Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems

Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a "heuristic argument" that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages"). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods.

Axisymmetric long liquid bridges in a time-dependent microgravity field

This paper deals with the dynamics of liquid bridges when subjected to an oscillatory microgravity field. The analysis has been performed by using a one-dimensional slice model, already used in liquid bridge problems, which allows to calculate not only the resonance frequencies of a wide range of such fluid configurations but also the dependence of the dynamic response of the liquid bridge on the frequency on the imposed perturbations. Theoretical results are compared with experimental ones obtained aboard Spacelab-Dl, the agreement between theoretical and experimental results being satisfactory

Control of time-dependent biological processes by temporally patterned input

Temporal patterning of biological variables, in the form of oscillations and rhythms on many time scales, is ubiquitous. Altering the temporal pattern of an input variable greatly affects the output of many biological processes. We develop here a conceptual framework for a quantitative understanding of such pattern dependence, focusing particularly on nonlinear, saturable, time-dependent processes that abound in biophysics, biochemistry, and physiology. We show theoretically that pattern dependence is governed by the nonlinearity of the input–output transformation as well as its time constant. As a result, only patterns on certain time scales permit the expression of pattern dependence, and processes with different time constants can respond preferentially to different patterns. This has implications for temporal coding and decoding, and allows differential control of processes through pattern. We show how pattern dependence can be quantitatively predicted using only information from steady, unpatterned input. To apply our ideas, we analyze, in an experimental example, how muscle contraction depends on the pattern of motorneuron firing.

Time-dependent vascular regression and permeability changes in established human tumor xenografts induced by an anti-vascular endothelial growth factor/vascular permeability factor antibody

The hyperpermeability of tumor vessels to macromolecules, compared with normal vessels, is presumably due to vascular endothelial growth factor/vascular permeability factor (VEGF/VPF) released by neoplastic and/or host cells. In addition, VEGF/VPF is a potent angiogenic factor. Removal of this growth factor may reduce the permeability and inhibit tumor angiogenesis. To test these hypotheses, we transplanted a human glioblastoma (U87), a human colon adenocarcinoma (LS174T), and a human melanoma (P-MEL) into two locations in immunodeficient mice: the cranial window and the dorsal skinfold chamber. The mice bearing vascularized tumors were treated with a bolus (0.2 ml) of either a neutralizing antibody (A4.6.1) (492 μg/ml) against VEGF/VPF or PBS (control). We found that tumor vascular permeability to albumin in antibody-treated groups was lower than in the matched controls and that the effect of the antibody was time-dependent and influenced by the mode of injection. Tumor vascular permeability did not respond to i.p. injection of the antibody until 4 days posttreatment. However, the permeability was reduced within 6 h after i.v. injection of the same amount of antibody. In addition to the reduction in vascular permeability, the tumor vessels became smaller in diameter and less tortuous after antibody injections and eventually disappeared from the surface after four consecutive treatments in U87 tumors. These results demonstrate that tumor vascular permeability can be reduced by neutralization of endogenous VEGF/VPF and suggest that angiogenesis and the maintenance of integrity of tumor vessels require the presence of VEGF/VPF in the tissue microenvironment. The latter finding reveals a new mechanism of tumor vessel regression—i.e., blocking the interactions between VEGF/VPF and endothelial cells or inhibiting VEGF/VPF synthesis in solid tumors causes dramatic reduction in vessel diameter, which may block the passage of blood elements and thus lead to vascular regression.

Temperature, ordering, and equilibrium with time-dependent confining forces

The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures, whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher. Simulations with 1,000 ions reach equilibrium between the degrees of freedom when only aperiodic displacements (secular motion) are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.

Apolipoprotein E competitively inhibits receptor-dependent low density lipoprotein uptake by the liver but has no effect on cholesterol absorption or synthesis in the mouse.

