Travelling waves in a complex Ginzburg-Landau equation with time-delay feedback

One of the simplest ways to create nonlinear oscillations is the Hopf bifurcation. The spatiotemporal dynamics observed in an extended medium with diffusion (e.g., a chemical reaction) undergoing this bifurcation is governed by the complex Ginzburg-Landau equation, one of the best-studied generic models for pattern formation, where besides uniform oscillations, spiral waves, coherent structures and turbulence are found. The presence of time delay terms in this equation changes the pattern formation scenario, and different kind of travelling waves have been reported. In particular, we study the complex Ginzburg-Landau equation that contains local and global time-delay feedback terms. We focus our attention on plane wave solutions in this model. The first novel result is the derivation of the plane wave solution in the presence of time-delay feedback with global and local contributions. The second and more important result of this study consists of a linear stability analysis of plane waves in that model. Evaluation of the eigenvalue equation does not show stabilisation of plane waves for the parameters studied. We discuss these results and compare to results of other models.

In-cavity pulse shaping and dissipative parametric instability mode-locking in fibre lasers

At the level of fundamental research, fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes, while at the applied research level, pulses with different and optimised features – e.g., in terms of pulse duration, temporal and/or spectral shape, energy, repetition rate and emission bandwidth – are sought with the general constraint of developing efficient cavity architectures. In this work, we review our recent progress on the realisation of pulse shaping in passively- mode-locked fibre lasers by inclusion of an amplitude and phase spectral filter into the laser cavity. We present a fibre laser design in which pulse shaping occurs through filtering of a spectrally nonlinearly broadened pulse in the cavity. This strategy of pulse shaping is illustrated through the numerical demonstration of the laser operation in different pulse-generation regimes, including parabolic, flattop and triangular waveform generations, depending on the amplitude profile of the in-cavity spectral filter [1]. As an application of this general approach, we show that the use of an in-cavity flat-top spectral filter makes it possible to directly generate sinc-shaped Nyquist pulses of high quality and of a widely tunable bandwidth from the laser [2]. We also report on a recently-developed versatile erbium-doped fibre laser, in which conventional soliton, dispersion-managed soliton (stretched-pulse) and dissipative soliton mode-locking regimes can be selectively and reliably targeted by programming different group-velocity dispersion profiles and bandwidths on an in-cavity programmable filter [3]. Further, we report on our recent results on the passive mode locking of a Raman fibre laser by a recently predicted new type of parametric instability – the dissipative Faraday instability [4], where spatially periodic zig-zag modulation of spectrally dependent losses can lead to pattern formation in the temporal domain. High-order harmonic mode locking is achieved in a very simple experimental configuration, with the laser cavity including an optical fibre and two chirped fibre Bragg gratings, and no additional mode-locking elements. The results not only open up new possibilities for the design of mode-locked lasers, but extend beyond fibre optics to other fields of physics and engineering. References [1] S. Boscolo, C. Finot, H. Karakuzu, P. Petropoulos, “Pulse shaping in mode-locked fiber laser by in-cavity spectral filter,” Opt. Lett., vol. 39, pp. 438–441, 2014. [2] S. Boscolo, C. Finot, S. K. Turitsyn, “Bandwidth programmable optical Nyquist pulse generation in passively mode-locked fiber laser,” IEEE Photon. J., vol. 7, 7802008(8), 2015. [3] J. Peng, S. Boscolo, “Filter-based dispersion-managed versatile ultrafast fibre laser,” Sci. Rep., 2016, In press. [4] A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett., vol. 116, 028701, 2016.

