Melting and Rippling Phenomenan in Two Dimensional Crystals with localized bonding

We calculate Root Mean Square (RMS) deviations from equilibrium for atoms in a two dimensional crystal with local (e.g. covalent) bonding between close neighbors. Large scale Monte Carlo calculations are in good agreement with analytical results obtained in the harmonic approximation. When motion is restricted to the plane, we find a slow (logarithmic) increase in fluctuations of the atoms about their equilibrium positions as the crystals are made larger and larger. We take into account fluctuations perpendicular to the lattice plane, manifest as undulating ripples, by examining dual layer systems with coupling between the layers to impart local rigidly (i.e. as in sheets of graphene made stiff by their finite thickness). Surprisingly, we find a rapid divergence with increasing system size in the vertical mean square deviations, independent of the strength of the interplanar coupling. We consider an attractive coupling to a flat substrate, finding that even a weak attraction significantly limits the amplitude and average wavelength of the ripples. We verify our results are generic by examining a variety of distinct geometries, obtaining the same phenomena in each case.Comment: 17 pages, 28 figure

Fragility and compressibility at the glass transition

Isothermal compressibilities and Brillouin sound velocities from the literature allow to separate the compressibility at the glass transition into a high-frequency vibrational and a low-frequency relaxational part. Their ratio shows the linear fragility relation discovered by x-ray Brillouin scattering [1], though the data bend away from the line at higher fragilities. Using the concept of constrained degrees of freedom, one can show that the vibrational part follows the fragility-independent Lindemann criterion; the fragility dependence seems to stem from the relaxational part. The physical meaning of this finding is discussed. [1] T. Scopigno, G. Ruocco, F. Sette and G. Monaco, Science 302, 849 (2003)Comment: 4 pages, 2 figures, 2 tables, 33 references. Slightly changed after refereein

Plasticization and antiplasticization of polymer melts diluted by low molar mass species

An analysis of glass formation for polymer melts that are diluted by structured molecular additives is derived by using the generalized entropy theory, which involves a combination of the Adam-Gibbs model and the direct computation of the configurational entropy based on a lattice model of polymer melts that includes monomer structural effects. Antiplasticization is accompanied by a "toughening" of the glass mixture relative to the pure polymer, and this effect is found to occur when the diluents are small species with strongly attractive interactions with the polymer matrix. Plasticization leads to a decreased glass transition temperature T_g and a "softening" of the fragile host polymer in the glass state. Plasticization is prompted by small additives with weakly attractive interactions with the polymer matrix. The shifts in T_g of polystyrene diluted by fully flexible short oligomers are evaluated from the computations, along with the relative changes in the isothermal compressibility at T_g to characterize the extent to which the additives act as antiplasticizers or plasticizers. The theory predicts that a decreased fragility can accompany both antiplasticization and plasticization of the glass by molecular additives. The general reduction in the T_g and fragility of polymers by these molecular additives is rationalized by analyzing the influence of the diluent's properties (cohesive energy, chain length, and stiffness) on glass formation in diluted polymer melts. The description of glass formation at fixed temperature that is induced upon change the fluid composition directly implies the Angell equation for the structural relaxation time as function of the polymer concentration, and the computed "zero mobility concentration" scales linearly with the inverse polymerization index N.Comment: 12 pages, 15 figure

Analysis of Dislocation Mechanism for Melting of Elements: Pressure Dependence

In the framework of melting as a dislocation-mediated phase transition we derive an equation for the pressure dependence of the melting temperatures of the elements valid up to pressures of order their ambient bulk moduli. Melting curves are calculated for Al, Mg, Ni, Pb, the iron group (Fe, Ru, Os), the chromium group (Cr, Mo, W), the copper group (Cu, Ag, Au), noble gases (Ne, Ar, Kr, Xe, Rn), and six actinides (Am, Cm, Np, Pa, Th, U). These calculated melting curves are in good agreement with existing data. We also discuss the apparent equivalence of our melting relation and the Lindemann criterion, and the lack of the rigorous proof of their equivalence. We show that the would-be mathematical equivalence of both formulas must manifest itself in a new relation between the Gr\"{u}neisen constant, bulk and shear moduli, and the pressure derivative of the shear modulus.Comment: 19 pages, LaTeX, 9 eps figure

