Patterns and Stability of Coupled Multi-Stable Nonlinear Oscillators.

Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and stability of coupled driven-damped Helmholtz-Duffing oscillators in bi-stability regimes. We find that despite the fact that the system parameters and the driving force are identical, the stability of the two states to spatially non-uniform perturbations is very different. Moreover, the final stable states, resulting from these spatial perturbations, are not solely dictated by the wavelength of the perturbing mode and take different spatial configurations in terms of the coupled oscillator phases.

Bubble lifetimes in DNA gene promoters and their mutations affecting transcription.

Relative lifetimes of inherent double stranded DNA openings with lengths up to ten base pairs are presented for different gene promoters and corresponding mutants that either increase or decrease transcriptional activity in the framework of the Peyrard-Bishop-Dauxois model. Extensive microcanonical simulations are used with energies corresponding to physiological temperature. The bubble lifetime profiles along the DNA sequences demonstrate a significant reduction of the average lifetime at the mutation sites when the mutated promoter decreases transcription, while a corresponding enhancement of the bubble lifetime is observed in the case of mutations leading to increased transcription. The relative difference in bubble lifetimes between the mutated and wild type promoters at the position of mutation varies from 20% to more than 30% as the bubble length decreases.

Attractive inverse square potential, U(1) gauge, and winding transitions.

The inverse square potential arises in a variety of different quantum phenomena, yet notoriously it must be handled with care: it suffers from pathologies rooted in the mathematical foundations of quantum mechanics. We show that its recently studied conformality breaking corresponds to an infinitely smooth winding-unwinding topological transition for the classical statistical mechanics of a one-dimensional system: this describes the tangling or untangling of floppy polymers under a biasing torque. When the ratio between torque and temperature exceeds a critical value the polymer undergoes tangled oscillations, with an extensive winding number. At lower torque or higher temperature the winding number per unit length is zero. Approaching criticality, the correlation length of the order parameter-the extensive winding number-follows a Kosterlitz-Thouless-type law. The model is described by the Wilson line of a (0+1) U(1) gauge theory, and applies to the tangling or untangling of floppy polymers and to the winding or diffusing kinetics in diffusion-convection reactions.

Thermomechanical stability and mechanochemical response of DNA: a minimal mesoscale model.

We show that a mesoscale model, with a minimal number of parameters, can well describe the thermomechanical and mechanochemical behavior of homogeneous DNA at thermal equilibrium under tension and torque. We predict critical temperatures for denaturation under torque and stretch, phase diagrams for stable DNA, probe/response profiles under mechanical loads, and the density of dsDNA as a function of stretch and twist. We compare our predictions with available single molecule manipulation experiments and find strong agreement. In particular we elucidate the difference between angularly constrained and unconstrained overstretching. We propose that the smoothness of the angularly constrained overstretching transition is a consequence of the molecule being in the vicinity of criticality for a broad range of values of applied tension.

RKKY interaction and intrinsic frustration in non-Fermi-liquid metals.

We study the RKKY interaction in non-Fermi-liquid metals. We find that the RKKY interaction mediated by some non-Fermi-liquid metals can be of much longer range than for a Fermi liquid. The oscillatory nature of the RKKY interaction thus becomes more important in such non-Fermi liquids, and gives rise to enhanced frustration when the spins form a lattice. Frustration suppresses the magnetic ordering temperature of the lattice spin system. Furthermore, we find that the spin system with a longer range RKKY interaction can be described by the Brazovskii model, where the ordering wave vector lies on a higher dimensional manifold. Strong fluctuations in such a model lead to a first-order phase transition and/or glassy phase. This may explain some recent experiments where glassy behavior was observed in stoichiometric heavy fermion material close to a ferromagnetic quantum critical point.

Inelastic electron tunneling spectroscopy for topological insulators.

Inelastic electron tunneling spectroscopy is a powerful spectroscopy that allows one to investigate the nature of local excitations and energy transfer in the system of interest. We study inelastic electron tunneling spectroscopy for topological insulators and investigate the role of inelastic scattering on the Dirac node states on the surface of topological insulators. Local inelastic scattering is shown to significantly modify the Dirac node spectrum. In the weak coupling limit, peaks and steps are induced in second derivative d2I/dV2. In the strong coupling limit, the local negative-U centers are formed at impurity sites, and the Dirac cone structure is fully destroyed locally. At intermediate coupling, resonance peaks emerge. We map out the evolution of the resonance peaks from weak to strong coupling, which interpolate nicely between the two limits. There is a sudden qualitative change of behavior at intermediate coupling, indicating the possible existence of a local quantum phase transition. We also find that, even for a simple local phonon mode, the inherent coupling of spin and orbital degrees in topological insulators leads to the spin-polarized texture in inelastic Friedel oscillations induced by the local mode.