Interactions between endothelin receptor B and transcription factors Sox10 and Pax3 in the melanocyte lineage

Genetic interactions that underlie developmental processes such as cell differentiation and pattern formation are complex and difficult to elucidate. Neural Crest (NC) cells and their derivatives offer an optimal system in which to probe for these complex interactions as they acquire different cell fates and constitute a variety of structures. The transcription factors Sox10 and Pax3 as well as the transmembrane receptor Endothelin receptor b (Ednrb) are temporally and spatially co-expressed early in NC cells and mutations in these genes lead to similar hypopigmentation phenotypes due to a reduced number of NC-derived melanocyte precursors, the melanoblasts. The goal of this study was to establish whether Sox10 and Ednrb or Pax3 and Ednrb interact to promote normal murine melanocyte development. Crosses of Sox10 or Pax3 with Ednrb heterozygous mutants showed that the double heterozygous hypopigmentation phenotype was significantly more pronounced than phenotypes of single heterozygotes, implying that a synergistic interaction exists between Sox10 and Ednrb and Pax3 and Ednrb. This interaction was further explored by the attempt to rescue the Sox10 and Pax3 hypopigmentation phenotypes by the transgenic addition of Ednrb to melanoblasts. Pigmentation was completely restored in the Sox10 and partially restored in the Pax3 mutant mice. The comparison of the number of melanoblasts in transgenic and non-transgenic Sox10 mutant embryos showed that the transgenic rescue occurred as early as E11.5, a critical time for melanoblast population expansion. Cell survival assays indicated that the rescue was not due to an effect of the transgene on melanoblast survival. A novel phenotype arose when studying the interaction between Ednrb and Pax3. Newborns appeared normal but by 3.5 weeks of age, the affected pups were smaller than normal littermates and developed a dome-shaped head; some also developed thoracic kyphosis. Affected pups were dead by 4 weeks of age: 80% were Pax3Sp/+ and 75% were female. When compared to normal littermates, affected mice had brains with enlarged 4th ventricles and more glia while skeletal staining showed kyphosis, wider rib cages and pelvic differences. An epistatic interaction resulting from the mixing of genetic backgrounds that is exacerbated in the presence of Pax3 heterozygosity is suspected.

Interactions between Endothelin Receptor B and Transcription Factors Sox10 and Pax3 in the Melanocyte Lineage

Genetic interactions that underlie developmental processes such as cell differentiation and pattern formation are complex and difficult to elucidate. Neural Crest (NC) cells and their derivatives offer an optimal system in which to probe for these complex interactions as they acquire different cell fates and constitute a variety of structures. The transcription factors Sox10 and Pax3 as well as the transmembrane receptor Endothelin receptor b (Ednrb) are temporally and spatially co-expressed early in NC cells and mutations in these genes lead to similar hypopigmentation phenotypes due to a reduced number of NC-derived melanocyte precursors, the melanoblasts. The goal of this study was to establish whether Sox10 and Ednrb or Pax3 and Ednrb interact to promote normal murine melanocyte development. Crosses of Sox10 or Pax3 with Ednrb heterozygous mutants showed that the double heterozygous hypopigmentation phenotype was significantly more pronounced than phenotypes of single heterozygotes, implying that a synergistic interaction exists between Sox10 and Ednrb and Pax3 and Ednrb. This interaction was further explored by the attempt to rescue the Sox10 and Pax3 hypopigmentation phenotypes by the transgenic addition of Ednrb to melanoblasts. Pigmentation was completely restored in the Sox10 and partially restored in the Pax3 mutant mice. The comparison of the number of melanoblasts in transgenic and non-transgenic Sox10 mutant embryos showed that the transgenic rescue occurred as early as E11.5, a critical time for melanoblast population expansion. Cell survival assays indicated that the rescue was not due to an effect of the transgene on melanoblast survival. A novel phenotype arose when studying the interaction between Ednrb and Pax3. Newborns appeared normal but by 3.5 weeks of age, the affected pups were smaller than normal littermates and developed a dome-shaped head; some also developed thoracic kyphosis. Affected pups were dead by 4 weeks of age: 80% were Pax3Sp/+ and 75% were female. When compared to normal littermates, affected mice had brains with enlarged 4th ventricles and more glia while skeletal staining showed kyphosis, wider rib cages and pelvic differences. An epistatic interaction resulting from the mixing of genetic backgrounds that is exacerbated in the presence of Pax3 heterozygosity is suspected.

Self-pulsating nonlinear systems via dissipative parametric instability

The recently discovered dissipative parametric instability is presented in the framework of the universal complex Ginzburg-Landau equation. The pattern formation associated with the instability is discussed in connection to the relevant applications in nonlinear photonics especially as a new tool for pulsed lasers design.

