On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis

This paper develops an asymptotic theory for a large class of Boltzmann type equations suitable to model the evolution of multicellular systems in biology with special attention to the onset of nonlinear phenomena. The mathematical method shows how various levels of diffusion phenomena, linear and non-linear, can be obtained by suitable asymptotic limits. The time scaling corresponding to different speeds related to cell movement and biological evolution plays a crucial role and different macroscopic equations corresponds to different scaling.     

Development of Ferromagnetic Materials Containing Co2P,Fe2P Phases from Organometallic Dendrimers Precursors

The development of synthesis methods to access advanced materials, such as magnetic materials that combine multimetallic phosphide phases, remains a worthy research challenge. The most widely used strategies for the synthesis of magnetic transition metal phosphides (TMPs) are organometallic approaches. In this study, Fe-containing homometallic dendrimers and Fe/Co-containing heterometallic dendrimers were used to synthesize magnetic materials containing multimetallic phosphide phases. The crystalline nature of the nearly aggregated particles was indicated for both designed magnetic samples. In contrast to heterometallic samples, homometallic samples showed dendritic effects on their magnetic properties. Specifically, saturation magnetization (M_s) and coercivity (H_c) decrease as dendritic generation increases. Incorporating cobalt into the homometallic dendrimers to prepare the heterometallic dendrimers markedly increases the magnetic properties of the magnetic materials from 60 to 75 emu/g. Ferromagnetism in homometallic and heterometallic particles shows different responses to temperature changes. For example, heterometallic samples were less sensitive to temperature changes due to the presence of Co₂P in contrast to the homometallic ones, which show an abrupt change in their slopes at a temperature close to 209 K, which appears to be related to the Fe₂P ratios. This study presents dendrimers as a new type of precursor for the assembly of magnetic materials containing a mixture of iron- and cobalt-phosphides phases with tunable magnetism, and provides an opportunity to understand magnetism in such materials.     

Resonance capture in a damped three-degree-of-freedom system: Experimental and analytical comparison

The dynamical behavior of a three-degree-of-freedom system is considered in the presence of a 1:1 resonance between two components with non-linear inertial coupling. One of the resonant frequencies is fixed, characterizing a translational oscillation, while the second frequency varies slowly in time and describes the angular velocity of an unbalanced rotational component. As the angular velocity approaches the translational frequency of oscillation, the system can either become locked into a sustained resonance or pass through the 1:1 resonance depending on the parameter values and initial conditions. When the system is attracted to a state of sustained resonance, the amplitude of the translational oscillations and the steady-state frequency of the sustained resonance vary, depending on the parameter values of the system. As the applied torque increases, both the resonant frequency and oscillation amplitude increases. If the applied torque is too large, the sustained resonance no longer exists and the system cannot be attracted to a long-term resonant motion. These variations in the response with parametric changes are described from a reduced-order model obtained with the method of averaging and are also seen in numerical simulations of the original equations of motion. Finally, the results are verified in an experimental rotordynamic system.     

Kinetic (cellular) models of cell progression and competition with the immune system

This paper deals with the modelling of the immune response to the evolution of progressing (corrupted) endothelial cells, i.e. cancer cells. A mathematical model is proposed, on the basis of mathematical methods of the kinetic theory for a large system of interacting cells. Then a qualitative analysis is carried out to prove the existence of the solutions of the Cauchy problem related to the model and to show some results on the asymptotic behavior. Some computational simulations complete the analysis on the asymptotic behavior of the solutions, which depending on parameters and initial conditions shows either the prevalence of progressing cells or their depletion due to the action of the immune system.     

Green Synthesis of Poly(aminomethylenephosphonic) Acids

The reaction of polyamines with phosphorous acid and formaldehyde in water under focused microwave irradiation provides a facile and rapid synthesis of poly(aminomethylenephosphonic) acids.     

Constant Mean Curvature Foliations of Globally Hyperbolic Spacetimes Locally Modelled on <Emphasis Type="Italic">AdS</Emphasis><Subscript>3</Subscript>

We prove that every three-dimensional maximal globally hyperbolic spacetime, locally modelled on the anti-de Sitter space AdS ₃, with closed orientable Cauchy surfaces, admits a unique CMC time function.     

Aqueous solution behavior of p(N-isopropyl acrylamide) in the presence of water-soluble macromolecular species

We report here the polymerization of N-isopropyl acrylamide (NIPAM) via the reversible addition fragmentation chain transfer (RAFT) process. Two trithiocarbonates (S,S′-bis(α,α′-dimethyl-α″-acetic acid)-trithiocarbonate and 2-dodecylsulfanylthiocarbonylsulfanyl-2-methyl propionic acid) were used as the chain transfer agents in conjunction with 4,4′-azobis(4-cyanovaleric acid) and 2,2′azobis(2-methylpropionamidine) dihydrochloride as the initiating species. Poly(NIPAM) is a thermo-responsive polymer that has a sharp lower critical solution temperature (LCST). Herein, we investigated the aqueous solution behaviour of well defined p(NIPAM) prepared by the RAFT process as a function of molecular weight (degree of polymerization: 50, 100 and 200) and temperature. Furthermore, we examine the influence of varying concentrations of macromolecular species (neutral polyethylene glycol (M_n - 3400 g/mol) and ionic bovine serum albumin (M_n - 63 000 g/mol)) on the LCST of p(NIPAM). The aqueous solution behaviour was assessed by spectrophotometry, dynamic light scattering and surface tensiometry. The macromolecular additives was found to have a significant effect on the coil to globular transition of the lower molecular weight p(NIPAM).