Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators

Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $(mN_c+1)$-th oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength $\epsilon_c$ with a scaling exponent $\gamma$. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents (CLEs) of the coupled systems. We find that the same scaling relation exists for $m$ couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength $\epsilon$. In addition, we have found that $\epsilon_c$ shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of R\"ossler and Lorenz oscillators.Comment: Accepted for Publication in Physical Review

Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit

We have identified the three prominent routes, namely Heagy-Hammel, fractalization and intermittency routes, and their mechanisms for the birth of strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic system constructed using a negative conductance series LCR circuit with a diode both numerically and experimentally. The birth of SNAs by these three routes is verified from both experimental and their corresponding numerical data by maximal Lyapunov exponents, and their variance, Poincar\'e maps, Fourier amplitude spectrum, spectral distribution function and finite-time Lyapunov exponents. Although these three routes have been identified numerically in different dynamical systems, the experimental observation of all these mechanisms is reported for the first time to our knowledge and that too in a single second order electronic circuit.Comment: 21 figure

Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems

We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a function of the delay time and external forcing parameters. In particular, we point out that the fixed point solution exhibits a stability island in the two parameter space of time delay and strength of nonlinearity. Significant role played by transients in attaining steady state solutions is pointed out. Various routes to chaos and existence of hyperchaos even for low values of time delay which is evidenced by multiple positive Lyapunov exponents are brought out. The study is extended to the case of two coupled systems, one with delay and the other one without delay.Comment: 34 Pages, 14 Figure

The Human Oral Microbiome Database: a web accessible resource for investigating oral microbe taxonomic and genomic information

The human oral microbiome is the most studied human microflora, but 53% of the species have not yet been validly named and 35% remain uncultivated. The uncultivated taxa are known primarily from 16S rRNA sequence information. Sequence information tied solely to obscure isolate or clone numbers, and usually lacking accurate phylogenetic placement, is a major impediment to working with human oral microbiome data. The goal of creating the Human Oral Microbiome Database (HOMD) is to provide the scientific community with a body site-specific comprehensive database for the more than 600 prokaryote species that are present in the human oral cavity based on a curated 16S rRNA gene-based provisional naming scheme. Currently, two primary types of information are provided in HOMD—taxonomic and genomic. Named oral species and taxa identified from 16S rRNA gene sequence analysis of oral isolates and cloning studies were placed into defined 16S rRNA phylotypes and each given unique Human Oral Taxon (HOT) number. The HOT interlinks phenotypic, phylogenetic, genomic, clinical and bibliographic information for each taxon. A BLAST search tool is provided to match user 16S rRNA gene sequences to a curated, full length, 16S rRNA gene reference data set. For genomic analysis, HOMD provides comprehensive set of analysis tools and maintains frequently updated annotations for all the human oral microbial genomes that have been sequenced and publicly released. Oral bacterial genome sequences, determined as part of the Human Microbiome Project, are being added to the HOMD as they become available. We provide HOMD as a conceptual model for the presentation of microbiome data for other human body sites

Nonlinear Dynamics of Moving Curves and Surfaces: Applications to Physical Systems

The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a variety of physical problems in different disciplines. Making use of the underlying geometry, one can very often relate the associated evolution equations to many interesting nonlinear evolution equations, including soliton possessing nonlinear dynamical systems. Typical examples include dynamics of filament vortices in ordinary and superfluids, spin systems, phases in classical optics, various systems encountered in physics of soft matter, etc. Such interrelations between geometric evolution and physical systems have yielded considerable insight into the underlying dynamics. We present a succinct tutorial analysis of these developments in this article, and indicate further directions. We also point out how evolution equations for moving surfaces are often intimately related to soliton equations in higher dimensions.Comment: Review article, 38 pages, 7 figs. To appear in Int. Jour. of Bif. and Chao

A Group Theoretical Identification of Integrable Equations in the Li\'enard Type Equation x¨+f(x)x˙+g(x)=0\ddot{x}+f(x)\dot{x}+g(x) = 0 : Part II: Equations having Maximal Lie Point Symmetries

