Interface Fluctuations Research Articles

Interplay between partnership formation and competition in generalized May-Leonard games

In order to better understand the interplay of partnership and competition in population dynamics we study a family of generalized May-Leonard models with $N$ species. These models have a very rich structure, characterized by different types of space-time patterns. Interesting partnership formations emerge following the maxim that "the enemy of my enemy is my friend." In specific cases cyclic dominance within coarsening clusters yields a peculiar coarsening behavior with intriguing pattern formation. We classify the different types of dynamics through the analysis of the square of the adjacency matrix. The dependence of the population densities on emerging pattern and propagating wave fronts is elucidated through a Fourier analysis. Finally, after having identified collaborating teams, we study interface fluctuations where we initially populate different parts of the system with different teams.

A fully discrete finite element scheme for the Derrida-Lebowitz-Speer-Spohn equation

The Derrida-Lebowitz-Speer-Spohn (DLSS) equation is a fourth order in space non-linear evolution equation. This equation arises in the study of interface fluctuations in spin systems and quantum semiconductor modelling. In this paper, we present a positive preserving finite element discrtization for a coupled-equation approach to the DLSS equation. Using the available information about the physical phenomena, we are able to set the corresponding boundary conditions for the coupled system. We prove existence of a global in time discrete solution by fixed point argument. Numerical results illustrate the quantum character of the equation. Finally a test of order of convergence of the proposed discretization scheme is presented.

Viscous fingering at ultralow interfacial tension

We experimentally study the viscous fingering instability in a fluid-fluid phase separated colloid-polymer mixture by means of laser scanning confocal microscopy and microfluidics. We focus on three aspects of the instability. (i) The interface between the two demixed phases has an ultralow surface tension, such that we can address the role of thermal interface fluctuations. (ii) We image the interface in three dimensions allowing us to study the interplay between interface curvature and flow. (iii) The displacing fluid wets all walls completely, in contrast to traditional viscous fingering experiments, in which the displaced fluid wets the walls. We also perform lattice Boltzmann simulations, which help to interpret the experimental observations.

Compositional interface dynamics within symmetric and asymmetric planar lipid bilayer membranes

Compositional domains within multicomponent lipid bilayer membranes are believed to facilitate many important cellular processes. In this work, we first derive the general equations that describe the dynamics of compositional domains within planar membranes with asymmetry in leaflet properties and in the presence of a thermodynamic coupling between the leaflets. These equations are then employed to develop analytical solutions for the dynamics of the recurrence of registration for circular domains in the case of weak coupling. In addition, a closed-form expression for the decay rate of interface fluctuations, when only one leaflet supports compositional domains, is derived.

Faunal dynamics of gastropods in the Bathonian (Middle Jurassic) ore-bearing clays at Gnaszyn, Kraków-Silesia Homocline, Poland

ABSTRACT Kaim, A. 2012. Faunal dynamics of gastropods in the Bathonian (Middle Jurassic) ore-bearing clays at Gnaszyn, Kraków-Silesia Homocline, Poland. Acta Geologica Polonica, 62(3), 367-380. Warszawa. The succession of gastropods in the Gnaszyn section is quite monotonous and shows significant changes only in the proximity of concretion layers, at least partially because of diagenetic reasons. Otherwise, the section is dominated by gastropods (cylidrobullinids, bullinids, and mathildids) most of which preyed probably on sedentary organisms (polychaetes and/or coelenterates) that possibly flourished on the sea bottom at that time. The other groups of gastropods are represented by larval or juvenile shells. Their presence shows that the environmental conditions that were probably unfavourable for gastropods living directly on the sea bottom most likely because of a soupy substrate consistency, possible oxygen deficiency near the sediment-water interface and/or oxygen content fluctuations. Adult and/or subadult individuals of these gastropods occur only in the higher part of the section, reflecting a time when these conditions improved. A new heterostrophic gastropod species, Promathildia gedli, is described.

Faunal dynamics of bivalves and scaphopods in the Bathonian (Middle Jurassic) ore-bearing clays at Gnaszyn, Kraków-Silesia Homocline, Poland

ABSTRACT Kaim, A. and Sztajner, P. 2012. Faunal dynamics of bivalves and scaphopods in the Bathonian (Middle Jurassic) ore-bearing clays at Gnaszyn, Kraków-Silesia Homocline, Poland. Acta Geologica Polonica, 62(3), 381- 395. Warszawa. The environment at the Gnaszyn section - as deduced from bivalve and scaphopod dynamics - was controlled by the substrate consistency and possibly oxygen deficiency near the sediment-water interface and/or oxygen content fluctuations. The middle part of the section dominated by nuculoid and corbulid bivalves and Laevidentalium -type scaphopods probably reflects a soupy substrate and possibly oxygen deficiency in the sediment. Slightly coarser and better-oxygenated silts in the upper and lower parts of the section offered a less soupy substrate consistency, allowing the development of communities dominated by astartids, byssate bivalves, and Dentalium - and Plagioglypta-type scaphopods.