Promoter polymorphisms in two overlapping 6p25 genes implicate mitochondrial proteins in cognitive deficit in schizophrenia.

In a previous study, we detected a 6p25-p24 region linked to schizophrenia in families with high composite cognitive deficit (CD) scores, a quantitative trait integrating multiple cognitive measures. Association mapping of a 10 Mb interval identified a 260 kb region with a cluster of single-nucleotide polymorphisms (SNPs) significantly associated with CD scores and memory performance. The region contains two colocalising genes, LYRM4 and FARS2, both encoding mitochondrial proteins. The two tagging SNPs with strongest evidence of association were located around the overlapping putative promoters, with rs2224391 predicted to alter a transcription factor binding site (TFBS). Sequencing the promoter region identified 22 SNPs, many predicted to affect TFBSs, in a tight linkage disequilibrium block. Luciferase reporter assays confirmed promoter activity in the predicted promoter region, and demonstrated marked downregulation of expression in the LYRM4 direction under the haplotype comprising the minor alleles of promoter SNPs, which however is not driven by rs2224391. Experimental evidence from LYRM4 expression in lymphoblasts, gel-shift assays and modelling of DNA breathing dynamics pointed to two adjacent promoter SNPs, rs7752203-rs4141761, as the functional variants affecting expression. Their C-G alleles were associated with higher transcriptional activity and preferential binding of nuclear proteins, whereas the G-A combination had opposite effects and was associated with poor memory and high CD scores. LYRM4 is a eukaryote-specific component of the mitochondrial biogenesis of Fe-S clusters, essential cofactors in multiple processes, including oxidative phosphorylation. LYRM4 downregulation may be one of the mechanisms involved in inefficient oxidative phosphorylation and oxidative stress, increasingly recognised as contributors to schizophrenia pathogenesis.

Measurement and memory in the periodically driven complex Ginzburg-Landau equation.

In the present work we illustrate that classical but nonlinear systems may possess features reminiscent of quantum ones, such as memory, upon suitable external perturbation. As our prototypical example, we use the two-dimensional complex Ginzburg-Landau equation in its vortex glass regime. We impose an external drive as a perturbation mimicking a quantum measurement protocol, with a given "measurement rate" (the rate of repetition of the drive) and "mixing rate" (characterized by the intensity of the drive). Using a variety of measures, we find that the system may or may not retain its coherence, statistically retrieving its original glass state, depending on the strength and periodicity of the perturbing field. The corresponding parametric regimes and the associated energy cascade mechanisms involving the dynamics of vortex waveforms and domain boundaries are discussed.

Thermomechanics of DNA: theory of thermal stability under load.

A theory for thermomechanical behavior of homogeneous DNA at thermal equilibrium predicts critical temperatures for denaturation under torque and stretch, phase diagrams for stable B-DNA, supercoiling, optimally stable torque, and the overstretching transition as force-induced DNA melting. Agreement with available single molecule manipulation experiments is excellent.

Strain-induced metal-insulator phase coexistence in perovskite manganites.

The coexistence of distinct metallic and insulating electronic phases within the same sample of a perovskite manganite, such as La(1-x-y)Pr(y)Ca(x)MnO3, presents researchers with a tool for tuning the electronic properties in materials. In particular, colossal magnetoresistance in these materials--the dramatic reduction of resistivity in a magnetic field--is closely related to the observed texture owing to nanometre- and micrometre-scale inhomogeneities. Despite accumulated data from various high-resolution probes, a theoretical understanding for the existence of such inhomogeneities has been lacking. Mechanisms invoked so far, usually based on electronic mechanisms and chemical disorder, have been inadequate to describe the multiscale, multiphase coexistence within a unified picture. Moreover, lattice distortions and long-range strains are known to be important in the manganites. Here we show that the texturing can be due to the intrinsic complexity of a system with strong coupling between the electronic and elastic degrees of freedom. This leads to local energetically favourable configurations and provides a natural mechanism for the self-organized inhomogeneities over both nanometre and micrometre scales. The framework provides a physical understanding of various experimental results and a basis for engineering nanoscale patterns of metallic and insulating phases.

DNA Breathing Dynamics in the Presence of a Terahertz Field.

We consider the influence of a terahertz field on the breathing dynamics of double-stranded DNA. We model the spontaneous formation of spatially localized openings of a damped and driven DNA chain, and find that linear instabilities lead to dynamic dimerization, while true local strand separations require a threshold amplitude mechanism. Based on our results we argue that a specific terahertz radiation exposure may significantly affect the natural dynamics of DNA, and thereby influence intricate molecular processes involved in gene expression and DNA replication.

