Stability, free energy and dynamics of multi-spikes in the minimal Keller-Segel model

<p style='text-indent:20px;'>One of the most impressive findings in chemotaxis is the aggregation that randomly distributed bacteria, when starved, release a diffusive chemical to attract and group with others to form one or several stable aggregates in a long time. This paper considers pattern formation within the minimal Keller–Segel chemotaxis model with a focus on the stability and dynamics of its multi-spike steady states. We first show that any steady-state must be a periodic replication of the spatially monotone one and they present multi-spikes when the chemotaxis rate is large; moreover, we prove that all the multi-spikes are unstable through their refined asymptotic profiles, and then find a fully-fledged hierarchy of free entropy energy of these aggregates. Our results also complement the literature by finding that when the chemotaxis is strong, the single boundary spike has the least energy hence is the most stable, the steady-state with more spikes has larger free energy, while the constant has the largest free energy and is always unstable. These results provide new insights into the model's intricate global dynamics, and they are illustrated and complemented by numerical studies which also demonstrate the metastability and phase transition behavior in chemotactic movement.</p>

Teaching Learning Based Optimization (TLBO) for energy efficiency in Fog Computing

Fog Computing is eminent to ensure quality of service in handling huge volume and variety of data and to display output, or for closed loop process control. It comprises of fog devices to manage huge data transmission but results in high energy consumption, end-to end-delay, latency. In this paper, an energy model for fog computing environment has been proposed and implemented based on teacher student learning model called Teaching Learning Based Optimization (TLBO) to improve the responsiveness of the fog network in terms of energy optimization. The results show the effectiveness of TLBO in choosing the shortest path with least energy consumption.

Existence and asymptotics of ground states to the nonlinear Dirac equation with Coulomb potential

In this paper we study the Dirac equation with Coulomb potential − i α · ∇ u + a β u − μ | x | u = f ( x , | u | ) u , x ∈ R 3 where a is a positive constant, μ is a positive parameter, α = ( α 1 , α 2 , α 3 ), α i and β are 4 × 4 Pauli–Dirac matrices. The Dirac operator is unbounded from below and above so the associate energy functional is strongly indefinite. Under some suitable conditions, we prove that the problem possesses a ground state solution which is exponentially decay, and the least energy has continuous dependence about μ. Moreover, we are able to obtain the asymptotic property of ground state solution as μ → 0 + , this result can characterize some relationship of the above problem between μ > 0 and μ = 0.

DESIGNING OF NANOCOMPOSITE MODEL STRUCTURE USING GLYCITEIN AND GENISTEIN WITH TWELVE DIFFERENT METAL ATOMS USING IN SILICO METHOD

Nanocomposite formulation is still in its evolving state. However due to its significant therapeutic applications it has grabbed the attention of many researchers. Isoflavonewhich is widely found in soy products have tremendous medicinal propertieswhen it interacts with nanoparticles can become a boon. Hence in this study, we are reporting the interaction properties/patterns of two ubiquitous flavones namelyGlycitein and Genistein forming a nanocomposite model with 12 different metals such as Gold, Silver, Palladium, Platinum, Ruthenium, Rhodium, Cadmium, Iron, Nickel, Zinc, Copper and Antimony based ontheir potency to form nanoparticles. To mimic the Nanocomposite, model the formulation was conducted in Avogadro Software for windows. Glycitein and Genistein create a possibility of selecting the most suitable -OH position that would serve as the binding site. On selection of the appropriate binding site the interaction amid two molecules of glycitein and genistein placed sidewise held together by above-mentioned metals also surrounded by the same metal on another vacant -OH position forming a close saturated structure subjected for interaction. Based on predominantly energy levels the least energy obtained model was Cadmium and the peak procured by Antimony making it least stable and unfavorable for the perceived result.