Front Pinning Research Articles

Deterministic Assembly of Colloidal Quantum Dots for Multifunctional Integrated Photonics.

Colloidal quantum dots (CQDs) are promising for photonic applications toward lasers, waveguides, and photodetectors. However, integration of high-quality photonic elements into multifunctional devices is still restricted by optical losses stemming from the accumulation of defects and disorder in the solution process. Herein, a platform with a directional Laplace pressure is created for eliminating undesired pinning of liquid fronts in the solution process and boosting ordered assembly of CQDs into designable micro-/nanostructures. The versatility and robustness of this method are demonstrated by deterministic patterning of CQDs with different components and photoluminescence spectra onto various substrates. On the basis of this platform, microring lasers with tunable emission modes, low-loss waveguides, and their coupled structures have been reached for direct on-chip generation and propagation of coherent light. A proof-of-concept demonstration of integrated circuits is also conducted by combining microcavity lasers with waveguides for encoding photonic outputs into information bits.

A continuum model of unstable infiltration in porous media endowed with an entropy function

We propose a thermodynamic approach to modeling unsaturated flow in porous media, where the liquid saturation is understood as the state variable. The free energy functional is designed as a symmetric expansion of the traditional capillary energy density in Richards equation, therefore removing ambiguities on the interpretation of the higher-order term in the model equation. The proposed definition renders a formulation that leads naturally to an entropy function of the system, and we show that the model describes an entropy-increasing process for an isolated system.The new formulation reproduces gravity fingering during infiltration in soil. We show that the nonlinear and singular structure of the capillary pinning function in the fourth-order term plays a fundamental role in the behavior and stability of infiltration fronts, promoting front pinning and the persistence of fingered infiltration at relatively large flux ratios.

Role of Poisson’s ratio mismatch on the crack path in glass matrix particulate composites

The improvement of the mechanical properties of glass matrix particulate composites has been extensively studied in the past 40 years. Emphasis has mostly been placed on the influence of mismatches of the elastic moduli and coefficient of thermal expansion. However, little attention was paid to Poisson’s ratio $$(\upnu )$$ so far, although we show by means of analytical analysis and finite element method (FEM) that it has a major influence on the stress field distribution, the stress intensity factor and thus on the crack path in the vicinity of the inclusion. Due to local stress changes, crack front pinning and bridging phenomena are predicted in the case of adhesive particles with $$\upnu $$ smaller than the one of the matrix. Nevertheless, when located close to the surface, such particles might play the role of stress concentrators. Glass offers a unique opportunity to vary composition and properties in a continuous manner, hence opening a new realm of possibilities for tuning Poisson’s ratio to improve the resistance the glass composite opposes to crack extension.

Splitting in the pinning-depinning transition of fronts in long-delayed bistable systems.

We investigate the formation of localized domains through front pinning in a periodically forced, bistable semiconductor laser with long-delayed optoelectronic feedback. At difference with 1D spatially extended systems, the transition from the pinning to the propagation regime occurs via two separated bifurcations, each corresponding to the unpinning of one of the fronts surrounding the localized domain. The bifurcation splitting is systematically explored, unveiling the crucial role played by the forcing frequency. The experimental results are reproduced and interpreted by means of a prototypical model of our system.

Forced snaking: Localized structures in the real Ginzburg-Landau equation with spatially periodic parametric forcing

We study spatial localization in the real subcritical Ginzburg-Landau equation u t = m 0 u + Q(x)u + u xx + d|u|2 u −|u|4 u with spatially periodic forcing Q(x). When d>0 and Q ≡ 0 this equation exhibits bistability between the trivial state u = 0 and a homogeneous nontrivial state u = u 0 with stationary localized structures which accumulate at the Maxwell point m 0 = −3d 2/16. When spatial forcing is included its wavelength is imprinted on u 0 creating conditions favorable to front pinning and hence spatial localization. We use numerical continuation to show that under appropriate conditions such forcing generates a sequence of localized states organized within a snakes-and-ladders structure centered on the Maxwell point, and refer to this phenomenon as forced snaking. We determine the stability properties of these states and show that longer lengthscale forcing leads to stationary trains consisting of a finite number of strongly localized, weakly interacting pulses exhibiting foliated snaking.