Distributions of bubble lifetimes and bubble lengths in DNA.

We investigate the distribution of bubble lifetimes and bubble lengths in DNA at physiological temperature, by performing extensive molecular dynamics simulations with the Peyrard-Bishop-Dauxois (PBD) model, as well as an extended version (ePBD) having a sequence-dependent stacking interaction, emphasizing the effect of the sequences' guanine-cytosine (GC)/adenine-thymine (AT) content on these distributions. For both models we find that base pair-dependent (GC vs AT) thresholds for considering complementary nucleotides to be separated are able to reproduce the observed dependence of the melting temperature on the GC content of the DNA sequence. Using these thresholds for base pair openings, we obtain bubble lifetime distributions for bubbles of lengths up to ten base pairs as the GC content of the sequences is varied, which are accurately fitted with stretched exponential functions. We find that for both models the average bubble lifetime decreases with increasing either the bubble length or the GC content. In addition, the obtained bubble length distributions are also fitted by appropriate stretched exponential functions and our results show that short bubbles have similar likelihoods for any GC content, but longer ones are substantially more likely to occur in AT-rich sequences. We also show that the ePBD model permits more, longer-lived, bubbles than the PBD system.

Axial oxygen-centered lattice instabilities and high-temperature superconductivity.

Copper K-edge x-ray absorption data indicate that an axial oxygen-centered lattice instability accompanying the 93 K superconducting transition in YBa(2)Cu(3)O(7) is of a pseudo-(anti)ferroelectric type, in that it appears to involve the softening of a double potential well into a structure in which the difference between the two copper-oxygen distances and the barrier height have both decreased. This softer structure is present only at temperatures within a fluctuation region around the transition. A similar process involving the analogous axial oxygen atom also accompanies the superconducting transition in T1Ba(2)Ca(3)Cu(4)O(11), where the superconducting transition temperature T(c) is ~120 K. The mean square relative displacement of this oxygen atom in YBa(2)Cu(3)O(7) is also specifically affected by a reduction in the oxygen content and by the substitution of cobalt for copper, providing further evidence for the sensitivity of the displacement to additional factors that also influence the superconductivity. On the basis of the implied coupling of this ionic motion to the superconductivity, a scenario for high-temperature superconductivity is presented in which both phonon and electronic (charge transfer) channels are synergistically involved.

Chaotic transport in deterministic sine-Gordon soliton ratchets.

We investigate homogeneous and inhomogeneous sine-Gordon ratchet systems in which a temporal symmetry and the spatial symmetry, respectively, are broken. We demonstrate that in the inhomogeneous systems with ac driving the soliton dynamics is chaotic in certain parameter regions, although the soliton motion is unidirectional. This is qualitatively explained by a one-collective-coordinate theory which yields an equation of motion for the soliton that is identical to the equation of motion for a single particle ratchet which is known to exhibit chaotic transport in its underdamped regime. For a quantitative comparison with our simulations we use a two-collective-coordinate (2CC) theory. In contrast to this, homogeneous sine-Gordon ratchets with biharmonic driving, which breaks a temporal shift symmetry, do not exhibit chaos. This is explained by a 2CC theory which yields two ODEs: one is linear, the other one describes a parametrically driven oscillator which does not exhibit chaos. The latter ODE can be solved by a perturbation theory which yields a hierarchy of linear equations that can be solved exactly order by order. The results agree very well with the simulations.

Discrete solitons and vortices in hexagonal and honeycomb lattices: existence, stability, and dynamics.

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrödinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the "hexapole" of alternating phases (0-pi) , as well as the vortex of topological charge S=2 have intervals of stability; among three-site states, only the vortex of topological charge S=1 may be stable in the case of focusing nonlinearity. These conclusions are confirmed both for hexagonal and for honeycomb lattices by means of detailed numerical bifurcation analysis of the stationary states from the anticontinuum limit, and by direct simulations to monitor the dynamical instabilities, when the latter arise. The dynamics reveal a wealth of nonlinear behavior resulting not only in single-site solitary wave forms, but also in robust multisite breathing structures.

Ultra-violet light induced changes in DNA dynamics may enhance TT-dimer recognition.

