arXiv subjects

Jorge Vinals

Publications and source records attributed to Jorge Vinals.

At least 37 records · Page 2Linked to original sources

arXiv2003

Motion of a transverse/parallel grain boundary in a block copolymer under oscillatory shear flow

A mesoscopic model of a diblock copolymer is used to study the motion of a grain boundary separating two regions of perfectly ordered lamellar structures under an oscillatory but uniform shear flow. The case considered is a grain boundary separating lamellae along the so called parallel orientation (with wavevector parallel to the velocity gradient direction) and along the transverse orientation (wavevector parallel to the shear direction). In the model considered lamellae in the parallel orientation are marginal with respect to the shear, whereas transverse lamellae are uniformly compressed instead. A multiple scale expansion valid in the weak segregation regime and for low shear frequencies leads to an envelope equation for the grain boundary. This equation shows that the grain boundary moves by the action of the shear, with a velocity that has two contributions. The first contribution, which arises from the change in orientation of the grain boundary as it is being sheared, describes variations in monomer density in the boundary region. This contribution is periodic in time with twice the frequency of the shear and, by itself, leads to no net motion of the boundary. The second contribution arises from a free energy increase within the bulk transverse lamellae under shear. It is also periodic with twice the frequency of the shear, but it does not average to zero, leading to a net reduction in the extent of the region occupied by the transverse lamellae. We find in the limit studied that the velocity of the grain boundary can be expressed as the product of a mobility coefficient times a driving force, the latter given by the excess energy stored in the transverse phase being sheared.

cond-mat.soft↗

arXiv2002

Numerical estimation of entropy loss on dimerization: improved prediction of the quaternary structure of the GCN4 leucine zipper

A lattice based model of a protein is used to study the dimerization equilibrium of the GCN4 leucine zipper. Replica exchange Monte Carlo is used to determine the free energy of both the monomeric and dimeric forms as a function of temperature. The method of coincidences is then introduced to explicitly calculate the entropy loss associated with dimerization, and from it the free energy difference between monomer and dimer, as well as the corresponding equilibrium reaction constant. We find that the entropy loss of dimerization is a strong function of energy (or temperature), and that it is much larger than previously estimated, especially for high energy states. The results confirm that it is possible to study the dimerization equilibrium of GCN4 at physiological concentrations within the reduced representation of the protein employed.

physics.bio-ph↗

arXiv2002

Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry

We study the motion of a grain boundary separating two otherwise stationary domains of hexagonal symmetry. Starting from an order parameter equation appropriate for hexagonal patterns, a multiple scale analysis leads to an analytical equation of motion for the boundary that shares many properties with that of a crystalline solid. We find that defect motion is generically opposed by a pinning force that arises from non-adiabatic corrections to the standard amplitude equation. The magnitude of this force depends sharply on the mis-orientation angle between adjacent domains so that the most easily pinned grain boundaries are those with an angle between four and eight degrees. Although pinning effects may be small, they do not vanish asymptotically near the onset of this subcritical bifurcation, and can be orders of magnitude larger than those present in smectic phases that bifurcate supercritically.

cond-mat.soft↗

arXiv2001

Linear bubble model of abnormal grain growth

A linear bubble model of grain growth is introduced to study the conditions under which an isolated grain can grow to a size much larger than the surrounding matrix average (abnormal growth). We first consider the case of bubbles of two different types such that the permeability of links joining unlike bubbles is larger than that of like bubbles (a simple model of grain boundary anisotropy). Stable abnormal growth is found both by mean field analysis and direct numerical solution. We next study the role of grain boundary pinning (e.g., due to impurities or precipitate phases) by introducing a linear bubble model that includes lower and upper thresholds in the driving force for bubble growth. The link permeability is assumed finite for driving forces above the upper threshold, zero below the lower threshold, and hysteretic in between. Abnormal growth is also observed in this case.

cond-mat.mtrl-sci↗

arXiv2001

Lamellar phase stability in diblock copolymers under reciprocating shear flows

A mesoscopic model of a diblock copolymer is used to study the stability of a uniform lamellar phase under a reciprocating shear flow. Approximate viscosity contrast between the microphases is allowed through a linear dependence of the (Newtonian) shear viscosity on monomer composition. We first show that viscosity contrast does not affect the composition of the base lamellar phase in an unbounded geometry, and that it only couples weakly to long wavelength perturbations. A perturbative analysis is then presented to address the stability of uniform lamellar structures under long wavelength perturbations by self-consistently solving for the composition and velocity fields of the perturbations. Stability boundaries are obtained as functions of the physical parameters of the polymer, the parameters of the flow and the initial orientation of the lamellae. We find that all orientations are linearly stable within specific ranges of parameters, but that the perpendicular orientation is generally stable within a larger range than the parallel orientation. Secondary instabilities are both of the Eckhaus type (longitudinal) and zig-zag type (transverse). The former is not expected to lead to re-orientation of the lamella, whereas in the second case the critical wavenumber is typically found to be along the perpendicular orientation.