Spinodal decomposition of a confined colloid-polymer system

We study the demixing via spinodal decomposition of a fluid-fluid phase separating colloid-polymer mixture confined between parallel plates, where one of the phases completely wets both walls. Using confocal scanning laser microscopy, we are able to obtain real space images, both parallel and perpendicular to the cell walls. We observe three distinct morphologies: the formation of a bicontinuous network, which coarsens into cylindrical tubes bridging the plates, and finally develops into a network structure in two dimensions. Through image analysis of the system as a whole, and the tracking of individual domains, we are able to perform a detailed study of the mechanisms of phase coarsening at each stage. We are able to directly test the condition for which bridges connecting both confining walls do not sever. Finally, we consider the role of hydrodynamics and of thermal interface fluctuations in our system.

Photonic Crystal Fiber With Two Infiltrated Air Holes for Temperature Sensing With Excellent Temporal Stability

A photonic crystal fiber sensor is created by infiltrating liquid with higher refractive index than background silica into two adjacent air holes situated in different layers. When the refractive index of the liquid is decreased to that of silica by heating, the two liquid rods and the solid core form a three-parallel-waveguide structure, which enables efficient mode energy coupling between the two eigenmodes and results in an interference fringe pattern. Theoretical analysis has been carried out to reveal the modes involved in the interference. Moreover, the temporal stability of the device is enhanced by inserting short sections of ultraviolet curable glue at both ends of the liquid, followed by solidification, to prevent the liquid-air interface fluctuation. The temperature sensitivity achieved is ~ -8.8 nm/°C, in the range between 45 and 50°C.

Break-up dynamics of fluctuating liquid threads

The thinning dynamics of a liquid neck before break-up, as may happen when a drop detaches from a faucet or a capillary, follows different rules and dynamic scaling laws depending on the importance of inertia, viscous stresses, or capillary forces. If now the thinning neck reaches dimensions comparable to the thermally excited interfacial fluctuations, as for nanojet break-up or the fragmentation of thermally annealed nanowires, these fluctuations should play a dominant role according to recent theory and observations. Using near-critical interfaces, we here fully characterize the universal dynamics of this thermal fluctuation-dominated regime and demonstrate that the cross-over from the classical two-fluid pinch-off scenario of a liquid thread to the fluctuation-dominated regime occurs at a well-defined neck radius proportional to the thermal length scale. Investigating satellite drop formation, we also show that at the level of the cross-over between these two regimes it is more probable to produce monodisperse droplets because fluctuation-dominated pinch-off may allow the unique situation where satellite drop formation can be inhibited. Nonetheless, the interplay between the evolution of the neck profiles from the classical to the fluctuation-dominated regime and the satellites' production remains to be clarified.

Vibration Spectroscopy of a Sessile Drop and Its Contact Line

Resonance frequencies of small sessile liquid drops (1-20 μL) were estimated from the power spectra of their height fluctuations after subjecting them to white noise vibration. Various resonance modes could be identified with this method as a function of the mass of the drop. Studies with water drops on such supports as polystyrene (θ ≈ 80°) and a superhydrophobic surface of microfibrillar silicone rubber (θ ≈ 162°) demonstrated that the resonant frequency decreases with the contact angle, θ. This trend is in remarkable agreement with the current models of the resonant vibration of sessile drops. A novel aspect of this study is the analysis of the modes of a slipping contact line that indicated that its higher frequency modes are more severely damped than its lower ones. Another case is with the glycerol-water solutions, where the resonance frequency decreases with the concentration of glycerol purely due to the capillary effects. The interface fluctuation, on the other hand, is strongly correlated with the kinematic viscosity of the liquid. Thus, these experiments provide a means to measure the surface tension and the viscosity of very small droplets.