Short-wave ultra-violet light promotes the formation of DNA dimers between adjacent thymine bases, and if unrepaired these dimers may induce skin cancer. Living cells have a very robust repair system capable of repairing hundreds of lesions every day. Although many of the details of the dimer repair mechanism are known, it is still a mystery how the dimers are recognized. Because the dimers are hidden from repair proteins diffusing in the cell nucleus, it has been surmised that dimer recognition is indirect. In this paper, a new recognition signal is suggested by a theory of the dimer-induced large amplitude, prolonged oscillations in the motion of the two strands in double-stranded DNA molecules. These large amplitude oscillations of the two DNA strands, localized around the dimer will unveil the dimer allowing the repair proteins to bind to the dimer site. The temperature dependence of the recognition rate is correlated with the inter-strand fluctuations and must decrease with decreasing temperature according to the findings in this paper. Moreover the probability for finding a large opening is localized to the dimer neighbourhood and these large openings may play an important role in dimer-repair protein biochemistry.

Speed-of-light pulses in the massless nonlinear Dirac equation with a potential.

We consider the massless nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction g^{2}/2(Ψ[over ¯]Ψ)^{2} in the presence of three external electromagnetic real potentials V(x), a potential barrier, a constant potential, and a potential well. By solving numerically the NLD equation, we find different scenarios depending on initial conditions, namely, propagation of the initial pulse along one direction, splitting of the initial pulse into two pulses traveling in opposite directions, and focusing of two initial pulses followed by a splitting. For all considered cases, the final waves travel with the speed of light and are solutions of the massless linear Dirac equation. During these processes the charge and the energy are conserved, whereas the momentum is conserved when the solutions possess specific symmetries. For the case of the constant potential, we derive exact analytical solutions of the massless NLD equation that are also solutions of the massless linearized Dirac equation. Decay or growth of the initial pulse is also predicted from the evolution of the charge for the case of a non-zero imaginary part of the potential.

Discrete solitons and vortices in the two-dimensional Salerno model with competing nonlinearities.

An anisotropic lattice model in two spatial dimensions, with on-site and intersite cubic nonlinearities (the Salerno model), is introduced, with emphasis on the case in which the intersite nonlinearity is self-defocusing, competing with on-site self-focusing. The model applies, for example, to a dipolar Bose-Einstein condensate trapped in a deep two-dimensional (2D) optical lattice. Soliton families of two kinds are found in the model: ordinary ones and cuspons, with peakons at the border between them. Stability borders for the ordinary solitons are found, while all cuspons (and peakons) are stable. The Vakhitov-Kolokolov criterion does not apply to cuspons, but for the ordinary solitons it correctly identifies the stability limits. In direct simulations, unstable solitons evolve into localized pulsons. Varying the anisotropy parameter, we trace a transition between the solitons in 1D and 2D versions of the model. In the isotropic model, we also construct discrete vortices of two types, on-site and intersite centered (vortex crosses and squares, respectively), and identify their stability regions. In simulations, unstable vortices in the noncompeting model transform into regular solitons, while in the model with the competing nonlinearities they evolve into localized vortical pulsons, which maintain their topological character. Bound states of regular solitons and vortices are constructed too, and their stability is identified.

Solitons in the Salerno model with competing nonlinearities.

We consider a lattice equation (Salerno model) combining onsite self-focusing and intersite self-defocusing cubic terms, which may describe a Bose-Einstein condensate of dipolar atoms trapped in a strong periodic potential. In the continuum approximation, the model gives rise to solitons in a finite band of frequencies, with sechlike solitons near one edge, and an exact peakon solution at the other. A similar family of solitons is found in the discrete system, including a peakon; beyond the peakon, the family continues in the form of cuspons. Stability of the lattice solitons is explored through computation of eigenvalues for small perturbations, and by direct simulations. A small part of the family is unstable (in that case, the discrete solitons transform into robust pulsonic excitations); both peakons and cuspons are stable. The Vakhitov-Kolokolov criterion precisely explains the stability of regular solitons and peakons, but does not apply to cuspons. In-phase and out-of-phase bound states of solitons are also constructed. They exchange their stability at a point where the bound solitons are peakons. Mobile solitons, composed of a moving core and background, exist up to a critical value of the strength of the self-defocusing intersite nonlinearity. Colliding solitons always merge into a single pulse.

Bubble statistics and dynamics in double-stranded DNA.

The dynamical properties of double-stranded DNA are studied in the framework of the Peyrard-Bishop-Dauxois model using Langevin dynamics. Our simulations are analyzed in terms of two distribution functions describing localized separations ("bubbles") of the double strand. The result that the bubble distributions are more sharply peaked at the active sites than thermodynamically obtained distributions is ascribed to the fact that the bubble lifetimes affect the distributions. Certain base-pair sequences are found to promote long-lived bubbles, and we argue that this is a result of length scale competition between the nonlinearity and disorder present in the system.