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Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift-Hohenberg EquationAug 22 2019In this paper, we carry out numerical bifurcation analysis of depinning of fronts near the homoclinic snaking region, involving a spatial stripe cellular pattern embedded in a quiescent state, in the two-dimensional Swift-Hohenberg equation with either ... More

Pattern localization to a domain edgeAug 20 2019The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive components have different ... More

From One Pattern into Another: Analysis of Turing Patterns in Heterogeneous Domains via WKBJAug 20 2019Symmetry breaking and pattern formation from homogeneity is well-studied, but much less is known concerning pattern-forming instabilities in heterogeneous media. In general it is difficult to separate observed spatial patterning due to inherent spatial ... More

Drift, stabilizing and destabilizing for a Keller-Siegel's system with the short-wavelength external signalAug 19 2019This article aims at exploring the short-wavelength stabilization and destabilization of the advection-diffusion systems formulated using the Patlak-Keller-Segel cross-diffusion. We study a model of the taxis partly driven by an external signal. We address ... More

Phase-separated symmetry-breaking vortex-lattice in a binary Bose-Einstein condensateAug 19 2019We study spontaneous-symmetry-breaking circularly-asymmetric phase separation of vortex lattices in a rapidly rotating harmonically-trapped quasi-two-dimensional (quasi-2D) binary Bose-Einstein condensate (BEC) with repulsive inter- and intra-species ... More

Dynamics of neural fields with exponential temporal kernelAug 17 2019In this paper, we consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatio-temporal wave patterns. ... More

Note on wavefront dislocation in surface water wavesAug 17 2019At singular points of a wave field, where the amplitude vanishes, the phase may become singular and wavefront dislocation may occur. In this Letter, we investigate for wave fields in one spatial dimension the appearance of these essentially linear phenomena. ... More

A model field theory with $(ψ\ln ψ)^2$ potential: Kinks with super-exponential profilesAug 14 2019We study a (1+1)-dimensional field theory based on $(\psi \ln \psi)^2$ potential. There are three degenerate minima at $\psi = 0$ and $\psi=\pm1$. There are novel, asymmetric kink solutions of the form $\psi = \mp\exp (-\exp(\pm x))$ connecting the minima ... More

Modulation instability, rogue waves and spectral analysis for the sixth-order nonlinear Schrodinger equationAug 14 2019Modulation instability, rogue wave and spectral analysis are investigated for the nonlinear Schrodinger equation with the higher-order terms. The modulation instability distribution characteristics from the sixth-order to the eighth-order nonlinear Schrodinger ... More

Topological Control of Extreme WavesAug 12 2019From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed because of the ... More

Nonlinear Spectroscopy and All-Optical Switching of Femtosecond Soliton MoleculesAug 12 2019The emergence of confined structures and pattern formation are exceptional manifestations of concurring nonlinear interactions found in a variety of physical, chemical and biological systems[1]. Optical solitons are a hallmark of extreme spatial or temporal ... More

Signaling gradients in surface dynamics as basis for planarian regenerationAug 12 2019Aug 13 2019We introduce and analyze a mathematical model for the regeneration of planarian flatworms. This system of differential equations incorporates dynamics of head and tail cells which express positional control genes that in turn translate into localized ... More

Signaling gradients in surface dynamics as basis for planarian regenerationAug 12 2019We introduce and analyze a mathematical model for the regeneration of planarian flatworms. This system of differential equations incorporates dynamics of head and tail cells which express positional control genes that in turn translate into localized ... More

Macroscopic oscillations locked and synchronized on fixed energy levels by two cooperating drivesAug 09 2019It was unknown whether the energy of a macroscopic object can be confined to a set of discrete values like the energy levels of microscopic systems. Here, through the numerical simulation and theoretical analysis based on an experimentally implementable ... More

Annihilation of magnetic domain walls induced spin wave burst intertwined with spin pumping: A multiscale time-dependent-quantum-transport/classical-micromagnetics approachAug 08 2019Motivated by recent experiments [S. Woo et al., Nat. Phys. 13, 448 (2017)] on magnetic-field-driven annihilation of two magnetic domain walls (DWs) and the ensuing burst of spin waves (SWs) of very short wavelengths, we predict that the same process is ... More