Phase behavior and structure of a fluid confined between competing (solvophobic and solvophilic) walls

We consider a model fluid with long-range r(-6) (dispersion) interparticle potentials confined between competing parallel walls. One wall is solvophilic and would be completely wet at bulk liquid-gas coexistence μ(co)(-), whereas the other is solvophobic and would be completely dry at μ=μ(co)(+). When the wall separation L is large and the system is below the bulk critical temperature T(C) and close to bulk liquid-gas coexistence, a delocalized interface or soft-mode phase forms with a liquid-gas interface near the center of the slit; this interacts with the walls via the power-law tails of the interparticle potentials. We use a coarse-grained effective Hamiltonian approach to derive explicit scaling expressions for the Gibbs adsorption Γ, the surface tension γ, the solvation force f(s), and the total susceptibility χ. These quantities depend on the dimensionless scaling variable (L/σ)(3)βδμ, where β=(k(B)T)(-1), σ is the diameter of the fluid particles and δμ=μ-μ(co) is the chemical potential deviation from bulk coexistence. Using a nonlocal density functional theory, we calculate density profiles for the asymmetrically confined fluid at different chemical potentials and for sufficiently large L confirm the scaling predictions for the four thermodynamic quantities. Since the upper critical dimension for complete wetting with power-law potentials is less than 3, we argue that our (mean-field) scaling predictions should remain valid in treatments that incorporate the effects of interfacial fluctuations. As the wall separation L is decreased at μ(co), we predict a capillary evaporation transition from the delocalized interface phase to a dilute gas state with just a thin adsorbed film of liquidlike density next to the solvophilic wall. This transition is closely connected to the first-order prewetting transition that occurs at the solvophilic wall in the semi-infinite system. We compare the phase diagram for the competing walls system with the phase diagrams for the fluid confined between identical solvophilic and identical solvophobic walls. Comparisons are also made with earlier studies of asymmetric confinement for systems with short-range forces.

Surface-induced weak orientational order and role of isotropic-nematic interface fluctuations in the appearance of an induced nematic film

Recently the nontrivial spatial and temperature dependence of the surface-induced weak planar orientational order parameter Q(z, T) was determined just above the isotropic-nematic (IN) phase transition point (Ji-H. Lee et al., Phys. Rev. Lett. 102, 167801 (2009)). In this paper we present a theoretical explanation of the observed behaviour. We obtain expressions for the short-range and long-range contributions to the interface potential of the induced nematic film and specify the repulsive character of the interaction between the soft IN interface and the external bounding substrate. It is shown that the small value of the IN interfacial tension results in the renormalization of the repulsive interaction potential due to the thermal fluctuations of the soft IN interface. This leads to an increase of the equilibrium thickness of the induced nematic film and the appearance of a step-like orientational order parameter profile. We find that only renormalized short-range and thermal pseudo-Casimir interactions are essential for the appearance of the induced nematic film, which provide the observed thickness, h ~ 30 nm, of this film. The long-range van der Waals interaction is shown to be negligibly small and the dominant role is played by the renormalized short-range repulsion. Fitting of the experimental order parameter profiles (Ji-H. Lee et al. (2009)) with the expressions based on these interactions makes it possible to determine the material parameters of the system, including the amplitudes of the surface interaction, the IN interfacial tension and the interfacial coherence length. The agreement between theory and experiment confirms the importance of the interface fluctuation renormalization of the interface potentials for soft interfaces.

Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar–Parisi–Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ-type Hamiltonians.

Cyclic competition of four species: domains and interfaces

We study numerically domain growth and interface fluctuations in one- and two-dimensional lattice systems composed of four species that interact in a cyclic way. Particle mobility is implemented through exchanges of particles located on neighboring lattice sites. For the chain we find that the details of the domain growth strongly depend on the mobility, with a higher mobility yielding a larger effective domain growth exponent. In two space dimensions, when also exchanges between mutually neutral particles are possible, both domain growth and interface fluctuations display universal regimes that are independent of the predation and exchange rates.

Coherent response of individual weakly confined exciton–biexciton systems

We investigate the coherent optical response of individual localized exciton–biexciton (X–XX) systems formed at interface fluctuations of a growth-interrupted GaAs/AlAs quantum well. We apply heterodyne spectral interferometry to perform two-dimensional four-wave mixing (FWM) spectroscopy. We retrieve the binding energy of bound and unbound XXs, as well as characterize the system in terms of biexciton–exciton dipole moment ratio and mutual FWM phase. Polarization selection rules of the FWM are determined. FWM hyperspectral imaging and autocorrelation analysis reveal the expected spatial colocalization of XXs with respect to their Xs. A value for the biexciton renormalization in a coherently coupled pair of Xs is retrieved. Our study gives insight into the coherent optical properties of an exciton–biexciton system with a confinement energy comparable to the biexciton binding energy.

