arXiv subjects

Luiza Angheluta

Publications and source records attributed to Luiza Angheluta.

At least 37 records · Page 2Linked to original sources

arXiv2022

Nucleation and kinematics of vortices in stirred Bose Einstein condensates

We apply the Halperin-Mazenco formalism within the Gross-Pitaevskii theory to characterise the kinematics and nucleation of quantum vortices in a two-dimensional stirred Bose Einstein condensate. We introduce a smooth defect density field measuring the superfluid vorticity and is a topologically conserved quantity. We use this defect density field and its associated current density to study the precursory pattern formations that occur inside the repulsive potential of an obstacle and determine the onset of vortex nucleation and shedding. We demonstrate that phase slips form inside hard potentials even in the absence of vortex nucleation, whereas for soft potentials they occur only above a critical stirring velocity leading to vortex nucleation. The Halperin-Mazenco formalism provides an elegant and accurate method of deriving the point vortex dynamic directly from the Gross-Pitaevskii equation.

cond-mat.quant-gas↗

arXiv2022

Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks

We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model captures better than previous formulations the dynamics of complex interfaces and dislocations in single crystals as well as grain boundary migration in poly-crystals where the long-range elastic field is properly relaxed. The proposed model features a diffusivity that depends non-linearly on the local phase. It induces more localized interfaces between a disordered phase (liquid-like) and an ordered phase, e.g., stripes or crystal lattices. For stripes, the interface dynamics are shown to be strongly anisotropic. We also show that the model is able to evolve the classical PFC at mechanical equilibrium. However, in contrast to previous approaches, it is not restricted to a single-crystal configuration or small distortions from a fixed reference lattice. To showcase the capabilities of this approach, we consider a few examples, from the annihilation of dislocation loops in a single crystal at mechanical equilibrium to the relaxation of a microstructure including crystalline domains with different orientations and grain boundaries. During the self-annihilation of a mixed type dislocation loop (i.e., not shear or prismatic), long-range elastic effects cause the loop to move out of plane before the annihilation event.

cond-mat.mtrl-sci↗

arXiv2022

Defect self-propulsion in active nematic films with spatially-varying activity

We study the dynamics of topological defects in active nematic films with spatially-varying activity and consider two setups: i) a constant activity gradient, and ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like $+1/2$ defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the $+1/2$ defect and has no effect on the $-1/2$ that remains a non-motile particle. A sharp jump in activity acts like a wall that traps the defects, affecting the translational and rotational motion of both charges. The $+1/2$ defect slows down as it approaches the interface and the net vorticity tends to reorient the defect polarization so that it becomes perpendicular to the interface. The $-1/2$ defect acquires a self-propulsion towards the activity interface, while the vorticity-induced active torque tends to align the defect to a preferred orientation. This effective attraction of the negative defects to the wall is consistent with the observation of an accumulation of negative topological charge at both active/passive interfaces and physical boundaries.

cond-mat.soft↗

arXiv2022

Trapping of active Brownian and run-and-tumble particles: a first-passage time approach

We use a first-passage time approach to study the statistics of the trapping times induced by persistent motion of active particles colliding with flat boundaries. The angular first-passage time distribution and mean first-passage time is calculated exactly for active Brownian and run-and-tumble particles and the results are compared. Theoretical predictions are in excellent agreement with Langevin simulations. Our results shed further light onto how active particles with different dynamics may be equivalent in the bulk, yet behave differently near boundaries or obstacles.

cond-mat.stat-mech↗

arXiv2022

Elasticity versus phase field driven motion in the phase field crystal model

The inherent inconsistency in identifying the phase field in the phase field crystal Theory with the material mass and, simultaneously, with material distortion is discussed. In its current implementation, elastic relaxation in the phase field crystal occurs on a diffusive time scale through a dissipative permeation mode. The very same phase field distortion that is included in solid elasticity drives diffusive motion, resulting in a non physical relaxation of the phase field crystal. We present two alternative theories to remedy this shortcoming. In the first case, it is assumed that the phase field only determines the incompatible part of the elastic distortion, and therefore one is free to specify an additional compatible distortion so as to satisfy mechanical equilibrium at all times (in the quasi static limit). A numerical solution of the new model for the case of a dislocation dipole shows that, unlike the classical phase field crystal model, it can account for the known law of relative motion of the two dislocations in the dipole. The physical origin of the compatible strain in this new theory remains to be specified. Therefore, a second theory is presented in which an explicit coupling between independent distortion and phase field accounts for the time dependence of the relaxation of fluctuations in both. Preliminary details of its implementation are also given.

cond-mat.mtrl-sci↗

arXiv2022

A phase field crystal theory of the kinematics of dislocation lines

We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion, including topological singularities, and the associated configurational stresses. We derive an exact expression for the velocity of dislocation line determined by the phase field evolution, and show that dislocation motion in the PFC is driven by a Peach-Koehler force. As is well known from earlier PFC model studies, the configurational stress is not divergence free for a general field configuration. Therefore, we also present a method (PFCMEq) to constrain the diffusive dynamics to mechanical equilibrium by adding an independent and integrable distortion so that the total resulting stress is divergence free. In the PFCMEq model, the far-field stress agrees very well with the predictions from continuum elasticity, while the near-field stress around the dislocation core is regularized by the smooth nature of the phase-field. We apply this framework to study the rate of shrinkage of an dislocation loop seeded in its glide plane.