Annihilation of magnetic domain walls induced spin wave burst intertwined with spin pumping: A multiscale time-dependent-quantum-transport/classical-micromagnetics approachAug 08 2019Aug 09 2019Motivated by recent experiments [S. Woo, Nat. Phys. 13, 448 (2017)] on magnetic-field-driven annihilation of magnetic domain walls (DWs) and the ensuing burst of spin waves (SWs) of very short wavelengths, we predict that this is also accompanied by pumping ... More

Mode-Locked Rotating Detonation Waves: Experiments and a Model EquationAug 08 2019Aug 17 2019Direct observation of a Rotating Detonation Engine combustion chamber has enabled the extraction of the kinematics of its detonation waves. These records exhibit a rich set of instabilities and bifurcations arising from the interaction of coherent wave ... More

Mode-Locked Rotating Detonation Waves: Experiments and a Model EquationAug 08 2019Direct observation of a Rotating Detonation Engine combustion chamber has enabled the extraction of the kinematics of its detonation waves. These records exhibit a rich set of instabilities and bifurcations arising from the interaction of coherent wave ... More

Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximationsAug 07 2019Phase field crystal (PFC) theory, extensively used for modelling the structure of solids, can be derived from dynamical density functional theory (DDFT) via a sequence of approximations. Standard derivations neglect a term of form $\nabla\cdot[n\nabla ... More

Nonlinear dynamics of Josephson vortices in merging superfluid ringsAug 07 2019We consider merger of two parallel toroidal atomic Bose-Einstein condensates with different vorticities in a three-dimensional (3D) trap. In the tunnel-coupling regime, Josephson vortices (rotational fluxons) emerge in the barrier between the superflows. ... More

Further comments on BPS systemsAug 06 2019We look at BPS systems involving two interacting Sine-Gordon like fields both when one of them has a kink solution and the second one either a kink or an antikink solution. The interaction between the two fields is controlled by a parameter $\lambda$ ... More

Frequency comb generation through the locking of domain walls in doubly resonant dispersive optical parametric oscillatorsAug 06 2019In this letter we theoretically investigate the formation of localized temporal dissipative structures, and their corresponding frequency combs in doubly resonant dispersive optical parametric oscillators. We derive a nonlocal mean field model, and show ... More

Control of spatially rotating structures in diffractive Kerr cavitiesAug 05 2019Turing patterns in self-focussing nonlinear optical cavities pumped by beams carrying orbital angular momentum (OAM) $m$ are shown to rotate with an angular velocity $\omega = 2m/R^2$ on rings of radii $R$. We verify this prediction in 1D models on a ... More

Lump wave dynamics of saturated two-dimensional superfluid He-film with nontrivial bottom boundary conditionsAug 05 2019In this article, the free surface dynamics of saturated superfluid 4 He film is considered under the condition that there exists a very weak downward superfluid flow velocity into the substrate. For saturated film, the effect of surface tension plays ... More

Observation of the resonance frequencies of a stable torus of fluidAug 05 2019We report the first quantitative measurements of the resonance frequencies of a torus of fluid confined in a horizontal Hele-Shaw cell. By using the unwetting property of a metal liquid, we are able to generate a stable torus of fluid with an arbitrary ... More

Introduction to nonlinear discrete systems: Theory and modelingAug 05 2019An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate droplets. In basic ... More

Generation of shock waves from localized sources: The case of the Burgers equationAug 04 2019It is shown that the shock wave solutions of the Burgers equation can be generated from localized sources. The evolution equation obeyed by the sources has a novel characteristic: It has a single-soliton solution as well as an infinite family of localized-hump ... More

Asymptotically consistent prediction of extremes in chaotic systems:1 stationary caseAug 03 2019Aug 16 2019In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of the extreme ... More

Asymptotically consistent prediction of extremes in chaotic systems:1 stationary caseAug 03 2019In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of the extreme ... More

Chimera States and Seizures in a Mouse Neuronal ModelAug 02 2019Chimera states---the coexistence of synchrony and asynchrony in a nonlocally-coupled network of identical oscillators---are often used as a model framework for epileptic seizures. Here, we explore the dynamics of chimera states in a network of modified ... More