Statistics of circular interface fluctuations in an off-lattice Eden model

Scale-invariant fluctuations of growing interfaces are studied for circularclusters of an off-lattice variant of the Eden model, which belongs to the(1 + 1)-dimensional Kardar–Parisi–Zhang (KPZ) universality class. Statistical properties of theheight (radius) fluctuations are numerically determined and compared with recenttheoretical developments as well as the author’s experimental result on growinginterfaces in turbulent liquid crystal (Takeuchi and Sano 2012 arXiv:1203.2530).We focus in particular on analytically unsolved properties such as the temporalcorrelation function and the persistence probability in space and time. Goodagreement with the experiment is found in their characteristic quantities, whichimplies that the geometry-dependent universality of the KPZ class holds hereas well, but a few dissimilarities are also found. Finite-time corrections in thecumulants of the distribution are also studied and shown to decay, for the mean, ast−2/3 within the time window of the simulations, instead oft−1/3 which arises as the typical leading term in the previously known cases.

The order of filling transitions in acute wedges

Using a square-gradient density functional model we test the prediction that the filling transition for a fluid in a wedge geometry changes from continuous to first-order as the wedge becomes more acute. Our numerical findings confirm such a change of order, but the value of the tilt angle at which it occurs, α* ≈ 45°, is considerably smaller than the original theoretical prediction. We critically reassess this work, which was based on allowing for the self-interaction of the fluid interface, and argue that the interfacial curvature and effective wavevector dependent surface tension can further lower the predicted value of α*, in keeping with our numerical findings. Interfacial fluctuation effects, occurring beyond mean-field level, are also discussed using effective Hamiltonian theory and are shown to substantially increase the value of α*.

Correlation between microstructure and electromagnetic properties in magnetic tunnel junctions with naturally oxidized MgO barrier

We investigated the correlation between the microstructure and the electromagnetic properties of magnetic tunnel junctions (MTJs) with MgO barriers fabricated by direct sputtering and natural oxidation of the Mg layers. The MTJ with an oxidized Mg barrier contained amorphous phases in both the barrier and the CoFeB free layer and exhibited large interface fluctuations in both the CoFeB reference/MgO and MgO/CoFeB interfaces This had a significant influence on the low MR ratio and large switching current. Inserting a CoFe seed layer under the oxidized Mg barrier greatly improved the crystallization of the oxidized MgO which ultimately led to a higher MR ratio and lower switching current. In addition to the textured CoFeB/MgO/CoFeB structures, the sharp interface of the MgO barrier, low B content in the MgO barrier, and Fe-rich composition in the free layer are thought to be of key importance for ensuring high magneto-transport properties.

Kinetic roughening, global quantities, and fluctuation–dissipation relations

Growth processes and interface fluctuations can be studied through the properties of global quantities. We here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width, but that is also directly conjugate to an experimentally accessible parameter, thereby allowing us to study in a consistent way the global response of the system to a global change of external conditions. Exploiting the full analyticity of the linear Edwards–Wilkinson and Mullins–Herring equations, we study in detail various two-time functions related to that quantity. This quantity fulfills the fluctuation–dissipation theorem when considering steady-state equilibrium fluctuations.

From Thermodynamic States to Biological Function by Einstein's Approach to Statistical Physics

Einstein founded statistical physics on an important generalization of the Boltzmann principle: Einstein's reversion, where not the model but the law of entropy is placed first. The advantage is that it assures the 2nd Law and requires no model assumptions. In particular, the existence of a complete molecular mechanism is not necessary. However, if the empirical behavior of a system is known, the entropy and the corresponding probability of the thermodynamic states can be directly derived. With his approach Einstein successfully explained Brownian motion, wave-particle dualism, quantum transitions as well as the Bose-Einstein condensation. Impossible to find in any textbook, we outline Einstein's approach and apply it to soft interfaces. The introduction of their proper entropy potential, its first, and its second derivatives predicts interfacial nonequilibrium excitation, propagation, and fluctuations, respectively. Experimental observations of the phenomenology of the membrane susceptibilities allow quantitative predictions. The propagation of waves as well as the existence of channel-like current fluctuations are experimentally confirmed and compared to measurements on living systems. Finally, we present experiments that confirm Einstein's approach to the interfacial reaction coordinate. Here the phenomenology of the system is derived from a proper entropy law even though hidden from direct observation. Not structure of molecules but entropy of the aqueous interfaces turns out to be the origin of catalysis and the associated surprising increase in reaction rate. Simultaneous specificity and activity appears now predictable and no more paradox. The theory derived from K.K. in 1999 is briefly outlined and confirmed in experiments on Acetylcholinesterases incorporated in lipid monolayers. Since enzyme activity is controlled from remote by these continuous layers, our results predict the ubiquitous, integrative action in biology of the excitable hydration interface.