Nonlinear Dynamics Near the Cell Membrane of Chara Corallina

The phenomenon of patterned distribution of pH near the cell membrane of the algae Chara corallina upon illumination is well-known. In this paper, we develop a mathematical model, based on the detailed kinetic analysis of proton fluxes across the cell membrane, to explain this phenomenon. The model yields two coupled nonlinear partial differential equations which describe the spatial dynamics of proton concentration changes and transmembrane potential generation. The experimental observation of pH pattern formation, its period and amplitude of oscillation, and also its hysteresis in response to changing illumination, are all reproduced by our model. A comparison of experimental results and predictions of our theory is made. Finally, a mechanism for pattern formation in Chara corallina is proposed.

Hexagonal patterns in finite domains

In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the possible patterns. In finite rectangular domains, it is shown that a regular hexagonal pattern cannot occur if the aspect ratio is rational. In practice, it is found experimentally that in a rectangular region, patterns of irregular hexagons are often observed. This work analyses the geometry and dynamics of irregular hexagonal patterns. These patterns occur in two different symmetry types, either with a reflection symmetry, involving two wavenumbers, or without symmetry, involving three different wavenumbers. The relevant amplitude equations are studied to investigate the detailed bifurcation structure in each case. It is shown that hexagonal patterns can bifurcate subcritically either from the trivial solution or from a pattern of rolls. Numerical simulations of a model partial differential equation are also presented to illustrate the behaviour.

Three-dimensional kinetic simulations of active suspensions: effect of chemotaxis and steric interaction

In this work, the effects of chemotaxis and steric interactions in active suspensions are analyzed by extending the kinetic model proposed by Saintillan and Shelley [1, 2]. In this model, a conservation equation for the active particle configuration is coupled to the Stokes equation for the flow arising from the force dipole exerted by the particles on the fluid. The fluid flow equations are solved spectrally and the conservation equation is solved by second-order finite differencing in space and second-order Adams-Bashforth time marching. First, the dynamics in suspensions of oxytactic run-and-tumble bacteria confined in thin liquid films surrounded by air is investigated. These bacteria modify their tumbling behavior by making temporal comparisons of the oxygen concentration, and, on average, swim towards high concentrations of oxygen. The kinetic model proposed by Saintillan and Shelley [1, 2] is modified to include run-and-tumble effects and oxygentaxis. The spatio-temporal dynamics of the oxygen and bacterial concentration are analyzed. For small film thicknesses, there is a weak migration of bacteria to the boundaries, and the oxygen concentration is high inside the film as a result of diffusion; both bacterial and oxygen concentrations quickly reach steady states. Above a critical film thickness (approximately 200 micron), a transition to chaotic dynamics is observed and is characterized by turbulent-like 3D motion, the formation of bacterial plumes, enhanced oxygen mixing and transport into the film, and hydrodynamic velocities of magnitudes up to 7 times the single bacterial swimming speed. The simulations demonstrate that the combined effects of hydrodynamic interactions and oxygentaxis create collective three-dimensional instabilities which enhances oxygen availability for the bacteria. Our simulation results are consistent with the experimental findings of Sokolov et al. [3], who also observed a similar transition with increasing film thickness. Next, the dynamics in concentrated suspensions of active self-propelled particles in a 3D periodic domain are analyzed. We modify the kinetic model of Saintillan and Shelley [1, 2] by including an additional nematic alignment torque proportional to the local concentration in the equation for the rotational velocity of the particles, causing them to align locally with their neighbors (Doi and Edwards [4]). Large-scale three- dimensional simulations show that, in the presence of such a torque both pusher and puller suspensions are unstable to random fluctuations and are characterized by highly nematic structures. Detailed measures are defined to quantify the degree and direction of alignment, and the effects of steric interactions on pattern formation will be presented. Our analysis shows that steric interactions have a destabilizing effect in active suspensions.