Camassa-Holm cuspons, solitons and their interactions via the dressing methodAug 02 2019A dressing method is applied to a matrix Lax pair for the Camassa-Holm equation, thereby allowing for the construction of several global solutions of the system. In particular solutions of system of soliton and cuspon type are constructed explicitly. ... More

User guide on Hopf bifurcation and time periodic orbits with pde2pathAug 02 2019We explain the setup for using the pde2path libraries for Hopf bifurcation and continuation of branches of periodic orbits and give implementation details of the associated demo directories. See [Uecker, Comm. in Comp. Phys., 2019] for a description of ... More

Nanophotonic supercontinuum based mid-infrared dual-comb spectroscopyAug 02 2019High resolution and fast detection of molecular vibrational absorption is important for organic synthesis, pharmaceutical process and environmental monitoring, and is enabled by mid-infrared (mid-IR) laser frequency combs via dual-comb spectroscopy. Here, ... More

Pattern formation with pde2path -- a tutorialAug 02 2019We explain some pde2path setups for pattern formation in 1D, 2D and 3D. A focus is on new pde2path functions for branch switching at steady bifurcation points of higher multiplicity, typically due to discrete symmetries, but we also review general concepts ... More

The $β$ Fermi-Pasta-Ulam-Tsingou Recurrence ProblemAug 01 2019We perform a thorough investigation of the first FPUT recurrence in the $\beta$-FPUT chain for both positive and negative $\beta$. We show numerically that the rescaled FPUT recurrence time $T_{r}=t_{r}/(N+1)^{3}$ depends, for large $N$, only on the parameter ... More

General rogue waves in the Boussinesq equationJul 31 2019We derive general rogue wave solutions of arbitrary orders in the Boussinesq equation by the bilinear Kadomtsev-Petviashvili (KP) reduction method. These rogue solutions are given as Gram determinants with $2N-2$ free irreducible real parameters, where ... More

Pattern formation and chimera states in 2D SQUID metamaterialsJul 31 2019The Superconducting QUantum Interference Device (SQUID) is a highly nonlinear oscillator with rich dynamical behavior, including chaos. When driven by a time-periodic magnetic flux, the SQUID exhibits extreme multistability at frequencies around the geometric ... More

Three-dimensional solitary waves with electrically tunable direction of propagation in nematicsJul 31 2019Production of stable multidimensional solitary waves is a grand challenge in modern science. Steering their propagation is an even harder problem. In this work we demonstrate three-dimensional solitary waves in a nematic, trajectories of which can be ... More

Scale-invariant relaxation dynamics in two-component Bose-Einstein condensates with large particle-number imbalanceJul 30 2019We theoretically study the scale-invariant relaxation dynamics in segregating two-component Bose-Einstein condensates with large particle-number imbalance, and uncover that random walk of droplet for the minor component plays a fundamental role in the ... More

Observation of Townes solitons in two-dimensional Bose gasesJul 29 2019New length scales often emerge in many-body systems driven out of equilibrium, leading to further development of delicate many-body states. Modulational instability, and the accompanying formation of solitons, is one important example. Here we report ... More

Breather arrest in a chain of damped oscillators with Hertzian contactJul 29 2019We explore breather propagation in the damped oscillatory chain with essentially nonlinear (non-linearizable) nearest-neighbour coupling. Combination of the damping and the substantially nonlinear coupling leads to rather unusual two-stage pattern of ... More

Excitation of bound states in the continuum via second harmonic generationsJul 29 2019A bound state in the continuum (BIC) on a periodic structure sandwiched between two homogeneous media is a guided mode with a frequency and a wavenumber such that propagating plane waves with the same frequency and wavenumber exist in the homogeneous ... More

Trait-space patterning and the role of feedback in antigen-immunity coevolutionJul 29 2019Coevolutionary arms races form between interacting populations that constitute each other's environment and respond to mutual changes. This inherently far-from-equilibrium process finds striking manifestations in the adaptive immune system, where highly ... More

Asymmetric behavior of surface waves induced by an underlying interfacial waveJul 25 2019We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial solitary-wave solutions ... More