cond-mat.mtrl-sci↗

arXiv2022

Collective states of active matter with stochastic reversals: emergent chiral states and spontaneous current switching

We study collective dynamical behavior of active particles with topological interactions and directional reversals. Surprising phenomena are shown to emerge as the interaction relaxation time is varied relative to the reversal rate, such as spontaneous formation of collective chiral states due to phase synchronization, and collective directional reversals in the presence of confinement. The results have a direct relevance to modelling and understanding collective reversals and synchronization phenomena in active matter.

cond-mat.soft↗

arXiv2022

Flow around topological defects in active nematic films

We study the active flow around isolated defects and the self-propulsion velocity of $+1/2$ defects in an active nematic film with both viscous dissipation (with viscosity $η$) and frictional damping $Γ$ with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length $\ell_d=\sqrt{η/Γ}$ that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the vortical flows around the defect is controlled by the system size $R$. In the presence of friction that leads to a finite value of $\ell_d$, the vorticity field decays to zero on the lengthscales larger than $\ell_d$. We show that the self-propulsion velocity of $+1/2$ defects grows with $R$ in small systems where $R<\ell_d$, while in the infinite system limit or when $R\gg \ell_d$, it approaches a constant value determined by $\ell_d$.

cond-mat.soft↗

arXiv2021

Stress in ordered systems: Ginzburg-Landau type density field theory

We present a theoretical method for deriving the stress tensor and elastic response of ordered systems within a Ginzburg-Landau type density field theory in the linear regime. This is based on spatially coarse graining the microscopic stress which is determined by the variation of a free energy with respect to mass displacements. We find simple expressions for the stress tensor for phase field crystal (PFC) models for different crystal symmetries in two and three dimensions. Using tetradic product sums of reciprocal lattice vectors, we calculate elastic constants and show that they are directly related to the symmetries of the reciprocal lattices. We also show that except for bcc lattices, there are regions of model parameters for which the elastic response is isotropic. The predicted elastic stress-strain curves are verified by numerical strain-controlled bulk and shear deformations. Since the method is independent of a reference state, it extends also to defected crystals. We exemplify this by considering an edge and screw dislocation in the simple cubic lattice.

cond-mat.mtrl-sci↗

arXiv2020

The role of fluid flow in the dynamics of active nematic defects

We adapt the Halperin-Mazenko formalism to analyze two-dimensional active nematics coupled to a generic fluid flow. The governing hydrodynamic equations lead to evolution laws for nematic topological defects and their corresponding density fields. We find that $\pm 1/2$ defects are propelled by the local fluid flow and by the nematic orientation coupled with the flow shear rate. In the overdamped and compressible limit, we recover the previously obtained active self-propulsion of the +1/2 defects. Non-local hydrodynamic effects are primarily significant for incompressible flows, for which it is not possible to eliminate the fluid velocity in favor of the local defect polarization alone. For the case of two defects with opposite charge, the non-local hydrodynamic interaction is mediated by non-reciprocal pressure-gradient forces. Finally, we derive continuum equations for a defect gas coupled to an arbitrary (compressible or incompressible) fluid flow.

cond-mat.soft↗

arXiv2020

Dislocation nucleation in the phase field crystal model

We use the phase field crystal model to study nucleation of edge dislocations in two dimensions under an applied stress field. A dislocation dipole nucleates under the applied stress, consistent with Burgers vector conservation. The phase field correctly accounts for elastic energy storage prior to nucleation, and for dissipative relaxation during the nucleation event. We show that a lattice incompatibility field is a sensitive diagnostic of the location of the nucleation event, and of the Burgers vector and slip direction of the dislocations that will be nucleated above threshold. A direct calculation of the phase field energy accurately correlates with the nucleation event, as signaled by the lattice incompatibility field. We show that a Schmid-like criterion concerning the resolved stress at the nucleation site correctly predicts the critical nucleation stress. Finally, we present preliminary results for a three-dimensional, body-centered cubic lattice. The phase field allows a direct computation of the lattice incompatibility tensor for both dislocation lines and loops.

cond-mat.mtrl-sci↗

arXiv2020

The escape problem for active particles confined to a disc

We study the escape problem for interacting, self-propelled particles confined to a disc, where particles can exit through one open slot on the circumference. Within a minimal 2D Vicsek model, we numerically study the statistics of escape events when the self-propelled particles can be in a flocking state. We show that while an exponential survival probability is characteristic for non-interaction self-propelled particles at all times, the interacting particles have an initial exponential phase crossing over to a sub-exponential late-time behavior. We propose a new phenomenological model based on non-stationary Poisson processes which includes the Allee effect to explain this sub-exponential trend and perform numerical simulations for various noise intensities.

