Pattern Formation

We investigate the formation of transverse patterns in a doubly resonant degenerate optical parametric oscillator. Extending previous work, we treat the more realistic case of a spherical mirror cavity with a finite-sized input pump field. Using numerical simulations in real space, we determine the conditions on the cavity geometry, pump size and detunings for which pattern formation occurs; we find multistability of different types of optical patterns. Below threshold, we analyze the dependence of the quantum image on the width of the input field, in the near and in the far field.

We investigate the effects of a time-correlated noise on an extended chaotic system. The chosen model is the Lorenz'96, a kind of toy model used for climate studies. The system is subjected to both temporal and spatiotemporal perturbations. Through the analysis of the system's time evolution and its time correlations, we have obtained numerical evidence for two stochastic resonance-like behaviors.

The Drosophila pair-rule gene odz (Tenm) has many patterning roles throughout development. We have identified four mammalian homologs of this gene, including one previously described as a mouse ER stress response gene, Doc4 (Wang et al., 1998). The Odz genes encode large polypeptides displaying the hallmarks of Drosophila Odz: a putative signal peptide; eight EGF-like repeats; and a putative transmembrane domain followed by a 1800-amino-acid stretch without homology to any proteins outside of this family. The mouse genes Odz3 and Doc4/Odz4 exhibit partially overlapping, but clearly distinct, embryonic expression patterns. The major embryonic sites of expression are in the nervous system, including the tectum, optic recess, optic stalk, and developing eye. Additional sites of expression include trachea and mesodermally derived tissues, such as mesentery, and forming limb and bone. Expression of the Odz2 gene is restricted to the nervous system. The expression patterns suggest that each of the genes has its own distinct developmental role. Comparisons of Drosophila and vertebrate Odz expression patterns suggest evolutionarily conserved functions.

Pattern formation basically involves forming a particular shape by altering the positions of each robots in a swarm. The most common problem in the field of swarm robotics is dealing with managing and directing how a sizable number of robots navigate in the search environment to accomplish an assignment in unity. This type of task is normally impracticable, demanding and laborious for a particular set of robots to accomplish. The inspiration of swarm robots is fundamentally drawn from the study of behaviour of animals in group like a flock of birds, a herd of cattle, and a shoal of fish. In this paper, we used our novel hybrid algorithm called Primal Dual PSO (pdPSO) to solve the pattern formation problem in swarm robotics. Our simulation result provides a clear indication of the effectiveness of the algorithm. The results of our simulations show that our hybrid algorithm’s performance is robust and scalable. It has great pattern formation capability for homogenous set of swarm robots compared to some other variants of PSO.

This report focuses on the effect of simultaneous Fe incorporation in the self-organized pattern formation on Si(001) by low-energy ion-beam sputtering. Experimental observations giving evidence for the correlation between different ion-beam parameters, Fe concentration on the substrate, and the resulting topography are shown. It was observed that the incorporation of Fe affects the evolution of the topography and it is a requisite for the formation of ripples at near-normal incidence. It is shown also that Fe is not homogeneously distributed on the surface, but there is a higher concentration at the crests of the ripples than at the valleys. For the experimental setup used for this study, the Fe flux that reaches the surface is determined mainly by the acceleration voltage (U acc), while the ion energy (E ion) and ion-beam incidence angle (α) control the concentration of Fe in the steady state. The adjustment of these operational parameters of the ion source enables the fine-tuning of surface patterns.

A new strain capable of forming distinctive patterns during colony development was identified by using a combination of phenotypic characterization, fatty acid analysis and analysis of the 16s rRNA gene sequence. The strain formed either a branched, tip-splitting colony ...

Some UV-curable coatings display matte surfaces after cure if they have undergone a certain period of leveling at a temperature above their glass transition temperature and the melting point of any crystalline co-reagents present in the formation. The matte finish of these coatings is due to the presence of coherent surface wrinkles after cure, which are similar in appearance to those induced by differential thermal contraction, when a metal layer is sputtered onto a rubbery or viscous substrate. However, the wrinkles in the UV-cured coatings appear under isothermal conditions, and it is, therefore, inferred that they are due to the dynamics of internal stresses induced by through-thickness variations in the extent of curing.

Liesegang rings in precipitation reactions are an example of pattern formation in chemical reaction-diffusion systems. Such patterns arise from the interplay between the reaction kinetics and the diffusion of chemical species. We discuss the occurrence of Liesegang rings in crystal growth experiments with two competing crystalline phases, and compare computational predictions with the results of laboratory experiments.

In this thesis, we are concerned with the dynamics of spiral wave solutions to Reaction-Diffsion systems of equations, and how they behave when subject to symmetry breaking perturbations. We present an asymptotic theory of the study of meandering (quasiperiodic spiral wave solutions) spiral waves which are drifting due to symmetry breaking perturbations. This theory is based on earlier theories: the 1995 Biktashev et al theory of drift of rigidly rotating spirals, and the 1996 Biktashev et al theory of meander of spirals in unperturbed systems. We combine the two theories by first rewriting the 1995 drift theory using the symmetry quotient system method of the 1996 meander theory, and then go on to extend the approach to meandering spirals by considering Floquet theory and using a singular perturbation method. We demonstrate the work of the newly developed theory on simple examples. We also develop a numerical implementation of the quotient system method, demonstrate its numerical convergence and its use in calculations which would be difficult to do by the standard methods, and also link this study to the problem of calculation of response functions of spiral waves.

