Intermittency in solutions of the three-dimensional Navier-Stokes equations

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Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe

Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure

The Evolution of Travelling Waves in a KPP Reaction-Diffusion Model with Cut-off Reaction Rate. I. Permanent Form Travelling Waves

We consider Kolmogorov--Petrovskii--Piscounov (KPP) type models in the presence of a discontinuous cut-off in reaction rate at concentration $u=u_c$. In Part I we examine permanent form travelling wave solutions (a companion paper, Part II, is devoted to their evolution in the large time limit). For each fixed cut-off value $0<u_c<1$, we prove the existence of a unique permanent form travelling wave with a continuous and monotone decreasing propagation speed $v^*(u_c)$. We extend previous asymptotic results in the limit of small $u_c$ and present new asymptotic results in the limit of large $u_c$ which are respectively obtained via the systematic use of matched and regular asymptotic expansions. The asymptotic results are confirmed against numerical results obtained for the particular case of a cut-off Fisher reaction function

Long-range and rapid transport of individual nano-objects by a hybrid electrothermoplasmonic nanotweezer

Plasmon-enhanced optical trapping is being actively studied to provide efficient manipulation of nanometre-sized objects. However, a long-standing issue with previously proposed solutions is how to controllably load the trap on-demand without relying on Brownian diffusion. Here, we show that the photo-induced heating of a nanoantenna in conjunction with an applied a.c. electric field can initiate rapid microscale fluid motion and particle transport with a velocity exceeding 10 μm s -1 , which is over two orders of magnitude faster than previously predicted. Our electrothermoplasmonic device enables on-demand long-range and rapid delivery of single nano-objects to specific plasmonic nanoantennas, where they can be trapped and even locked in place. We also present a physical model that elucidates the role of both heat-induced fluidic motion and plasmonic field enhancement in the plasmon-assisted optical trapping process. Finally, by applying a d.c. field or low-frequency a.c. field (below 10 Hz) while the particle is held in the trap by the gradient force, the trapped nano-objects can be immobilized into plasmonic hotspots, thereby providing the potential for effective low-power nanomanufacturing on-chip

Quantum dynamics in strong fluctuating fields

A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong time-dependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. Herein, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis the influence of nonequilibrium fluctuations and periodic electrical fields on quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance.Comment: review article, Advances in Physics (2005), in pres

Analysis of Microsatellite Polymorphism in Inbred Knockout Mice

Previously, we found that the genotype of 42 out of 198 mouse microsatellite loci, which are distributed among all chromosomes except the Y chromosome, changed from monomorphism to polymorphism (CMP) in a genetically modified inbred mouse strain. In this study, we further examined whether CMP also relates to the homologous recombination in gene knockout (KO) mouse strains. The same 42 microsatellite loci were analyzed by polymerase chain reaction (PCR) in 29 KO inbred mouse strains via short tandem sequence repeat (STR) scanning and direct sequence cloning to justify microsatellite polymorphisms. The C57BL/6J and 129 mouse strains, from which these 29 KO mice were derived, were chosen as the background controls. The results indicated that 10 out of 42 (23.8%) loci showed CMP in some of these mouse strains. Except for the trinucleotide repeat locus of D3Mit22, which had microsatellite CMP in strain number 9, the core sequences of the remaining 41 loci were dinucleotide repeats, and 9 out of 41 (21.95%) showed CMPs among detected mouse strains. However, 11 out of 29 (37.9%) KO mice strains were recognized as having CMPs. The popular dinucleotide motifs in CMP were (TG)n (50%, 2/4), followed by (GT)n (27.27%, 3/11) and (CA)n (23.08%, 3/13). The microsatellite CMP in (CT)n and (AG)n repeats were 20% (1/5). According to cloning sequencing results, 6 KO mouse strains showed insertions of nucleotides whereas 1 showed a deletion. Furthermore, 2 loci (D13Mit3 and D14Mit102) revealed CMP in 2 strains, and mouse strain number 9 showed CMPs in two loci (D3Mit22 and D13Mit3) simultaneously. Collectively, these results indicated that microsatellite polymorphisms were present in the examined inbred KO mice

Intertwining personal and reward relevance: evidence from the drift-diffusion model.

In their seminal paper 'Is our self nothing but reward', Northoff and Hayes (Biol Psychiatry 69(11):1019-1025, Northoff, Hayes, Biological Psychiatry 69(11):1019-1025, 2011) proposed three models of the relationship between self and reward and opened a continuing debate about how these different fields can be linked. To date, none of the proposed models received strong empirical support. The present study tested common and distinct effects of personal relevance and reward values by de-componenting different stages of perceptual decision making using a drift-diffusion approach. We employed a recently developed associative matching paradigm where participants (N = 40) formed mental associations between five geometric shapes and five labels referring personal relevance in the personal task, or five shape-label pairings with different reward values in the reward task and then performed a matching task by indicating whether a displayed shape-label pairing was correct or incorrect. We found that common effects of personal relevance and monetary reward were manifested in the facilitation of behavioural performance for high personal relevance and high reward value as socially important signals. The differential effects between personal and monetary relevance reflected non-decisional time in a perceptual decision process, and task-specific prioritization of stimuli. Our findings support the parallel processing model (Northoff & Hayes, Biol Psychiatry 69(11):1019-1025, Northoff, Hayes, Biological Psychiatry 69(11):1019-1025, 2011) and suggest that self-specific processing occurs in parallel with high reward processing. Limitations and further directions are discussed

Cleavage of von Willebrand Factor by Granzyme M Destroys Its Factor VIII Binding Capacity

Von Willebrand factor (VWF) is a pro-hemostatic multimeric plasma protein that promotes platelet aggregation and stabilizes coagulation factor VIII (FVIII) in plasma. The metalloproteinase ADAMTS13 regulates the platelet aggregation function of VWF via proteolysis. Severe deficiency of ADAMTS13 is associated with thrombotic thrombocytopenic purpura, but does not always correlate with its clinical course. Therefore, other proteases could also be important in regulating VWF activity. In the present study, we demonstrate that VWF is cleaved by the cytotoxic lymphocyte granule component granzyme M (GrM). GrM cleaved both denaturated and soluble plasma-derived VWF after Leu at position 276 in the D3 domain. GrM is unique in that it did not affect the multimeric size and pro-hemostatic platelet aggregation ability of VWF, but instead destroyed the binding of VWF to FVIII in vitro. In meningococcal sepsis patients, we found increased plasma GrM levels that positively correlated with an increased plasma VWF/FVIII ratio in vivo. We conclude that, next to its intracellular role in triggering apoptosis, GrM also exists extracellularly in plasma where it could play a physiological role in controlling blood coagulation by determining plasma FVIII levels via proteolytic processing of its carrier VWF