Coerced Mechanical Coarsening of Nanoparticle Assemblies

Coarsening is a ubiquitous phenomenon [1-3] that underpins countless processes in nature, including epitaxial growth [1,3,4], the phase separation of alloys, polymers and binary fluids [2], the growth of bubbles in foams5, and pattern formation in biomembranes6. Here we show, in the first real-time experimental study of the evolution of an adsorbed colloidal nanoparticle array, that tapping-mode atomic force microscopy (TM-AFM) can drive the coarsening of Au nanoparticle assemblies on silicon surfaces. Although the growth exponent has a strong dependence on the initial sample morphology, our observations are largely consistent with modified Ostwald ripening processes [7-9]. To date, ripening processes have been exclusively considered to be thermally activated, but we show that nanoparticle assemblies can be mechanically coerced towards equilibrium, representing a new approach to directed coarsening. This strategy enables precise control over the evolution of micro- and nanostructures.

Stable spike clusters for the one-dimensional Gierer-Meinhardt system

We consider the Gierer-Meinhardt system with precursor inhomogeneity in a one-dimensional interval. A spike cluster is the combination of several spikes which all approach the same point in the singular limit of small activator diffusivity. We rigorously prove the existence of a steady-state spike cluster consisting of N spikes near a non-degenerate local minimum point of the smooth inhomogeneity, where N is an arbitrary positive integer. Further, we show that this solution is linearly stable. We explicitly compute all eigenvalues, both large (of order O(1)) and small (of order o(1)). The main features of studying the Gierer-Meinhardt system in this setting are as follows: (i) it is biologically relevant since it models a hierarchical process (pattern formation of small-scale structures induced by a pre-existing large-scale inhomogeneity), (ii) it contains three different spatial scales two of which are small. (iii) all the expressions can be made explicit and often have a particularly simple form.

Wavelengths in bioconvection patterns

Unicellular bottom-heavy swimming microorganisms are usually denser than the fluid in which they swim. In shallow suspensions, the bottom heaviness results in a gravitational torque that orients the cells to swim vertically upwards in the absence of fluid flow. Swimming cells thus accumulate at the upper surface to form a concentrated layer of cells. When the cell concentration is high enough, the layer overturns to form bioconvection patterns. Thin concentrated plumes of cells descend rapidly and cells return to the upper surface in wide, slowly moving upwelling plumes. When there is fluid flow, a second viscous torque is exerted on the swimming cells. The balance between the local shear flow viscous and the gravitational torques determines the cells' swimming direction, (gyrotaxis). In this thesis, the wavelengths of bioconvection patterns are studied experimentally as well as theoretically as follow; First, in aquasystem it is rare to find one species lives individually and when they swim they can form complex patterns. Thus, a protocol for controlled experiments to mix two species of swimming algal cells of \emph{C. rienhardtii} and \emph{C. augustae} is systematically described and images of bioconvection patterns are captured. A method for analysing images using wavelets and extracting the local dominant wavelength in spatially varying patterns is developed. The variation of the patterns as a function of the total concentration and the relative concentration between two species is analysed. Second, the linear stability theory of bioconvection for a suspension of two mixed species is studied. The dispersion relationship is computed using Fourier modes in order to calculate the neutral curves as a function of wavenumbers $k$ and $m$. The neutral curves are plotted to compare the instability onset of the suspension of the two mixed species with the instability onset of each species individually. This study could help us to understand which species contributes the most in the process of pattern formation. Finally, predicting the most unstable wavelength was studied previously around a steady state equilibrium situation. Since assuming steady state equilibrium contradicts with reality, the pattern formation in a layer of finite depth of an evolving basic state is studied using the nonnormal modes approach. The nonnormal modes procedure identifies the optimal initial perturbation that can be obtained for a given time $t$ as well as a given set of parameters and wavenumber $k$. Then, we measure the size of the optimal perturbation as it grows with time considering a range of wavenumbers for the same set of parameters to be able to extract the most unstable wavelength.