Spatial Localization in Dissipative Systems

Spatial localization is a common feature of physical systems, occurring in both conservative and dissipative systems. This article reviews the theoretical foundations of our understanding of spatial localization in forced dissipative systems, from both a mathematical point of view and a physics perspective. It explains the origin of the large multiplicity of simultaneously stable spatially localized states present in a parameter region called the pinning region and its relation to the notion of homoclinic snaking. The localized states are described as bound states of fronts, and the notions of front pinning, self-pinning, and depinning are emphasized. Both one-dimensional and two-dimensional systems are discussed, and the reasons behind the differences in behavior between dissipative systems with conserved and nonconserved dynamics are explained. The insights gained are specific to forced dissipative systems and are illustrated here using examples drawn from fluid mechanics (convection and shear flows) and a simple model of crystallization.

Species coexistence by front pinning

The spatial competition between two plant species that make different compromises in capturing soil water and sunlight is studied using a mathematical model. A precipitation range along the rainfall gradient is identified where two alternative stable states coexist. The first state describes a uniform distribution of a plant species that specializes in capturing soil water, whereas the second state describes a periodic pattern of a species that specializes in capturing light. We show that this bistability range generally divides into three parts according to the dynamics of the front or ecotone that separates the two plant populations: a low precipitation range where the superior competitor for water displaces the superior competitor for light, a high precipitation range where the displacement is reversed, and an intermediate range where neither species displaces the other. While in the low and high precipitation ranges one species outcompetes the other, the intermediate range allows for species coexistence in the form of a multitude of stable localized solutions consisting of fixed domains of one species in areas otherwise occupied by the other species. These localized solutions can only be realized when one of the alternative stable states is spatially patterned. We further study two factors that affect the size of the species coexistence range: the strength of the competition for light and the form of the tradeoff between the competitive abilities to capture water and light.

Strong pinning of propagation fronts in adverse flow.

Reaction fronts evolving in a porous medium exhibit a rich dynamical behavior. In the presence of an adverse flow, experiments show that the front slows down and eventually gets pinned, displaying a particular sawtooth shape. Extensive numerical simulations of the hydrodynamic equations confirm the experimental observations. Here we propose a stylized model, predicting two possible outcomes of the experiments for large adverse flow: either the front develops a sawtooth shape or it acquires a complicated structure with islands and overhangs. A simple criterion allows one to distinguish between the two scenarios and its validity is reproduced by direct hydrodynamical simulations. Our model gives a better understanding of the transition and is relevant in a variety of domains, when the pinning regime is strong and only relies on a small number of sites.

Effects of asymmetry in an output function on the pinning of rotating waves in a ring neural oscillator with asymmetric bidirectional coupling and self-coupling

Effects of asymmetry in a sigmoidal output function of neurons on rotating waves in a ring of neurons with asymmetric bidirectional coupling and self-coupling were studied. Propagation of wave fronts in rotating waves failed, i.e., the pinning of rotating waves occurred not only when self-coupling was excitatory but also when self-coupling was inhibitory, in which there were unsaturated neurons at wave fronts. Conditions for the pinning of wave fronts were derived by using a piecewise linear output function. The pinning conditions depended on whether bidirectional coupling was excitatory or inhibitory in the presence of asymmetry in an output function.

Front Pinning and Localized States Analogues in Long-Delayed Bistable Systems

Localized structures have been observed in many spatially extended systems of either biological, chemical, or physical nature. Here, we study experimentally front pinning and dissipative localized structures in a delayed optical system based on a bistable semiconductor laser with optoelectronic feedback. We observe that many of the concepts known to apply to spatially localized structures also apply in this context, with specificities related to the lack of reversibility symmetry. Numerical simulations based on purely prototypical modeling reproduce very well the experimental findings, which indicates that the results do not depend on the specific physical system under consideration, but are, on the contrary, very generic features of time delayed systems.