Physical Aspects of Axonemal Beating and Swimming

We discuss a two-dimensional model for the dynamics of axonemal deformations driven by internally generated forces of molecular motors. Our model consists of an elastic filament pair connected by active elements. We derive the dynamic equations for this system in presence of internal forces. In the limit of small deformations, a perturbative approach allows us to calculate filament shapes and the tension profile. We demonstrate that periodic filament motion can be generated via a self-organization of elastic filaments and molecular motors. Oscillatory motion and the propagation of bending waves can occur for an initially non-moving state via an instability termed Hopf bifurcation. Close to this instability, the behavior of the system is shown to be independent of microscopic details of the axoneme and the force-generating mechanism. The oscillation frequency however does depend on properties of the molecular motors. We calculate the oscillation frequency at the bifurcation point and show that a large frequency range is accessible by varying the axonemal length between 1 and 50$\mu$m. We calculate the velocity of swimming of a flagellum and discuss the effects of boundary conditions and externally applied forces on the axonemal oscillations.Comment: 14 pages, 8 figures, REVTE

Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration

Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum–fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape—no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems

Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory

We demonstrate the accuracy of the hypernetted chain closure and of the mean-field approximation for the calculation of the fluid-state properties of systems interacting by means of bounded and positive-definite pair potentials with oscillating Fourier transforms. Subsequently, we prove the validity of a bilinear, random-phase density functional for arbitrary inhomogeneous phases of the same systems. On the basis of this functional, we calculate analytically the freezing parameters of the latter. We demonstrate explicitly that the stable crystals feature a lattice constant that is independent of density and whose value is dictated by the position of the negative minimum of the Fourier transform of the pair potential. This property is equivalent with the existence of clusters, whose population scales proportionally to the density. We establish that regardless of the form of the interaction potential and of the location on the freezing line, all cluster crystals have a universal Lindemann ratio L = 0.189 at freezing. We further make an explicit link between the aforementioned density functional and the harmonic theory of crystals. This allows us to establish an equivalence between the emergence of clusters and the existence of negative Fourier components of the interaction potential. Finally, we make a connection between the class of models at hand and the system of infinite-dimensional hard spheres, when the limits of interaction steepness and space dimension are both taken to infinity in a particularly described fashion.Comment: 19 pages, 5 figures, submitted to J. Chem. Phys; new version: minor changes in structure of pape

Fine Carbohydrate Structure of Dietary Resistant Glucans Governs the Structure and Function of Human Gut Microbiota

Increased dietary fiber consumption has been shown to increase human gut microbial diversity, but the mechanisms driving this effect remain unclear. One possible explanation is that microbes are able to divide metabolic labor in consumption of complex carbohydrates, which are composed of diverse glycosidic linkages that require specific cognate enzymes for degradation. However, as naturally derived fibers vary in both sugar composition and linkage structure, it is challenging to separate out the impact of each of these variables. We hypothesized that fine differences in carbohydrate linkage structure would govern microbial community structure and function independently of variation in glycosyl residue composition. To test this hypothesis, we fermented commercially available soluble resistant glucans, which are uniformly composed of glucose linked in different structural arrangements, in vitro with fecal inocula from each of three individuals. We measured metabolic outputs (pH, gas, and short-chain fatty acid production) and community structure via 16S rRNA amplicon sequencing. We determined that community metabolic outputs from identical glucans were highly individual, emerging from divergent initial microbiome structures. However, specific operational taxonomic units (OTUs) responded similarly in growth responses across individuals’ microbiota, though in context-dependent ways; these data suggested that certain taxa were more efficient in competing for some structures than others. Together, these data support the hypothesis that variation in linkage structure, independent of sugar composition, governs compositional and functional responses of microbiota

Immersed nano-sized Al dispersoids in an Al matrix; effects on the structural and mechanical properties by Molecular Dynamics simulations

We used molecular dynamics simulations based on a potential model in analogy to the Tight Binding scheme in the Second Moment Approximation to simulate the effects of aluminum icosahedral grains (dispersoids) on the structure and the mechanical properties of an aluminum matrix. First we validated our model by calculating several thermodynamic properties referring to the bulk Al case and we found good agreement with available experimental and theoretical data. Afterwards, we simulated Al systems containing Al clusters of various sizes. We found that the structure of the Al matrix is affected by the presence of the dispersoids resulting in well ordered domains of different symmetries that were identified using suitable Voronoi analysis. In addition, we found that the increase of the grain size has negative effect on the mechanical properties of the nanocomposite as manifested by the lowering of the calculated bulk moduli. The obtained results are in line with available experimental data.Comment: 15 pages, 8 figures. Submitted to J. Phys: Condens. Matte