Cell fusion reprogramming leads to a specific hepatic expression pattern during mouse bone marrow derived hepatocyte formation In Vivo

The fusion of bone marrow (BM) hematopoietic cells with hepatocytes to generate BM derived hepatocytes (BMDH) is a natural process, which is enhanced in damaged tissues. However, the reprogramming needed to generate BMDH and the identity of the resultant cells is essentially unknown. In a mouse model of chronic liver damage, here we identify a modification in the chromatin structure of the hematopoietic nucleus during BMDH formation, accompanied by the loss of the key hematopoietic transcription factor PU.1/Sfpi1 (SFFV proviral integration 1) and gain of the key hepatic transcriptional regulator HNF-1A homeobox A (HNF-1A/Hnf1a). Through genome-wide expression analysis of laser captured BMDH, a differential gene expression pattern was detected and the chromatin changes observed were confirmed at the level of chromatin regulator genes. Similarly, Tranforming Growth Factor-β1 (TGF-β1) and neurotransmitter (e.g. Prostaglandin E Receptor 4 [Ptger4]) pathway genes were over-expressed. In summary, in vivo BMDH generation is a process in which the hematopoietic cell nucleus changes its identity and acquires hepatic features. These BMDHs have their own cell identity characterized by an expression pattern different from hematopoietic cells or hepatocytes. The role of these BMDHs in the liver requires further investigation.

Evaluation of Bubble Formation and Break Up in Suppression Pools by Using Pattern Recognition Methods

During a possible loss of coolant accident in BWRs, a large amount of steam will be released from the reactor pressure vessel to the suppression pool. Steam will be condensed into the suppression pool causing dynamic and structural loads to the pool. The formation and break up of bubbles can be measured by visual observation using a suitable pattern recognition algorithm. The aim of this study was to improve the preliminary pattern recognition algorithm, developed by Vesa Tanskanen in his doctoral dissertation, by using MATLAB. Video material from the PPOOLEX test facility, recorded during thermal stratification and mixing experiments, was used as a reference in the development of the algorithm. The developed algorithm consists of two parts: the pattern recognition of the bubbles and the analysis of recognized bubble images. The bubble recognition works well, but some errors will appear due to the complex structure of the pool. The results of the image analysis were reasonable. The volume and the surface area of the bubbles were not evaluated. Chugging frequencies calculated by using FFT fitted well into the results of oscillation frequencies measured in the experiments. The pattern recognition algorithm works in the conditions it is designed for. If the measurement configuration will be changed, some modifications have to be done. Numerous improvements are proposed for the future 3D equipment.

The dependence of contrail formation on the weather pattern and altitude in the North Atlantic

Aircraft flying through cold ice-supersaturated air produce persistent contrails which contribute to the climate impact of aviation. Here, we demonstrate the importance of the weather situation, together with the route and altitude of the aircraft through this, on estimating contrail coverage. The results have implications for determining the climate impact of contrails as well as potential mitigation strategies. Twenty-one years of re-analysis data are used to produce a climatological assessment of conditions favorable for persistent contrail formation between 200 and 300 hPa over the north Atlantic in winter. The seasonal-mean frequency of cold ice-supersaturated regions is highest near 300 hPa, and decreases with altitude. The frequency of occurrence of ice-supersaturated regions varies with large-scale weather pattern; the most common locations are over Greenland, on the southern side of the jet stream and around the northern edge of high pressure ridges. Assuming aircraft take a great circle route, as opposed to a more realistic time-optimal route, is likely to lead to an error in the estimated contrail coverage, which can exceed 50% for westbound north Atlantic flights. The probability of contrail formation can increase or decrease with height, depending on the weather pattern, indicating that the generic suggestion that flying higher leads to fewer contrails is not robust.

RGMa and RGMb expression pattern during chicken development suggest unexpected roles for these repulsive guidance molecules in notochord formation, somitogenesis, and myogenesis

Background: Repulsive guidance molecules (RGM) are high-affinity ligands for the Netrin receptor Neogenin, and they are crucial for nervous system development including neural tube closure; neuronal and neural crest cell differentiation and axon guidance. Recent studies implicated RGM molecules in bone morphogenetic protein signaling, which regulates a variety of developmental processes. Moreover, a role for RGMc in iron metabolism has been established. This suggests that RGM molecules may play important roles in non-neural tissues. Results: To explore which tissues and processed may be regulated by RGM molecules, we systematically investigated the expression of RGMa and RGMb, the only RGM molecules currently known for avians, in the chicken embryo. Conclusions: Our study suggests so far unknown roles of RGM molecules in notochord, somite and skeletal muscle development. Developmental Dynamics, 2012. (C) 2012 Wiley Periodicals, Inc.