial properties

In modern drug designing, molecular docking is routinely used for understanding drug-receptor interaction. In the present study six imidazole derivatives containing substituted pyrazole moiety (2a,b and 4a–d) were synthesized. Structures of the newly synthesized compounds were characterized by spectral studies. Compounds were screened for their antibacterial activity. Compound 4c was found to be potent antimicrobial against Pseudomonas aeruginosa at concentrations of 1 and 0.5 mg/mL compared to standard drug Streptomycin. All the compounds were subjected to molecular docking studies for the inhibition of the enzyme l-glutamine: d-fructose-6-phosphate amidotransferase[GlcN-6-P] (EC 2.6.1.16). The in silico molecular docking study results showed that, all the synthesized compounds having minimum binding energy and have good affinity toward the active pocket, thus, they may be considered as good inhibitor of GlcN-6-P synthase.