Behavioral similarity of dissipative solitons in an ultrafast fiber laserJul 25 2019Dissipative solitons are non-dispersive localized waves that exhibit intriguing dynamics. In optical systems, the discovery of new soliton dynamics and how to accurately manipulate dissipative solitons are still largely unexplored and challenging in the ... More

The effects of coating culture dishes with collagen on fibroblast cell shape and swirling pattern formationJul 25 2019Motile human-skin fibroblasts form macroscopic swirling patterns when grown to confluence on a culture dish. In this paper, we investigate the effect of coating the culture-dish surface with collagen on the resulting pattern, using human-skin fibroblast ... More

Cross-Diffusion Waves as a Mesoscopic Uncertainty Relationship for Multi-Physics InstabilitiesJul 25 2019We propose a generic uncertainty relationship for cross-diffusion (quasi-soliton) waves triggered by local instabilities through Thermo-Hydro-Mechano-Chemical (THMC) coupling and cross-scale feedbacks. Cross-diffusion waves nucleate when the overall stress ... More

Mass-conservation sets excitable pulse collisions to be spatiotemporal organizing centersJul 24 2019Outcomes of propagating pulse collisions are of fundamental importance in many fields, ranging from physiology to industrial devices. Pulses are traditionally classified as solitons if upon collision they behave as particles, or excitable-pulses if they ... More

Spatially modulated two- and three-component Rabi-coupled Gross-Pitaevskii systemsJul 24 2019Vector rogue wave (RW) formation and their dynamics in Rabi coupled two- and three-species Bose-Einstein condensates with spatially varying dispersion and nonlinearity are studied. For this purpose, we obtain the RW solution of the two- and three-component ... More

The Replacement Rule for Nonlinear Shallow Water WavesJul 24 2019When a $(1+1)$-dimensional nonlinear PDE in real function $\eta(x,t)$ admits localized traveling solutions we can consider $L$ to be the average width of the envelope, $A$ the average value of the amplitude of the envelope, and $V$ the group velocity ... More

Ice Spiral Patterns on the Ocean SurfaceJul 22 2019We investigate a new two-dimensional compressible Navier-Stokes hydrodynamic model design to explain and study large scale ice swirls formation at the surface of the ocean. The linearized model generates a basis of Bessel solutions from where various ... More

Discontinuous shock solutions of the Whitham modulation equations as dispersionless limits of traveling wavesJul 22 2019Whitham modulation theory describes the zero dispersion limit of nonlinear waves by a system of conservation laws for the parameters of modulated periodic traveling waves. Here, admissible, discontinuous, weak solutions of the Whitham modulation equations--termed ... More

Discontinuous shock solutions of the Whitham modulation equations as dispersionless limits of traveling wavesJul 22 2019Aug 15 2019Whitham modulation theory describes the zero dispersion limit of nonlinear waves by a system of conservation laws for the parameters of modulated periodic traveling waves. Here, admissible, discontinuous, weak solutions of the Whitham modulation equations--termed ... More

Controlling capillary fingering using pore size gradients in disordered mediaJul 22 2019Capillary fingering is a displacement process that can occur when a non-wetting fluid displaces a wetting fluid from a homogeneous disordered porous medium. Here, we investigate how this process is influenced by a pore size gradient. Using microfluidic ... More

Soliton transmutations in KdV--Burgers layered mediaJul 21 2019We study the behavior of the soliton which, while moving in non-dissipative medium encounters a barrier with dissipation. The modelling included the case of a finite dissipative layer as well as a wave passing from a dissipative layer into a non-dissipative ... More

Effect of discrete breathers on macroscopic properties of the Fermi-Pasta-Ulam chainJul 20 2019For a number of crystals the existence of spatially localized nonlinear vibrational modes, called discrete breathers (DBs) or intrinsic localized modes (ILMs), has been demonstrated using molecular dynamics and in a few cases the first-principle simulations. ... More

Effect of discrete breathers on macroscopic properties of the Fermi-Pasta-Ulam chainJul 20 2019Aug 13 2019For a number of crystals the existence of spatially localized nonlinear vibrational modes, called discrete breathers (DBs), has been demonstrated using molecular dynamics and in a few cases the first-principle simulations. High-resolution imaging of DBs ... More