cond-mat.soft↗

arXiv2001

Ordering kinetics of stripe patterns

We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain boundary motion through a background of largely immobile curved stripes. A numerical study of the distribution of local stripe curvatures, of the structure factor of the order parameter, and a finite size scaling analysis of the grain boundary perimeter, suggest that the linear scale of the structure grows as a power law of time with a craracteristic exponent z=3. We interpret theoretically the exponent z=3 from the law of grain boundary motion.

cond-mat.soft↗

arXiv2000

Interface and contact line motion in a two phase fluid under shear flow

A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The fluid is set in motion by displacing two parallel, infinite solid boundaries along their own plane. Dissipative relaxation of the order parameter leads to interfacial slip at the contact line, even when no-slip boundary conditions for the fluid velocity are considered. This relaxation occurs within a characteristic length scale l that depends on the order parameter mobility, the equilibrium interfacial tension, the imposed wall velocity, the thermal correlation length, the equilibrium miscibility gap, and the mutual diffusion coefficient. Steady-state interface equations which describe the system on a length scale large compared to the correlation length are derived. Scaling forms which involve the ratio l/L, where L is the width of the fluid layer, and the capillary number follow from the interface equations. The scaling results are verified by direct numerical solution of the governing equations.

cond-mat.stat-mech↗

arXiv2000

Flow induced by a randomly vibrating boundary

We study the flow induced by random vibration of a solid boundary in an otherwise quiescent fluid. The analysis is motivated by experiments conducted under the low level and random effective acceleration field that is typical of a microgravity environment. When the boundary is planar and is being vibrated along its own plane, the variance of the velocity field decays as a power law of distance away from the boundary. If a low frequency cut-off is introduced in the power spectrum of the boundary velocity, the variance decays exponentially for distances larger than a Stokes layer thickness based on the cut-off frequency. Vibration of a gently curved boundary results in steady streaming in the ensemble average of the tangential velocity. Its amplitude diverges logarithmically with distance away from the boundary, but asymptotes to a constant value instead if a low frequency cut-off is considered. This steady component of the velocity is shown to depend logarithmically on the cut-off frequency. Finally, we consider the case of a periodically modulated solid boundary that is being randomly vibrated. We find steady streaming in the ensemble average of the first order velocity, with flow extending up to a characteristic distance of the order of the boundary wavelength. The structure of the flow in the vicinity of the boundary depends strongly on the correlation time of the boundary velocity.

nlin.PS↗

arXiv1999

Shear induced alignment in a model of a block copolymer

A mesoscopic model of a diblock copolymer is used to study the stability of a lamellar structure under a uniform shear flow. We first obtain the nonlinear lamellar solutions under both steady and oscillatory shear flows. Regions of existence of these solutions are determined as a function of the parameters of the model and of the flow. Finally, we address the stability of the lamellar solution against long wavelength perturbations.

cond-mat.soft↗

arXiv1997

Amplitude equations and pattern selection in Faraday waves

A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude equation is derived from the governing equations. The amplitude equation is of gradient form, and the coefficients of the associated Lyapunov function are computed for regular patterns of various symmetries as a function of a viscous damping parameter gamma. For gamma approximately 1, the selected wave pattern comprises a single standing wave (stripe pattern). For gamma much less than 1, patterns of square symmetry are obtained in the capillary regime (large frequencies). At lower frequencies (the mixed gravity-capillary regime), a sequence of six-fold (hexagonal), eight-fold,... patterns are predicted. For even lower frequencies (gravity waves) a stripe pattern is again selected. Our predictions of the stability regions of the various patterns are in quantitative agreement with recent experiments conducted in large aspect ratio systems.

patt-sol↗

arXiv1997

Adiabatic reduction near a bifurcation in stochastically modulated systems

We re-examine the procedure of adiabatic elimination of fast relaxing variables near a bifurcation point when some of the parameters of the system are stochastically modulated. Approximate stationary solutions of the Fokker-Planck equation are obtained near threshold for the pitchfork and transcritical bifurcations. Stochastic resonance between fast variables and random modulation may shift the effective bifurcation point by an amount proportional to the intensity of the fluctuations. We also find that fluctuations of the fast variables above threshold are not always Gaussian and centered around the (deterministic) center manifold as was previously believed. Numerical solutions obtained for a few illustrative examples support these conclusions.

patt-sol↗

arXiv1997

Self-similarity and coarsening of three dimensional particles on a one or two dimensional matrix

We examine the validity of the hypothesis of self-similarity in systems coarsening under the driving force of interface energy reduction in which three dimensional particles are intersected by a one or two dimensional diffusion matrix. In both cases, solute fluxes onto the surface of the particles, assumed spherical, depend on both particle radius and inter-particle distance. We argue that overall mass conservation requires independent scalings for particle sizes and inter-particle distances under magnification of the structure, and predict power law growth for the average particle size in the case of a one dimensional matrix (3D/1D), and a weak breakdown of self-similarity in the two dimensional case (3D/2D). Numerical calculations confirm our predictions regarding self-similarity and power law growth of average particle size with an exponent 1/7 for the 3D/1D case, and provide evidence for the existence of logarithmic factors in the laws of boundary motion for the 3D/2D case. The latter indicate a weak breakdown of self-similarity.

