Matrix exponential-based closures for the turbulent subgrid-scale stress tensor

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy

Torsion and bending of nucleic acids studied by subnanosecond time-resolved fluorescence depolarization of intercalated dyes

Subnanosecond time‐resolved fluorescence depolarization has been used to monitor the reorientation of ethidium bromide intercalated in native DNA, synthetic polynucleotide complexes, and in supercoiled plasmid DNA. The fluorescence polarization anisotropy was successfully analyzed with an elastic model of DNA dynamics, including both torsion and bending, which yielded an accurate value for the torsional rigidity of the different DNA samples. The dependence of the torsional rigidity on the base sequence, helical structure, and tertiary structure was experimentally observed. The magnitude of the polyelectrolyte contribution to the torsional rigidity of DNA was measured over a wide range of ionic strength, and compared with polyelectrolyte theories for the persistence length. We also observed a rapid initial reorientation of the intercalated ethidium which had a much smaller amplitude in RNA than in DNA

Shaping Social Activity by Incentivizing Users

Events in an online social network can be categorized roughly into endogenous events, where users just respond to the actions of their neighbors within the network, or exogenous events, where users take actions due to drives external to the network. How much external drive should be provided to each user, such that the network activity can be steered towards a target state? In this paper, we model social events using multivariate Hawkes processes, which can capture both endogenous and exogenous event intensities, and derive a time dependent linear relation between the intensity of exogenous events and the overall network activity. Exploiting this connection, we develop a convex optimization framework for determining the required level of external drive in order for the network to reach a desired activity level. We experimented with event data gathered from Twitter, and show that our method can steer the activity of the network more accurately than alternatives

The lifetime of excess atmospheric carbon dioxide

We explore the effects of a changing terrestrial biosphere on the atmospheric residence time of CO2 using three simple ocean carbon cycle models and a model of global terrestrial carbon cycling. We find differences in model behavior associated with the assumption of an active terrestrial biosphere (forest regrowth) and significant differences if we assume a donor-dependent flux from the atmosphere to the terrestrial component (e.g., a hypothetical terrestrial fertilization flux). To avoid numerical difficulties associated with treating the atmospheric CO2 decay (relaxation) curve as being well approximated by a weighted sum of exponential functions, we define the single half-life as the time it takes for a model atmosphere to relax from its present-day value half way to its equilibrium pCO2 value. This scenario-based approach also avoids the use of unit pulse (Dirac Delta) functions which can prove troublesome or unrealistic in the context of a terrestrial fertilization assumption. We also discuss some of the numerical problems associated with a conventional lifetime calculation which is based on an exponential model. We connect our analysis of the residence time of CO2 and the concept of single half-life to the residence time calculations which are based on using weighted sums of exponentials. We note that the single half-life concept focuses upon the early decline of CO2under a cutoff/decay scenario. If one assumes a terrestrial biosphere with a fertilization flux, then our best estimate is that the single half-life for excess CO2 lies within the range of 19 to 49 years, with a reasonable average being 31 years. If we assume only regrowth, then the average value for the single half-life for excess CO2 increases to 72 years, and if we remove the terrestrial component completely, then it increases further to 92 years

Openings of the rat recombinant alpha1 homomeric glycine receptor as a function of the number of sgonist molecules bound

The functional properties of rat homomeric {alpha}1 glycine receptors were investigated using whole-cell and outside-out recording from human embryonic kidney cells transfected with rat {alpha}1 subunit cDNA. Whole-cell dose-response curves gave EC50 estimates between 30 and 120 µM and a Hill slope of ~3.3. Single channel recordings were obtained by steady-state application of glycine (0.3, 1, or 10 µM) to outside-out patches. Single channel conductances were mostly 60–90 pS, but smaller conductances of ~40 pS were also seen (10% of the events) with a relative frequency that did not depend on agonist concentration. The time constants of the apparent open time distributions did not vary with agonist concentration, but short events were more frequent at low glycine concentrations. There was also evidence of a previously missed short-lived open state that was more common at lower glycine concentrations. The time constants for the different components of the burst length distributions were found to have similar values at different concentrations. Nevertheless, the mean burst length increased with increasing glycine. This was because the relative area of each burst-length component was concentration dependent and short bursts were favored at lower glycine concentrations. Durations of adjacent open and shut times were found to be strongly (negatively) correlated. Additionally, long bursts were made up of longer than average openings separated by short gaps, whereas short bursts usually consisted of single isolated short openings. The most plausible explanation for these findings is that long bursts are generated when a higher proportion of the five potential agonist binding sites on the receptor is occupied by glycine. On the basis of the concentration dependence and the intraburst structure we provide a preliminary kinetic scheme for the activation of the homomeric glycine receptor, in which any number of glycine molecules from one to five can open the channel, although not with equal efficiency

Existence of Dynamical Scaling in the Temporal Signal of Time Projection Chamber

The temporal signals from a large gas detector may show dynamical scaling due to many correlated space points created by the charged particles while passing through the tracking medium. This has been demonstrated through simulation using realistic parameters of a Time Projection Chamber (TPC) being fabricated to be used in ALICE collider experiment at CERN. An interesting aspect of this dynamical behavior is the existence of an universal scaling which does not depend on the multiplicity of the collision. This aspect can be utilised further to study physics at the device level and also for the online monitoring of certain physical observables including electronics noise which are a few crucial parameters for the optimal TPC performance.Comment: 5 pages, 6 figure