Stability of topologically protected edge states in nonlinear quantum walks: Additional bifurcations unique to Floquet nonlinear systemsJul 19 2019Quantum walk, a kind of systems with time-periodic driving (Floquet systems), is defined by a time-evolution operator, and can possess non-trivial topological phases. Recently, the stability of topologically protected edge states in a nonlinear quantum ... More

Rogue Heat and Diffusion WavesJul 18 2019In this paper, we numerically show and discuss the existence and characteristics of rogue heat and diffusion waves. More specifically, we use two different nonlinear heat (diffusion) models and show that modulation instability leads to the generation ... More

Bound state soliton gas dynamics underlying the noise-induced modulational instabilityJul 18 2019We investigate theoretically the fundamental phenomenon of the spontaneous, noise-induced modulational instability (MI) of a plane wave. The long-term statistical properties of the noise-induced MI have been previously observed in experiments and in simulations ... More

High-order couplings in geometric complex networks of neuronsJul 15 2019We explore the consequences of introducing higher-order interactions in a geometric complex network of Morris-Lecar neurons. We focus on the regime where travelling synchronization waves are observed out of a first-neighbours based coupling, to evaluate ... More

Inverse scattering transform for two-level systems with nonzero backgroundJul 14 2019We formulate the inverse scattering transform for the scalar Maxwell-Bloch system of equations describing the resonant interaction of light and active optical media in the case when the light intensity does not vanish at infinity. We show that pure background ... More

Spontaneous and engineered transformations of topological structures in nonlinear media with gain and lossJul 14 2019In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological transformations ... More

Attractors of Hamilton nonlinear partial differential equationsJul 13 2019We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global attraction to stationary states, to solitons and to stationary orbits, on adiabatic effective dynamics ... More

Which wavenumbers determine the thermodynamic stability of soft matter quasicrystals?Jul 12 2019For soft matter to form quasicrystals an important ingredient is to have two characteristic lengthscales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular ... More

Pattern formation in the presence of memoryJul 11 2019We study reaction-diffusion systems beyond the Markovian approximation to take into account the effect of memory on the formation of spatio-temporal patterns. Using a non-Markovian Brusselator model as a paradigmatic example, we show how to use reductive ... More

Phonon and Shifton from a Real Modulated ScalarJul 09 2019We study a massive real scalar field that breaks translation symmetry dynamically. Higher-gradient terms favour modulated configurations and neither finite density nor temperature are needed. In the broken phase, the energy density depends on the spatial ... More

Self-Localized Solitons of the Nonlinear Wave Blocking ProblemJul 08 2019Jul 15 2019In this paper, we propose a numerical framework to study the shapes, dynamics and the stabilities of the self-localized solutions of the nonlinear wave blocking problem. With this motivation, we use the nonlinear Schr\"odinger equation (NLSE) derived ... More

Self-Localized Solitons of the Nonlinear Wave Blocking ProblemJul 08 2019In this paper, we propose a numerical framework to study the shapes, dynamics and the stabilities of the self-localized solutions of the nonlinear wave blocking problem. With this motivation, we use the nonlinear Schr\"odinger equation (NLSE) derived ... More

Effect of discrete breathers on the specific heat of a nonlinear chainJul 07 2019In the present study, employing a one-dimensional nonlinear lattice with an on-site potential, we analyze the effect of discrete breathers (DBs) on its specific heat. In the most transparent way, this can be done by monitoring the chain temperature in ... More

Car following behavioral stochasticity analysis and modellingJul 07 2019This paper analyzes the car following behavioral stochasticity based on the experimental trajectory data by measuring the wave travel time Tn(t) of vehicle n. The analysis shows that the Tn(t) does not follow a consistent pattern. In particular, we found ... More

On a nonlinear model of the localized vacuum hypothesis, for solving the cosmological constant problemJul 05 2019Jul 18 2019A new model of oscillators was suggested, in which an oscillating particle in the minimum energy state has a nonzero velocity. A system consisting of a point material particle and a scalar field described by the nonlinear Klein-Gordon equation has been ... More