cond-mat.mtrl-sci↗

arXiv1997

Onset of oscillatory instabilities under stochastic modulation

We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random component in both the control parameter of the bifurcation and in the modulation amplitude. Stability boundaries are computed by either solving the stationary Fokker-Planck equation in the vicinity of the center manifold of the underlying deterministic system whenever possible, or by direct numerical solution otherwise. If the modulation amplitude has a stochastic component, the primary bifurcation is always to standing waves at a value of the control parameter that depends on the intensity of the fluctuations. More precisely, and to contrast our results with the case of a deterministic periodic forcing, the onset of instability in the standing wave regime is shifted from its deterministic location, and the region of primary bifurcation to traveling waves disappears yielding instead standing waves at negative values of the control parameter.

patt-sol↗

arXiv1997

Amplitude equations and pattern selection in Faraday waves

We present a systematic nonlinear theory of pattern selection for parametric surface waves (Faraday waves), not restricted to fluids of low viscosity. A standing wave amplitude equation is derived from the Navier-Stokes equations that is of gradient form. The associated Lyapunov function is calculated for different regular patterns to determine the selected pattern near threshold. For fluids of large viscosity, the selected wave pattern consists of parallel stripes. At lower viscosity, patterns of square symmetry are obtained in the capillary regime (large frequencies). At lower frequencies (the mixed gravity-capillary regime), a sequence of six-fold (hexagonal), eight-fold, ... patterns are predicted. The regions of stability of the various patterns are in quantitative agreement with recent experiments conducted in large aspect ratio systems.

patt-sol↗

arXiv1997

Pattern formation in weakly damped parametric surface waves driven by two frequency components

A quasi-potential approximation to the Navier-Stokes equation for low viscosity fluids is developed to study pattern formation in parametric surface waves driven by a force that has two frequency components. A bicritical line separating regions of instability to either one of the driving frequencies is explicitly obtained, and compared with experiments involving a frequency ratio of 1/2. The procedure for deriving standing wave amplitude equations valid near onset is outlined for an arbitrary frequency ratio following a multiscale asymptotic expansion of the quasi-potential equations. Explicit results are presented for subharmonic response to a driving force of frequency ratio 1/2, and used to study pattern selection. Even though quadratic terms are prohibited in this case, hexagonal or triangular patterns are found to be stable in a relatively large parameter region, a fact that is in qualitative agreement with experimental results.

patt-sol↗

arXiv1996

Pattern formation in weakly damped Faraday waves

We present a theoretical study of nonlinear pattern formation in parametric surface waves for fluids of low viscosity, and in the limit of large aspect ratio. The analysis is based on a quasi-potential approximation to the equations governing fluid motion, followed by a multiscale asymptotic expansion in the distance away from threshold. Close to onset, the asymptotic expansion yields an amplitude equation which is of gradient form, and allows the explicit calculation of the functional form of the cubic nonlinearities. In particular, we find that three-wave resonant interactions contribute significantly to the nonlinear terms, and therefore are important for pattern selection. Minimization of the associated Lyapunov functional predicts a primary bifurcation to a standing wave pattern of square symmetry for capillary-dominated surface waves, in agreement with experiments. In addition, we find that patterns of hexagonal and quasi-crystalline symmetry can be stabilized in certain mixed capillary-gravity waves, even in this case of single frequency forcing. Quasi-crystalline patterns are predicted in a region of parameters readily accessible experimentally.

patt-sol↗

arXiv1996

Motion of buoyant particles and coarsening of solid-liquid mixtures in a random acceleration field

Flow induced by a random acceleration field (g-jitter) is considered in two related situations that are of interest for microgravity fluid experiments: the random motion of an isolated buoyant particle and coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. We then study the motion of a solid particle suspended in an incompressible fluid that is subjected to such random accelerations. The displacement of the particle is shown to have a diffusive component if the correlation time of the stochastic acceleration is finite or zero, and mean squared velocities and effective diffusion coefficients are obtained explicitly. Finally, the effect of g-jitter on coarsening of a solid-liquid mixture is considered. Corrections due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, experiment to be conducted in microgravity in the near future.

patt-sol↗

arXiv1996

Modeling of Dislocation Structures in Materials

A phenomenological model of the evolution of an ensemble of interacting dislocations in an isotropic elastic medium is formulated. The line-defect microstructure is described in terms of a spatially coarse-grained order parameter, the dislocation density tensor. The tensor field satisfies a conservation law that derives from the conservation of Burgers vector. Dislocation motion is entirely dissipative and is assumed to be locally driven by the minimization of plastic free energy. We first outline the method and resulting equations of motion to linear order in the dislocation density tensor, obtain various stationary solutions, and give their geometric interpretation. The coupling of the dislocation density to an externally imposed stress field is also addressed, as well as the impact of the field on the stationary solutions.

mtrl-th↗