Finite-barrier corrections for multidimensional barriers in colored noise.

The usual identification of reactive trajectories for the calculation of reaction rates requires very time-consuming simulations, particularly if the environment presents memory effects. In this paper, we develop a method that permits the identification of reactive trajectories in a system under the action of a stochastic colored driving. This method is based on the perturbative computation of the invariant structures that act as separatrices for reactivity.

Invariant Manifolds and Rate Constants in Driven Chemical Reactions.

Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state trajectory. Here, we extend our recent methods by constructing points on the NHIM accurately even for multidimensional cases. We also advance the implementation of machine learning approaches to construct smooth versions of the NHIM from a known high-accuracy set of its points.

Transition state theory for activated systems with driven anharmonic barriers.

Classical transition state theory has been extended to address chemical reactions across barriers that are driven and anharmonic. This resolves a challenge to the naive theory that necessarily leads to recrossings and approximate rates because it relies on a fixed dividing surface. We develop both perturbative and numerical methods for the computation of a time-dependent recrossing-free dividing surface for a model anharmonic system in a solvated environment that interacts strongly with an oscillatory external field.

Transition state theory for solvated reactions beyond recrossing-free dividing surfaces.

The accuracy of rate constants calculated using transition state theory depends crucially on the correct identification of a recrossing-free dividing surface. We show here that it is possible to define such optimal dividing surface in systems with non-Markovian friction. However, a more direct approach to rate calculation is based on invariant manifolds and avoids the use of a dividing surface altogether, Using that method we obtain an explicit expression for the rate of crossing an anharmonic potential barrier.

Transition state geometry of driven chemical reactions on time-dependent double-well potentials.

Reaction rates across time-dependent barriers are difficult to define and difficult to obtain using standard transition state theory approaches because of the complexity of the geometry of the dividing surface separating reactants and products. Using perturbation theory (PT) or Lagrangian descriptors (LDs), we can obtain the transition state trajectory and the associated recrossing-free dividing surface. With the latter, we are able to determine the exact reactant population decay and the corresponding rates to benchmark the PT and LD approaches.

Chemical reactions induced by oscillating external fields in weak thermal environments.

Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally varying external field, the transition state that the reaction must pass through during the transformation from reactant to product is no longer a fixed geometric structure, but is instead time-dependent. For a periodically forced model reaction, we develop a recrossing-free dividing surface that is attached to a transition state trajectory [T.

Communication: Transition state trajectory stability determines barrier crossing rates in chemical reactions induced by time-dependent oscillating fields.

When a chemical reaction is driven by an external field, the transition state that the system must pass through as it changes from reactant to product--for example, an energy barrier--becomes time-dependent. We show that for periodic forcing the rate of barrier crossing can be determined through stability analysis of the non-autonomous transition state. Specifically, strong agreement is observed between the difference in the Floquet exponents describing stability of the transition state trajectory, which defines a recrossing-free dividing surface [G.

Persistence of transition-state structure in chemical reactions driven by fields oscillating in time.

Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition-state barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving, barrier top also fails to be recrossing-free. We construct a moving dividing surface in phase space over a transition-state trajectory.

Chaotic dynamics in multidimensional transition states.

The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that channel the system towards and away from the transition state. The existence of these structures can only be guaranteed if the invariant hyper-sphere is normally hyperbolic, i.e.

Reaction rate calculation with time-dependent invariant manifolds.

The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in particular if the reactive system is exposed to the influence of a heat bath. As an efficient alternative, we propose here to compute invariant surfaces in the phase space of the reactive system that separate reactive from nonreactive trajectories.

Communication: transition state theory for dissipative systems without a dividing surface.

Transition state theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when the reactive system is coupled to an environment.

Phase-space geometry of the generalized Langevin equation.

The generalized Langevin equation is widely used to model the influence of a heat bath upon a reactive system. This equation will here be studied from a geometric point of view. A dynamical phase space that represents all possible states of the system will be constructed, the generalized Langevin equation will be formally rewritten as a pair of coupled ordinary differential equations, and the fundamental geometric structures in phase space will be described.

Transition-state theory rate calculations with a recrossing-free moving dividing surface.