On the Soliton Model of the Local Vacuum Hypothesis, suggested to solve the cosmological constant problemJul 05 2019A new model of oscillators was suggested, in which an oscillating particle in the minimum energy state has a nonzero velocity. A system consisting of a point material particle and a scalar field described by the nonlinear Klein-Gordon equation has been ... More

Long time behavior of dynamic solution to Peierls--Nabarro dislocation modelJul 03 2019In this paper we study the relaxation process of Peierls-Nabarro dislocation model, which is a gradient flow with singular nonlocal energy and double well potential describing how the materials relax to its equilibrium with the presence of a dislocation. ... More

Model of pattern formation in marsh ecosystems with nonlocal interactionsJul 03 2019Smooth cordgrass Spartina alterniflora is a grass species commonly found in tidal marshes. It is an ecosystem engineer, capable of modifying the structure of its surrounding environment through various feedbacks. The scale-dependent feedback between marsh ... More

Darboux transformation and soliton solutions of the semi-discrete massive Thirring modelJul 03 2019A one-fold Darboux transformation between solutions of the semi-discrete massive Thirring model is derived using the Lax pair and dressing methods. This transformation is used to find the exact expressions for soliton solutions on zero and nonzero backgrounds. ... More

Kerr Frequency combs and dissipative Kerr solitons in non-linear coupled-cavity waveguidesJul 02 2019We derive a non-linear formalism from first principles to study Kerr frequency combs and dissipative Kerr solitons (DKS) in coupled-cavity waveguides (CCW), with Kerr non-linearity and two-photon absorption. We arrive to a system of non-linear coupled-mode ... More

New variational characterization of periodic waves in the fractional Korteweg-de Vries equationJul 02 2019Jul 23 2019Periodic waves in the fractional Korteweg-de Vries equation have been previously characterized as constrained minimizers of energy subject to fixed momentum and mass. Here we characterize these periodic waves as constrained minimizers of the quadratic ... More

New variational characterization of periodic waves in the fractional Korteweg-de Vries equationJul 02 2019Periodic waves in the fractional Korteweg-de Vries equation have been previously characterized as constrained minimizers of energy subject to fixed momentum and mass. Here we characterize these periodic waves as constrained minimizers of the quadratic ... More

Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue WavesJul 02 2019A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evidence ... More

MCF solitons and laser pulse self-compression at light bullet excitation in the central core of MCFJul 02 2019The propagation of laser pulses in multi-core fibers (MCF) made of a central core and an even number of cores located in a ring around it is studied. Approximate quasi-soliton homogeneous solutions of the wave field in the considered MCF are found. The ... More

MCF solitons and laser pulse self-compression at light bullet excitation in the central core of MCFJul 02 2019Jul 12 2019The propagation of laser pulses in multi-core fibers (MCF) made of a central core and an even number of cores located in a ring around it is studied. Approximate quasi-soliton homogeneous solutions of the wave field in the considered MCF are found. The ... More

Swirling of buckled pre-stressed active elastic filaments in a fluidJul 01 2019Slender filaments clamped at both ends and pre-stressed into a buckled planar shape are known to exhibit stable flapping oscillations in a dissipative medium under nonconservative follower forces. However, beyond a critical pre-stress value clamped rods ... More

Emergence of multiplicity of time scales in the modeling of climate, matter, life, and economyJul 01 2019We address dfferences between characteristic times in climate change and show the universal emergence of multiple time scales in material sciences, biomedicine and economics.

The Lefever-Lejeune nonlinear lattice: convergence dynamics and the structure of equilibrium statesJul 01 2019We consider the Lefever-Lejeune nonlinear lattice, a spatially discrete propagation-inhibition model describing the growth of vegetation densities in dry-lands. We analytically identify parametric regimes distinguishing between decay (associated with ... More

An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal EquationJun 28 2019In this paper we propose and analyze an energy stable numerical scheme for the square phase field crystal (SPFC) equation, a gradient flow modeling crystal dynamics at the atomic scale in space but on diffusive scales in time. In particular, a modification ... More