Analytical Results for Front Pinning between an Hexagonal Pattern and a Uniform State in Pattern-Formation Systems

In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an homogeneous background. In two dimensions, the ordered pattern is most often hexagonal and the conditions for fronts to stabilize are still unknown. In this Letter, we show how the locking of these fronts depends on their orientation relative to the pattern. The theory rests on general asymptotic arguments valid when the spatial scale of the front is slow compared to that of the hexagonal pattern. Our analytical results are confirmed by numerical simulations with the Swift-Hohenberg equation, relevant to hydrodynamical and buckling instabilities, and a nonlinear optical cavity model.

Autocatalytic reaction fronts inside a porous medium of glass spheres.

We analyze experimentally chemical wave propagation in the disordered flow field of a porous medium. The reaction fronts travel at a constant velocity that drastically depends on the mean flow direction and rate. The fronts may propagate either downstream and upstream but, surprisingly, they remain static over a range of flow rate values. Resulting from the competition between the chemical reaction and the disordered flow field, these frozen fronts display a particular sawtooth shape. The frozen regime is likely to be associated with front pinning in low velocity zones, the number of which varies with the ratio of the mean flow and the chemical front velocities.

Finite size effects on crack front pinning at heterogeneous planar interfaces: Experimental, finite elements and perturbation approaches

Understanding the role played by the microstructure of materials on their macroscopic failure properties is an important challenge in solid mechanics. Indeed, when a crack propagates at a heterogeneous brittle interface, the front is trapped by tougher regions and deforms. This pinning induces non-linearities in the crack propagation problem, even within Linear Elastic Fracture Mechanics theory, and modifies the overall failure properties of the material. For example crack front pinning by tougher places could increase the fracture resistance of multilayer structures, with interesting technological applications. Analytical perturbation approaches, based on Bueckner–Rice elastic line models, focus on the crack front perturbations, and hence allow for a description of these phenomena. Here, they are applied to experiments investigating the propagation of a purely interfacial crack in a simple toughness pattern: a single defect strip surrounded by homogeneous interface. We show that by taking into account the finite size of the body, quantitative agreement with experimental and finite elements results is achieved. In particular this method allows to predict the toughness contrast, i.e. the toughness difference between the single defect strip and its homogeneous surrounding medium. This opens the way to a more accurate use of the perturbation method to study more disordered heterogeneous materials, where the finite elements method is less adequate. From our results, we also propose a simple method to determine the adhesion energy of tough interfaces by measuring the crack front deformation induced by known interface patterns.

Traveling and pinned fronts in bistable reaction-diffusion systems on networks.

Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed.

Depinning, front motion, and phase slips

Pinning and depinning of fronts bounding spatially localized structures in the forced complex Ginzburg-Landau equation describing the 1:1 resonance is studied in one spatial dimension, focusing on regimes in which the structure grows via roll insertion instead of roll nucleation at either edge. The motion of the fronts is nonlocal but can be analyzed quantitatively near the depinning transition.

Vapor-Liquid-Solid 成長を用いて作製した人工ピン導入 REBa2Cu3O7−y 膜の微細組織

In order to improve a critical current density under applied magnetic fields, an addition of BaMO3 (BMO; M=Zr, Sn) nanorods into REBa2Cu3Oy (REBCO) films is actively discussed. Although superconducting properties of the REBCO films are dramatically enhanced by self-assembled BMO nanorods, the growth mechanisms of the BMO nanorods have not been clarified yet. In this study, in order to clarify the growth mechanisms of the BZrO3 (BZO) nanorods and to further improve the superconducting properties, we fabricated a BZO-doped Sm1+xBa2−xCu3Oy (Sm+BZO) film by using modified Vapor-Liquid-Solid (VLS) technique (VLS-Sm+BZO/i). From the surface morphologies, there are BZO particles grown at step in the spiral growth measured by Br-etched VLS films doped with BZO. In general the impurity-related phase was pinning of growth fronts on REBCO films on substrate. Thus, we can conclude the variation of the surface morphology in VLS films is explained, not by the difference the step energy, but impurity phase could be responsible for the pinning and bending of different growth fronts, resulting in the formation of screw dislocations. From the plan-view TEM images, VLS-SmBCO+BZO film is approximately 9 nm in diameter of BZO nanorods, whereas VLS-SmBCO+BZO/i film is 7-8 nm. To create the BZO nano island/dots on the seed layer introduced the increase of the density of BZO nanorods. From the cross-sectional TEM images, columns of BZO nanorods aligned along [001] or the c-axis of SmBCO are clearly seen in the VLS films. Columnar BZO structures growing from the substrate to the surface have been observed. Nano BZO particles grown on the seed layer remained after the VLS growth. Nano BZO rods separated by 5 nm SmBCO spacer layers are shown to exhibit self-organized growth along c-axis of SmBCO.