This tutorial was prepared for the Biomodelling School held during the 4th International Conference
on Science and Applied Research: Post-Genome Methods of Analysis in Biology and Laboratory
and Clinical Medicine (PostGenome.ru). It is partly based on the teaching materials previously
developed for teaching computational biology at the Computational Biology group, D-BSSE, ETH
Zurich. The tutorial is accompanied by an introductory lecture and assumes a basic understanding
of finite element methods and differential calculus. One of the tutorials assumes a basic knowledge
of MATLAB.
The goal of this tutorial is to provide a step by step introduction to computational modelling
of pattern formation and morphogenesis in biology with COMSOL Multiphysics. This tutorial was
developed and tested for COMSOL 4.4 (build 195).

Model files are available at http://www.silva.bsse.ethz.ch/cobi/people/dzianism/teaching1

This paper proposes the Ricci–flow equation from Riemannian geometry as a general geometric framework for various nonlinear reaction–diffusion systems (and related dissipative solitons) in mathematical biology. More precisely, we propose a conjecture that any kind of reaction–diffusion processes in biology, chemistry, and physics can be modeled by the combined geometric–diffusion system. In order to demonstrate the validity of this hypothesis, we review a number of popular nonlinear reaction–diffusion systems and try to show that they can all be subsumed by the presented geometric framework of the Ricci flow.

1. Functional diversity (FD) has become a principal concept for revealing mechanisms driving community assembly and ecosystem function. Multiple assembly processes, including abiotic filtering, competition and multi-trophic relationships, operate simultaneously to structure FD. In water-limited plant communities, FD is likely to reflect trade-offs between drought resistance vs. disturbance resistance and competitive ability. 2. We propose a mathematical mechanistic model for understanding the organization and function of water-limited plant communities. The approach captures the interplay between abiotic filtering, below-and above-ground competition and disturbance. We exploit this powerful model to uncover mechanisms underlying changes in functional diversity along stress gradients. 3. Our approach links biomass production and FD to environmental conditions through plant resource capture ability. Functional groups are defined along a single trade-off axis according to investment in capturing light (shoot) vs. water (root). Species growth rate is determined dynamically by the species traits, water availability and grazing stress. We derive biomass production, functional diversity and composition along precipitation and grazing gradients. 4. Model's results revealed several regimes structuring FD along the precipitation gradient: 'Struggle for water' at low precipitation, 'competition for water' at intermediate precipitation and 'competition for light' at high precipitation. 5. We observed a shift in grazing effect on FD from negative at very low precipitation, to positive at higher precipitation. Unimodal FD–grazing intensity relationship was observed under high precipitation , while under low precipitation, FD decreased moderately with increasing grazing intensity. 6. Synthesis. Our model showcases how fundamental tradeoffs in plant traits may drive functional diversity and ecosystem function along environmental gradients. It offers a mechanism through which novel understandings can be obtained regarding the interplay between water stress, below-and above-ground competition and disturbance intensity and history. We discuss further model testing possibilities as well as required empirical work.

Abstract: We construct a model based on social balance theory proposed by Fritz Heider to analyze the interpersonal network among social agents. The model of social balance theory provides us an interesting tool to see how a social group evolves to the possible balance ...

This paper proposes the Ricci–flow equation from Riemannian geometry as a general geometric framework for various nonlinear reaction–diffusion systems (and related dissipative solitons) in mathematical biology. More precisely, we propose a conjecture that any kind of reaction–diffusion processes in biology, chemistry, and physics can be modeled by the combined geometric–diffusion system. In order to demonstrate the validity of this hypothesis, we review a number of popular nonlinear reaction–diffusion systems and try to show that they can all be subsumed by the presented geometric framework of the Ricci flow.

Synchrony is a pervasive concept relevant to diverse domains in physics, biology, and the social sciences. This article reviews some of the evidence both from natural and human systems. Our main focus is on the role of synchrony in psychotherapy research. Its association with empathy, rapport and the therapeutic relationship has been pointed out repeatedly, yet close evaluation of empirical studies suggests that the evidence remains inconclusive. Particularly in naturalistic studies, research em- ploying synchrony as a specific measure is still lacking. We suggest a new approach to studying synchrony in psychotherapies under field conditions: Image-differen- cing is a video-based algorithm quantifying the amount of movement in pre-selec- ted regions. Our methodology can be compared to the approach from the seminal work of Condon & Ogston (1966). The statistical analysis we employ detects syn- chrony on a global level, irrespective of the specific body parts moving. Synchrony thus defined is considered a general measure of coordination of interacting indivi- duals. Exemplary data show the feasibility of this approach and its potential contri- bution to psychotherapy research.