Kinetics of coarsening have dramatic effects on the microstructure: self-similarity breakdown induced by viscosity contrastJun 28 2019The viscous coarsening of a phase separated mixture is studied and the effects of the viscosity contrast between the phases are investigated. From an analysis of the microstructure, it appears that for moderate departure from the perfectly symmetric regime ... More

Orbital Bifurcations and Shoaling of Cnoidal WavesJun 27 2019We study the parameter space of cnoidal waves -- the periodic solitons of the Korteweg-de Vries equation -- from the perspective of Virasoro coadjoint orbits. The monodromy method familiar from inverse scattering implies that many, but not all, of these ... More

Stable controllable giant vortex in a trapped Bose-Einstein condensateJun 26 2019Jul 04 2019In a harmonically-trapped rotating Bose-Einstein condensate (BEC), a vortex of large angular momentum decays to multiple vortices of unit angular momentum from an energetic consideration. We demonstrate the formation of a robust and dynamically stable ... More

The ampsys tool of pde2pathJun 25 2019The computation of coefficients of amplitude systems for Turing bifurcations is a straightforward but sometimes elaborate task, in particular for 2D or 3D wave vector lattices. The Matlab tool ampsys automates such computations for two classes of problems, ... More

Snaking branches of planar BCC fronts in the 3D BrusselatorJun 25 2019We present results of the application of the numerical continuation and bifurcation package pde2path to the 3D Brusselator model, focusing on snaking branches of planar fronts between body centered cubes (BCCs) and the spatial homogeneous solution, and ... More

Study of strongly nonlinear oscillators using the Aboodh transform and the homotopy perturbation methodJun 25 2019A generalized equation is constructed for a class of classical oscillators with strong anharmonicity which are not exactly solvable. Aboodh transform based homotopy perturbation method (ATHPM) is applied to get the approximate analytical solution for ... More

Birth and decay of tensional wrinkles in hyperelastic sheetsJun 24 2019We demonstrate with experiments that wrinkling in stretched latex sheets occur over finite strains, and that their amplitudes grow and then decay to zero over a greater range of applied strains compared with linear elastic materials. The wrinkles occur ... More

Emergence of localized persistent weakly-evanescent cortical brain wave loopsJun 24 2019An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of non--evanescent (weakly damped) wave--like modes propagating in the thin cortex layers transverse to both the mean neural fiber direction and to ... More

Universal mechanism of low-frequency brain rhythm formation through nonlinear coupling of high-frequency spiking-like activityJun 24 2019A universal mechanism of emergence of synchronized low frequency brain wave field activity is presented as a result of nonlinear coupling with flat frequency neuronal forcing. The mechanism utilizes a unique dispersion properties of weakly-evanescent ... More

Semi-discrete quantum droplets and vorticesJun 23 2019We consider a binary bosonic condensate with weak mean-field (MF) repulsion, loaded in an array of nearly one-dimensional traps coupled by transverse hopping. With the MF force balanced by the effectively one-dimensional attraction, induced in each trap ... More

Turing-like patterns from purely reactive systemsJun 21 2019Almost 70 years ago A. Turing showed how species diffusion can lead to the emergence of coherent patterns in otherwise stable reactive systems. In this letter, we introduce a novel mechanism to generate spontaneous patterns even in absence of diffusion. ... More

A parity violating $φ^6$ soliton modelJun 20 2019In the present paper we propose an analytically solvable $\phi^6$ model with non-trivial soliton solutions connecting the trivial vacua. The model does not respect parity symmetry and like $\phi^4$ theory has two minima. The soliton solutions and the ... More

Spatiotemporal Stabilization of Locally PT-symmetric Semiconductor LasersJun 20 2019We provide a feasible and compact scheme to control and stabilize the spatiotemporal dynamics of BAS lasers. The proposal is based on the ability of non-Hermitian potentials with given local symmetries to manage the flow of light. A local PT-symmetric ... More

Spatiotemporal Stabilization of Locally PT-symmetric Semiconductor LasersJun 20 2019Jul 05 2019We provide a feasible and compact scheme to control and stabilize the spatiotemporal dynamics of BAS lasers. The proposal is based on the ability of non-Hermitian potentials with given local symmetries to manage the flow of light. A local PT-symmetric ... More