This study examines the question of whether apolipoprotein E (apoE) alters steady-state concentrations of plasma cholesterol carried in low density lipoproteins (LDL-C) by acting as a competitive inhibitor of hepatic LDL uptake or by altering the rate of net cholesterol delivery from the intestinal lumen to the liver. To differentiate between these two possibilities, rates of cholesterol absorption and synthesis and the kinetics of hepatic LDL-C transport were measured in vivo in mice with either normal (apoE+/+) or zero (apoE-/-) levels of circulating apoE. Rates of cholesterol absorption were essentially identical in both genotypes and equaled approximately 44% of the daily dietary load of cholesterol. This finding was consistent with the further observation that the rates of cholesterol synthesis in the liver (approximately 2,000 nmol/h) and extrahepatic tissues (approximately 3,000 nmol/h) were also essentially identical in the two groups of mice. However, the apparent Michaelis constant for receptor-dependent hepatic LDL-C uptake was markedly lower in the apoE-/- mice (44 +/- 4 mg/dl) than in the apoE+/+ animals (329 +/- 77 mg/dl) even though the maximal transport velocity for this uptake process was essentially the same (approximately 400 micrograms/h per g) in the two groups of mice. These studies, therefore, demonstrate that apoE-containing lipoproteins can act as potent competitive inhibitors of hepatic LDL-C transport and so can significantly increase steady-state plasma LDL-C levels. This apolipoprotein plays no role, however, in the regulation of cholesterol absorption, sterol biosynthesis, or hepatic LDL receptor number, at least in the mouse.

Difference schemes for time-dependent heat conduction models with delay

Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

Time-dependent descriptors for the Poisson queue.

Bibliography: p. 67-68.

Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

A time-harmonic target-field method for designing unshielded RF coils in MRI

Time-harmonic methods are required in the accurate design of RF coils as operating frequency increases. This paper presents such a method to find a current density solution on the coil that will induce some desired magnetic field upon an asymmetrically located target region within. This inverse method appropriately considers the geometry of the coil via a Fourier series expansion, and incorporates some new regularization penalty functions in the solution process. A new technique is introduced by which the complex, time-dependent current density solution is approximated by a static coil winding pattern. Several winding pattern solutions are given, with more complex winding patterns corresponding to more desirable induced magnetic fields.

Determination of chromophore charge states in the low pH color transition of the fluorescent protein Rtms5(H146S) via time-dependent DFT

The red fluorescent protein Rtms5H146S displays a transition from blue (absorbance λmax 590 nm) to yellow (absorbance λmax not, vert, similar453 nm) upon titration to low pH. The pKa of the reaction depends on the concentration of halide, offering promise for new expressible halide sensors. The protonation state involved in the low pH form of the chromophore remains, however, ambiguous. We report calculated excitation energies of different protonation states of an RFP chromophore model. These suggest that the relevant titration site is the phenoxy moiety of the chromophore, and the relevant base and conjugate acid are anionic and neutral chromophore species, respectively.

Time-dependent evolution of tissue markers by MALDI-MS imaging

We have used MALDI-MS imaging (MALDI-MSI) to monitor the time dependent appearance and loss of signals when tissue slices are brought rapidly to room temperature for short to medium periods of time. Sections from mouse brain were cut in a cryostat microtome, placed on a MALDI target and allowed to warm to room temperature for 30 s to 3 h. Sections were then refrozen, fixed by ethanol treatment and analysed by MALDI-MSI. The intensity of a range of markers were seen to vary across the time course, both increasing and decreasing, with the intensity of some markers changing significantly within 30 s and markers also showed tissue location specific evolution. The markers resulting from this autolysis were compared directly to those that evolved in a comparable 16 h on-tissue trypsin digest, and the markers that evolved in the two studies were seen to be substantially different. These changes offer an important additional level of location-dependent information for mapping changes and seeking disease-dependent biomarkers in the tissue. They also indicate that considerable care is required to allow comparison of biomarkers between MALDI-MSI experiments and also has implications for the standard practice of thaw-mounting multiple tissue sections onto MALDI-MS targets.