Direct observation and analysis of crack front morphology during crack pinning by heterogeneous interface

Adhesion of thin film multilayers deposited on gla ss is a crucial issue for many industrial applications. Thus, it becomes of g reat interest to measure and also to increase the adhesion. Many mechanisms of toughening a brittle solid can be found in literature; but few of them can be applied to thin film layer. By introducing a heterogeneous interfacial toughness field, it shoul d be possible to increase adhesion. This toughness modification would be the consequence of the existence of a pinning regime due to a local change of the toughness. To e xperimentally validate this new approach of adhesion modification, we investigate t he crack front pinning by performing cleavage tests on multilayer coated samples with a heterogeneous interfacial toughness. We have tested different patterns of pinning region . The crack front morphology was nicely described in the framework of the perturbati ve approach initially developed by Gao and Rice and allowed us to determine the local v alue of the energy release rate (~adhesion).

Crack front pinning by design in planar heterogeneous interfaces

The propagation of an interfacial crack front along the weak plane of a thin film stack is considered. A simple patterning technique is used to create a toughness contrast within this perfectly two-dimensional weak interface. The transparency of the specimens allows us to directly observe the propagation of the purely planar crack obtained during a DCB (double cantilever beam) test. The effect on the crack front morphology of macroscopic unidimensional patterns in the direction of propagation is studied. In these weak pinning conditions, the geometry of the front quantitatively agrees with the first-order expansion proposed by Gao and Rice [1989. First-order perturbation analysis of crack trapping by arrays of obstacles. J. Appl. Mech. 56, 828–836] which accounts for the effect of the interfacial crack front geometry on the stress intensity factor.

Front pinning in capillary filling of chemically coated channels

The dynamics of capillary filling in the presence of chemically coated heterogeneous boundaries is investigated both theoretically and numerically. In particular, by mapping the equations of front motion onto the dynamics of a dissipative driven oscillator, an analytical criterion for front pinning is derived under the condition of diluteness of the coating spots. The criterion is tested against two-dimensional lattice Boltzmann simulations and found to provide satisfactory agreement as long as the width of the front interface remains much thinner than the typical heterogeneity scale of the chemical coating.

Stability of front solutions in inhomogeneous media

We use the FitzHugh–Nagumo (F–N) model to study front solutions in inhomogeneous media. Inhomogeneity is modeled by adding a space-dependent term, z( x), in the equations. Changes in z shift the cubic nullcline up and down in the phase-plane of the F–N model. This is used to mimic shifts in the cubic-shaped nullcline of a bidomain model of calcium waves in egg cells [Physica D, in press] caused by changes in the total calcium concentration. Conditions for the existence and stability of stationary front solutions for a general class of z functions are obtained analytically when the dynamics are piecewise linear. We show that spatial inhomogeneities cause pinning and oscillations of front solutions. This is best demonstrated when z( x) is a linear ramp. When the slope is large, a linear ramp breaks the translational invariance of the stationary front and stabilizes the front. The front becomes less stable as the slope decreases. At a critical slope, the front becomes unstable through a Hopf bifurcation beyond which oscillations in the front occur. This also occurs for nonlinear spatial inhomogeneities including a step increase with varying magnitude and steepness. This bifurcation has been found previously [Physica D 106 (1997) 270; Phys. Rev. E 55 (1997) 366] in a local analysis of the F–N model near a co-dimension two point (sometimes called a non-equilibrium Ising–Bloch (NIB) bifurcation) and with inhomogeneities of small magnitude. The analysis presented here applies globally in parameter space and is valid for inhomogeneities of arbitrary magnitude. We show that this bifurcation need not occur in conjunction with the NIB point. It is caused exclusively by spatial inhomogeneity. A rich variety of wave phenomena including front oscillation, front pinning, and front reflection are shown to occur in inhomogeneous media.