Sliding mode control for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation

We consider the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation perturbed by a maximal monotone nonlinearity. We prove existence and regularity of strong solutions and, under further assumptions, a uniqueness result. Then, we show that the chosen SMC law forces the system to reach within finite time a sliding manifold that we chose in order that the tumor phase remains constant in time.     

Auger electron emission in proton-induced interactions in living matter: A TILDA-V Monte Carlo tracking

The present work focuses on studying the contribution of the Auger electron emission in proton-induced interactions in biological matter. The Monte Carlo track-structure code, TILDA-V, was then used for modeling the protons beams of 10 keV to 100 MeV in biological matter, namely, water vapor and hydrated DNA. The main ionizing processes are described by means of an extensive set of ab initio differential and total cross sections computed within a quantum-mechanical CDW-EIS approximation.     

Human mobility and COVID-19 initial dynamics

Nonlinear Dynamics - Countries in Europe took different mobility containment measures to curb the spread of COVID-19. The European Commission asked mobile network operators to share on a...     

Quantum line defects and refined BPS spectra

Letters in Mathematical Physics - In this note, we study refined BPS invariants associated with certain quantum line defects in quantum field theories of class $${{\mathcal {S}}}$$. Such defects...     

Effect of anodizing conditions on the cell morphology of anodic films on AA2024-T3 alloy

The effects of applied current density, anodizing time, and electrolyte temperature on the cell and pore morphology of anodic films and the voltage-time response obtained during galvanostatic anodizing of AA2024-T3 alloy in sulphuric acid electrolytes have been studied. Scanning electron microscopy was employed to observe the film morphology. Sponge-like porous structure was promoted by anodizing at relatively low current density and high electrolyte temperature. In contrast, linear porous structure was favoured under the converse conditions. Intermediate conditions resulted in films containing either sequential layers of the 2 morphologies or a morphology incorporating features of the 2 types; such conditions were associated with anodizing voltages in the range 25 to 35 V. The reasons for the morphological differences are proposed to be due to interactions between film growth stresses and stresses arising from oxygen evolution on the development of the alumina cells.     

Solid-State Dynamics and High-Pressure Studies of a Supramolecular Spiral Gear

The structures and solid-state dynamics of the supramolecular salts of the general formula [(12-crown-4)₂ ⋅ DABCOH₂](X)₂ (where DABCO=1,4-diazabicyclo[2.2.2]octane, X=BF₄, ClO₄) have been investigated as a function of temperature (from 100 to 360 K) and pressure (up to 3.4 GPa), through the combination of variable-temperature and variable-pressure XRD techniques and variable-temperature solid-state NMR spectroscopy. The two salts are isomorphous and crystallize in the enantiomeric space groups P3₂2₁ and P3₁2₁. All building blocks composing the supramolecular complex display dynamic processes at ambient temperature and pressure. It has been demonstrated that the motion of the crown ethers is maintained on lowering the temperature (down to 100 K) or on increasing the pressure (up to 1.5 GPa) thanks to the correlation between neighboring molecules, which mesh and rotate in a concerted manner similar to spiral gears. Above 1.55 GPa, a collapse-type transition to a lower-symmetry ordered structure, not attainable at a temperature of 100 K, takes place, proving, thus, that the pressure acts as the means to couple and decouple the gears. The relationship between temperature and pressure effects on molecular motion in the solid state has also been discussed.     

The Impact of pH on Catalytically Critical Protein Conformational Changes: The Case of the Urease,a Nickel Enzyme

Urease uses a cluster of two Ni^II ions to activate a water molecule for urea hydrolysis. The key to this unsurpassed enzyme is a change in the conformation of a flexible structural motif, the mobile flap, which must be able to move from an open to a closed conformation to stabilize the chelating interaction of urea with the Ni^II cluster. This conformational change brings the imidazole side chain functionality of a critical histidine residue, αHis323, in close proximity to the site that holds the transition state structure of the reaction, facilitating its evolution to the products. Herein, we describe the influence of the solution pH in modulating the conformation of the mobile flap. High-resolution crystal structures of urease inhibited in the presence of N-(n-butyl)phosphoric triamide (NBPTO) at pH 6.5 and pH 7.5 are described and compared to the analogous structure obtained at pH 7.0. The kinetics of urease in the absence and presence of NBPTO are investigated by a calorimetric assay in the pH 6.0–8.0 range. The results indicate that pH modulates the protonation state of αHis323, which was revealed to have pK_a=6.6, and consequently the conformation of the mobile flap. Two additional residues (αAsp224 and αArg339) are shown to be key factors for the conformational change. The role of pH in modulating the catalysis of urea hydrolysis is clarified through the molecular and structural details of the interplay between protein conformation and solution acidity in the paradigmatic case of a metalloenzyme.