In this second of the set of two papers on Lie symmetry analysis of a class of Li\'enard type equation of the form $\ddot {x} + f(x)\dot {x} + g(x)= 0$, where over dot denotes differentiation with respect to time and $f(x)$ and $g(x)$ are smooth functions of their variables, we isolate the equations which possess maximal Lie point symmetries. It is well known that any second order nonlinear ordinary differential equation which admits eight parameter Lie point symmetries is linearizable to free particle equation through point transformation. As a consequence all the identified equations turn out to be linearizable. We also show that one can get maximal Lie point symmetries for the above Li\'enard equation only when $f_{xx} =0$ (subscript denotes differentiation). In addition, we discuss the linearising transformations and solutions for all the nonlinear equations identified in this paper.Comment: Accepted for publication in Journal of Mathematical Physic

Ligation of anti-cancer drugs to self-assembling ultrashort peptides by click chemistry for localized therapy

Self-assembling ultrashort peptides from aliphatic amino acids were functionalized with platinum anti-cancer drugs by click chemistry. Oxaliplatin-derived hybrid peptide hydrogels with up to 40% drug loading were tested for localized breast cancer therapy. Stably injected gels showed significant tumor growth inhibition in mice and a better tolerance compared to the free platinum drug

In situ synthesis of size-controlled, stable silver nanoparticles within ultrashort peptide hydrogels and their anti-bacterial properties

We have developed a silver-releasing biomaterial with promising potential for wound healing applications. The material is made of ultrashort peptides which can self-assemble in water to form hydrogels. Silver nanoparticles (Ag NPs) were synthesized in situ within the biomaterial, using only UV irradiation and no additional chemical reducing agents. The synthetic strategy allows precise control of the nanoparticle size, with the network of peptide fibers preventing aggregation of Ag NPs. The biomaterial shows increased mechanical strength compared to the hydrogel control. We observed a sustained release of Ag NPs over a period of 14 days. This is a crucial prerequisite for effective anti-bacterial therapy. The ability to inhibit bacterial growth was tested using different bacterial strains, namely gram-negative Escherichia coli and Pseudomonas aeruginosa and gram-positive Staphylococcus aureus. Inhibition of bacterial growth was observed for all strains. The best results were obtained for Pseudomonas aeruginosa which is known for exhibiting multidrug resistance. Biocompatibility studies on HDFa cells, using Ag NP-containing hydrogels, did not show any significant influence on cell viability. We propose this silver-releasing hydrogel as an excellent biomaterial with great potential for applications in wound healing due to its low silver content, sustained silver nanoparticle release and biocompatibility

Preface

Population growth, urbanization and global climate change have increased urban and agricultural water demands, stressing aquifer systems where groundwater is a source of water supply. The availability and utility of groundwater may further be threatened by factors stressing the quality of groundwater, such as industrial and domestic wastes and agricultural intensification. Consequences include, for example, over-allocation of groundwater, groundwater overdraft, declining well yields and land subsidence; degraded groundwater quality due to mobilization of natural pollutants (arsenic), salt contamination caused by seawater intrusion; increased demand for conjunctively used surface water, and resulting conflicts with junior users; and streamflow capture and resulting damage to ecosystems. These consequences may occur incrementally and inequitably across an aquifer. Natural environmental problems can further complicate use of groundwater and increase strain on the aquifer system; for example, underground structures, geothermal heating (such as heat islands), and geochemical evolution (such as karst formation, excessive salinity, acidity, fluoride, radioactivity, hardness, or turbidity). To address this issue, a joint symposium on the Trends and Sustainability of Groundwater in Highly Stressed Aquifers was held during the 8th Scientific Assembly of the International Association of Hydrological Sciences, IAHS, and the 37th Congress of the International Association of Hydrogeology, IAH, in Hyderabad, India, September 2009. The symposium was organized by the IAHS International Commission on Groundwater (ICGW), supported IAH and by the IAHS International Commission on Water Quality (ICWQ). This symposium brought together scientists, including modellers, geochemists and hydro-geologists, with water supply managers and policy makers to discuss scientific and management ideas and approaches for improving the sustainability of highly stressed aquifers. The importance of this topic was reflected in the large number of contributions to the symposium. Selected papers from this symposium have been compiled in this volume. The editors gratefully acknowledge the assistance of the reviewers who made valuable contributions to this volume. We thank Penny Perrins and Cate Gardner from IAHS Press for their professional approach and help with the processing of the manuscripts