The behavior of an extra roll extending into otherwise regular convection pattern is studied as a function Rayleigh number, Prandtl $P$, and wavelength, by means fully resolved numerical simulation the Boussinesq equations with free-slip boundary conditions. For reduced numbers order one or less $P\ensuremath{\gtrsim}40$, simulations lowest-order amplitude reproduce results semiquantitatively. In particular, we find that when this class defects stable, they move constant velocity $v$,...

Abstract Background Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disorder characterized by the selective loss of motor neurons (MN) in brain stem and spinal cord. Intracellular disruptions cytosolic mitochondrial calcium have been associated with MN degeneration, but underlying mechanisms are not well understood. The present evidence supports hypothesis that mitochondria target mutant SOD1-mediated toxicity familial amyotrophic (fALS) intracellular alterations might...

We discuss the spatio-temporal correlations of stress fluctuations in viscoelastic fluids, including colloidal dispersions, polymer melts and glass-forming liquids. First, we relate tensor auto-correlation functions to its corresponding generalized Onsager transport kernels. The relation is valid at finite wavelengths frequencies, serves as basis for continuum mechanics approximations, where it leads viscosities a fluid elastic constants solid. Second, consider long wavelength limit...

A new secondary instability has been found for nearly parallel rolls that eliminates all wavelengths previously thought to be stable Prandtl numbers less than 0.301 or 0.782, depending on the circumstances. There is currently no known counterpart this between rigid boundaries.

Within the Mori theory, a kinetic equation for phase-space density of tagged particle in classical liquid is derived which describes motion self-consistent wave number and frequency-dependent effective potential. It shown that small numbers $q$ almost bound trapping potential, at some critical ${q}_{0}$ potential breaks down, large propagates freely. The theory applied to calculation self-correlation function ${S}_{s}(q,\ensuremath{\omega})$ argon rubidium, breakdown explain observed...

We compute the coefficient of restitution $\ensuremath{\epsilon}$ starting from a microscopic model elastic disks. Collisions are found to be inelastic, in general, with finite fraction translational energy being transferred vibrations. The depends on relative velocity colliding disks, such that collisions become increasingly more inelastic for larger velocities. predictions agreement approach Hertz [J. Reine Angew. Math. 92, 156 (1882)] quasistatic limit. constants material via Poisson's...

We propose a semimicroscopic model for the glass transformation. The long-lived nonequlibrium fluctuations are represented by quenched disorder in an equilibrium ensemble. predicts sharp transition without latent heat. liquid cannot be supercooled below temperature, even though adjustment of cooling rate glassy phase can obtained at various temperatures. is characterized local static density and finite zero-frequency shear modulus.

Large-scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations slow particles via the four-point structure factor ${S}_{4}(q,t)$. Both cases, elastic ($ϵ=1$) and inelastic ($ϵ<1$) collisions, are studied. As fluid approaches structural arrest, i.e., for packing fractions in range $0.6\ensuremath{\le}\ensuremath{\phi}\ensuremath{\le}0.805$, scaling is shown hold:...

A fluid droplet, in general, deforms if subject to active driving, such as a finite slip velocity or tractions on its interface. Starting from Stokes equations, we show that these deformations and their dynamics can be computed analytically perturbation theory the inverse of surface tension γ, by using an approach based vector spherical harmonics. We consider squirmer models general tractions, inhomogeneous tensions, which may result Marangoni effects. In lowest order, deformation is order...

A freely falling stream of weakly cohesive granular particles is modeled and analyzed with the help event driven simulations continuum hydrodynamics. The former show a breakup into droplets, whose size measured as function energy. Extensional flow an exact solution one-dimensional Navier-Stokes equation, corresponding to strain rate, decaying like t(-1) from its initial value, γ[over ˙](0). Expanding around this basic state, we that stable for short times, ˙](0)t<<1, whereas long ˙](0)t>>1,...

We inquire about the possible coexistence of macroscopic and microstructured phases in random Q-block copolymers built incompatible monomer types A B with equal average concentrations. In our microscopic model, one block comprises M identical monomers. The block-type sequence distribution is Markovian characterized by correlation \lambda. Upon increasing incompatibility \chi\ (by decreasing temperature) disordered state, known ordered form: for \lambda\ > \lambda_c, two coexisting A- B-rich...

We analyze the flow curves of a two-dimensional assembly granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, fluid undergoes large scale instability, implying range stress and strain rates where no stationary can exist. Whereas small systems were shown previously to exhibit hysteretic jumps between low high branches, continuous shear thickening arising from averaging unsteady, spatially heterogeneous flows. The observed...

We study the self-propulsion of spherical droplets as simplified hydrodynamic models swimming micro-organisms or artificial micro-swimmers. In contrast to approaches that start from active velocity fields produced by system, we consider interface tractions, body force densities and stresses origin autonomous swimming. For negligible Reynolds number given activity, compute external internal flow well centre mass angular droplet at fixed time. To construct trajectories single time snapshots,...

Abstract We work out the propulsion of a viscous drop which is driven by two mechanisms: active velocity an encapsulated squirmer and externally applied force acting on squirmer. Of particular interest existence stable comoving state squirmer, allowing for controlled manipulation external forcing. The velocities droplet as well conditions are worked analytically axisymmetric configuration with general displacement from center Graphic abstract

Goldstone modes in the amorphous solid state, resulting from spontaneous breaking of translational symmetry due to random localisation particles, are discussed. Starting a microscopic model with quenched disorder, broken is identified be that relative translations replicas. excitations, corresponding pure shear deformations, constructed long-wavelength distortions order parameter. The elastic free energy computed, and it shown fluctuations destroy two spatial dimensions, yielding...

The physical properties of blends distinct homopolymers, cross-linked beyond the gelation point, are addressed via a Landau approach involving pair coupled order-parameter fields: one describing vulcanisation, other local phase separation. Thermal concentration fluctuations, present at time cross-linking, frozen in by and structure resulting glassy fluctuations is analysed Gaussian level various regimes, determined relative values certain length scales. enhancement, due to gelation,...

We develop a microscopic picture of shear thickening in dense suspensions which emphasizes the role frictional forces, coupling rotational and translational degrees freedom. Simulations with contact forces viscous drag only, reveal pronounced simultaneous increase number energy dissipation by forces. At high densities, when motion is severely constrained, we observe liquid-like gear-states relative rotations particles coexisting solid-like regions rotate as whole. The latter are stabilised...

Within the formalism of Mori and Zwanzig a kinetic equation for phase-space density simple classical liquids is derived whose relaxation kernel obtained as solution second equation. The latter closed by introducing phenomenological rate. resulting equations can be reduced to evaluation self-correlation function tagged particle, studied earlier present authors. calculated scattering functions $S(q, \ensuremath{\omega})$ liquid argon rubidium are compared with neutron experiments well...

The question of the local stability (replica-symmetric) amorphous solid state is addressed for a class systems undergoing continuous liquid to amorphous-solid phase transition driven by effect random constraints. Hessian matrix, associated with infinitesimal fluctuations around stationary point corresponding state, obtained. eigenvalues this matrix are all shown be strictly positive near transition, except one---the zero mode spontaneously broken translational symmetry system. Thus established.

We consider self-propelled droplets which are driven by internal flow. Tracer particles, advected the flow, in general follow chaotic trajectories, even though motion of autonomous swimmer is completely regular. The flow mixing, and for P\'{e}clet Batchelor numbers, realized e.g. eucaryotic cells, advective mixing can substantially accelerate dominate transport diffusion.