Two different methods for transition-state theory (TST) rate calculations are presented that use the recently developed notions of the moving dividing surface and the associated moving separatrices: one is based on the flux-over-population approach and the other on the calculation of the reactive flux. The flux-over-population rate can be calculated in two ways by averaging the flux first over the noise and then over the initial conditions or vice versa. The former entails the calculation of reaction probabilities and is closely related to previous TST rate derivations.

Transition state theory for laser-driven reactions.

Recent developments in transition state theory brought about by dynamical systems theory are extended to time-dependent systems such as laser-driven reactions. Using time-dependent normal form theory, the authors construct a reaction coordinate with regular dynamics inside the transition region. The conservation of the associated action enables one to extract time-dependent invariant manifolds that act as separatrices between reactive and nonreactive trajectories and thus make it possible to predict the ultimate fate of a trajectory.

Autologous mononuclear stem cell transplantation in patients with peripheral occlusive arterial disease.

Unlabelled: Patients with chronic peripheral occlusive arterial disease often are not candidates for conventional revascularization procedures. Preclinical trials have shown that the transplantation of autologous bone marrow cells induces and increases the collateral vessel formation. We analyzed the clinical benefit of combined intraarterial and intramuscular transplantation of adult autologous mononuclear bone marrow stem cells in patients with lower-limb peripheral occlusive arterial disease.

Extracting multidimensional phase space topology from periodic orbits.

We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our findings for the hydrogen atom in crossed electric and magnetic fields.

Identifying reactive trajectories using a moving transition state.

A time-dependent no-recrossing dividing surface is shown to lead to a new criterion for identifying reactive trajectories well before they are evolved to infinite time. Numerical dynamics simulations of a dissipative anharmonic two-dimensional system confirm the efficiency of this approach. The results are compared to the standard fixed transition state dividing surface that is well-known to suffer from recrossings and therefore requires trajectories to be evolved over a long time interval before they can reliably be classified as reactive or nonreactive.

[Effects of exercise training on mobilization of BM-CPCs and migratory capacity as well as LVEF after AMI].

Background And Purpose: Bone marrow-derived circulating progenitor cells (BM-CPCs) are mobilized in adult peripheral blood (PB) during the acute myocardial infarction (AMI) period and contribute to the regeneration of infarcted myocardium. In this study, the influence of physical training on the mobilization and the migratory activity of the BM-CPCs as well as on the left ventricular function (LVEF) after AMI was examined.

Patients And Methods: 26 patients with AMI were analyzed in two groups.

[Transplantation of autologous adult bone marrow stem cells in patients with severe peripheral arterial occlusion disease].

Background: For many patients with severe peripheral arterial occlusion disease (PAOD) an interventional or surgical treatment is not feasible. The regenerative potential of adult autologous mononuclear stem cells could contribute to neoangiogenesis.

Patients And Methods: Ten patients with severe PAOD were included.

Stochastic transition states: reaction geometry amidst noise.

Classical transition state theory (TST) is the cornerstone of reaction-rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface.

Regeneration of human infarcted heart muscle by intracoronary autologous bone marrow cell transplantation in chronic coronary artery disease: the IACT Study.

Objectives: Stem cell therapy may be useful in chronic myocardial infarction (MI); this is conceivable, but not yet demonstrated in humans.

Background: After acute MI, bone marrow-derived cells improve cardiac function.

Methods: We treated 18 consecutive patients with chronic MI (5 months to 8.

[Rapid healing of a therapy-refractory diabetic foot after transplantation of autologous bone marrow stem cells].

Background: The diabetic foot mainly depends on painless pressure lesions, which are based on diabetic polyneuropathy and microangiopathy. In these cases the regenerative potential of adult autologous mononuclear stem cells could serve as causal therapy.

History And Clinical Findings: A 63-year-old patient with long-lasting type 2 diabetes mellitus suffers from a reduced walking distance of 200 m and a therapy-refractory ulcer at the right ball of the great toe.

Transition state in a noisy environment.

Transition state theory overestimates reaction rates in solution because conventional dividing surfaces between reagents and products are crossed many times by the same reactive trajectory. We describe a recipe for constructing a time-dependent dividing surface free of such recrossings in the presence of noise. The no-recrossing limit of transition state theory thus becomes generally available for the description of reactions in a fluctuating environment.