cond-mat.stat-mech↗

arXiv2020

Onset of turbulence in channel flows with scale-invariant roughness

Using 3D direct numerical simulations of the Navier--Stokes equations, we study the effect of wall roughness on the onset of turbulence in channel flow. The dependence of the friction factor on the Reynolds number, $\mathrm{Re}$, is found to follow a generalized Forchheimer law, which interpolates between the laminar and inertial asymptotes. The transition between these two asymptotes occurs at a first critical $\mathrm{Re}$, $\mathrm{Re}_{\mathrm{c}}$, that depends nontrivially on the roughness amplitude. We identify the transition from subcritical to supercritical onset by looking at the dependence of the velocity fluctuations on Re for different roughness amplitudes. We find that this second critical $\mathrm{Re}$ is comparable in magnitude to $\mathrm{Re}_{\mathrm{c}}$, implying that transitional flow is an integral part of flow in open fractures when $\mathrm{Re}$ and the roughness amplitude are sufficiently high.

physics.flu-dyn↗

arXiv2020

Spectral link of the generalized Townsend-Perry constants in turbulent boundary layers

We propose a minimal spectral theory for boundary layer turbulence that captures very well the profile of the mean square velocity fluctuations in the stream-wise direction, and gives a quantitative prediction of the Townsend-Perry constants. The phenomenological model is based on connecting the statistics in the streamwise direction with the energy spectrum of the streamvise velocity fluctuations. The original spectral theory was proposed earlier to explain the friction factor and the von Kármán law. We generalized it by including fluctuations in the wall-shear stress and the streamwise velocity. The predicted profiles for the mean velocity and mean square fluctuations are compared with velocity data from wind tunnel experiments.

physics.flu-dyn↗

arXiv2020

Classical analogies for the force acting on an impurity in a Bose-Einstein condensate

We study the hydrodynamic forces acting on a small impurity moving in a two-dimensional Bose-Einstein condensate at non-zero temperature. The condensate is modelled by the damped-Gross Pitaevskii (dGPE) equation and the impurity by a Gaussian repulsive potential coupled to the condensate. For weak coupling, we obtain analytical expressions for the forces acting on the impurity, and compare them with those computed through direct numerical simulations of the dGPE and with the corresponding expressions for classical forces. For non-steady flows, there is a time-dependent force dominated by inertial effects and which has a correspondence in the Maxey-Riley theory for particles in classical fluids. In the steady-state regime, the force is dominated by a self-induced drag. Unlike at zero temperature, where the drag force vanishes below a critical velocity, at low temperatures the impurity experiences a net drag even at small velocities, as a consequence of the energy dissipation through interactions of the condensate with the thermal cloud. This dissipative force due to thermal drag is similar to the classical Stokes' drag. There is still a critical velocity above which steady-state drag is dominated by acoustic excitations and behaves non-monotonically with impurity's speed.

cond-mat.quant-gas↗

arXiv2019

A coarse-grained phase-field crystal model of plastic motion

The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the elastic distortion and stress regularization at a dislocation core and show how the Burgers vector density can be directly computed from the topological singularities of the phase-field amplitudes. Distortions arising from these amplitudes are then supplemented with non-singular displacements to enforce mechanical equilibrium. This allows for the consistent separation of plastic and elastic time scales in this framework. A finite element method is introduced to solve the combined amplitude and elasticity equations, which is applied to a few prototypical configurations in two spatial dimensions for a crystal of triangular lattice symmetry: i) the stress field induced by an edge dislocation with an analysis of how the amplitude equation regularizes stresses near the dislocation core, ii) the motion of a dislocation dipole as a result of its internal interaction, and iii) the shrinkage of a rotated grain. We also compare our results with those given by other extensions of classical elasticity theory, such as strain-gradient elasticity and methods based on the smoothing of Burgers vector densities near defect cores.

cond-mat.mtrl-sci↗

arXiv2018

Mesoscale model of dislocation motion and crystal plasticity

A consistent, small scale description of plastic motion in a crystalline solid is presented based on a phase field description. By allowing for independent mass motion given by the phase field, and lattice distortion, the solid can remain in mechanical equilibrium on the timescale of plastic motion. Singular (incompatible) strains are determined by the phase field, to which smooth distortions are added to satisfy mechanical equilibrium. A numerical implementation of the model is presented, and used to study a benchmark problem: the motion of an edge dislocation dipole in a hexagonal lattice. The time dependence of the dipole separation agrees with classical elasticity without any adjustable parameters.

cond-mat.mtrl-sci↗

arXiv2017

Dislocation dynamics and crystal plasticity in the phase field crystal model

A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy and show that it obeys the stress strain relation of linear elasticity. Dislocations in a two dimensional hexagonal lattice are shown to be composite topological defects in the amplitude expansion of the phase field, with topological charges given by the Burgers vector. This allows us to introduce a formal relation between dislocation velocity and the evolution of the coarse grained envelopes of the phase field. Standard dissipative dynamics of the phase field crystal model is shown to determine the velocity of the dislocations. When the amplitude equation is valid, we derive the Peach-Koehler force on a dislocation, and compute the associated defect mobility. A numerical integration of the phase field crystal equations in two dimensions is used to compute the motion of a dislocation dipole, and good agreement is found with the theoretical predictions.

cond-mat.mtrl-sci↗