On 2D Viscoelasticity with Small Strain

An exact two-dimensional rotation-strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under the smallness assumptions only on the size of initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, which is revealed by passing the partial dissipation to the whole system.Comment: Different contributions of strain and rotation of the deformation are studied for viscoelastic fluids of Oldroyd-B type in 2

Oxidative protein folding in the mitochondrial intermembrane space

Disulfide bond formation is a crucial step for oxidative folding and necessary for the acquisition of a protein's native conformation. Introduction of disulfide bonds is catalyzed in specialized subcellular compartments and requires the coordinated action of specific enzymes. The intermembrane space of mitochondria has recently been found to harbor a dedicated machinery that promotes the oxidative folding of substrate proteins by shuttling disulfide bonds. The newly identified oxidative pathway consists of the redox-regulated receptor Mia40 and the sulfhydryl oxidase Erv1. Proteins destined to the intermembrane space are trapped by a disulfide relay mechanism that involves an electron cascade from the incoming substrate to Mia40, then on to Erv1, and finally to molecular oxygen via cytochrome c. This thiol–disulfide exchange mechanism is essential for the import and for maintaining the structural stability of the incoming precursors. In this review we describe the mechanistic parameters that define the interaction and oxidation of the substrate proteins in light of the recent publications in the mitochondrial oxidative folding field

Injectable and Spatially Patterned Microporous Annealed Particle (MAP) Hydrogels for Tissue Repair Applications.

Spatially patterned hydrogels are becoming increasingly popular in the field of regenerative medicine and tissue repair because of their ability to guide cell infiltration and migration. However, postfabrication technologies are usually required to spatially pattern a hydrogel, making these hydrogels difficult to translate into the clinic. Here, an injectable spatially patterned hydrogel is reported using hyaluronic acid (HA)-based particle hydrogels. These particle hydrogels are sequentially loaded into a syringe to form a pattern and, once injected, they maintain the pattern. The applicability of this hydrogel in a wound healing skin model, a subcutaneous implant model, as well as a stroke brain model is examined and distinct patterning in all models tested is shown. This injectable and spatially patterned hydrogel can be used to create physical or biochemical gradients. Further, this design can better match the scaffold properties within the physical location of the tissue (e.g., wound border vs wound center). This allows for better design features within the material that promote repair and regeneration

Global Solutions for Incompressible Viscoelastic Fluids

We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial data. The results hold in both two and three dimensional spaces. The results and methods presented in this paper are also valid for a wide range of elastic complex fluids, such as magnetohydrodynamics, liquid crystals and mixture problems.Comment: We prove the existence of global smooth solutions to the Cauchy problem for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial dat

Fluctuations Do Matter: Large Noise-Enhanced Halos in Charged-Particle Beams

The formation of beam halos has customarily been described in terms of a particle-core model in which the space-charge field of the oscillating core drives particles to large amplitudes. This model involves parametric resonance and predicts a hard upper bound to the orbital amplitude of the halo particles. We show that the presence of colored noise due to space-charge fluctuations and/or machine imperfections can eject particles to much larger amplitudes than would be inferred from parametric resonance alone.Comment: 13 pages total, including 5 figure

Global exponential stability of classical solutions to the hydrodynamic model for semiconductors

In this paper, the global well-posedness and stability of classical solutions to the multidimensional hydrodynamic model for semiconductors on the framework of Besov space are considered. We weaken the regularity requirement of the initial data, and improve some known results in Sobolev space. The local existence of classical solutions to the Cauchy problem is obtained by the regularized means and compactness argument. Using the high- and low- frequency decomposition method, we prove the global exponential stability of classical solutions (close to equilibrium). Furthermore, it is also shown that the vorticity decays to zero exponentially in the 2D and 3D space. The main analytic tools are the Littlewood-Paley decomposition and Bony's para-product formula.Comment: 18 page

Production of Enhanced Beam Halos via Collective Modes and Colored Noise

We investigate how collective modes and colored noise conspire to produce a beam halo with much larger amplitude than could be generated by either phenomenon separately. The collective modes are lowest-order radial eigenmodes calculated self-consistently for a configuration corresponding to a direct-current, cylindrically symmetric, warm-fluid Kapchinskij-Vladimirskij equilibrium. The colored noise arises from unavoidable machine errors and influences the internal space-charge force. Its presence quickly launches statistically rare particles to ever-growing amplitudes by continually kicking them back into phase with the collective-mode oscillations. The halo amplitude is essentially the same for purely radial orbits as for orbits that are initially purely azimuthal; orbital angular momentum has no statistically significant impact. Factors that do have an impact include the amplitudes of the collective modes and the strength and autocorrelation time of the colored noise. The underlying dynamics ensues because the noise breaks the Kolmogorov-Arnol'd-Moser tori that otherwise would confine the beam. These tori are fragile; even very weak noise will eventually break them, though the time scale for their disintegration depends on the noise strength. Both collective modes and noise are therefore centrally important to the dynamics of halo formation in real beams.Comment: For full resolution pictures please go to http://www.nicadd.niu.edu/research/beams

Dispersion and collapse of wave maps

We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures. The first conjecture states that singularities which are produced in the evolution of sufficiently large initial data are approached in a universal manner given by the profile of a stable self-similar solution. The second conjecture states that the codimension-one stable manifold of a self-similar solution with exactly one instability determines the threshold of singularity formation for a large class of initial data. Our results can be considered as a toy-model for some aspects of the critical behavior in formation of black holes.Comment: 14 pages, Latex, 9 eps figures included, typos correcte

Development of singularities for the compressible Euler equations with external force in several dimensions

We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.Comment: 23 page