S-shooting: a Bennett–Chandler-like method for the computation of rate constants from committor trajectories

Mechanisms of rare transitions between long-lived stable states are often analyzed in terms of commitment probabilities, determined from swarms of short molecular dynamics trajectories. Here, we present a computer simulation method to determine rate constants from such short trajectories combined with free energy calculations. The method, akin to the Bennett–Chandler approach for the calculation of reaction rate constants, requires the definition of a valid reaction coordinate and can be applied to both under- and overdamped dynamics. We verify the correctness of the algorithm using a one-dimensional random walker in a double-well potential and demonstrate its applicability to complex transitions in condensed systems by calculating cavitation rates for water at negative pressures.

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Ethyl cation transfer from diethylchloronium to alkyl aromatics studied by high pressure mass spectrometry

Canadian Journal of Chemistry ◽

10.1139/v88-202 ◽

1988 ◽

Vol 66 (5) ◽

pp. 1239-1248

Author(s):

Peggy Jane Mathews ◽

John A. Stone

Keyword(s):

High Pressure ◽

Temperature Coefficient ◽

Rate Constants ◽

Negative Temperature ◽

Ion Source ◽

Positive Temperature ◽

Reaction Rate Constants ◽

Benzene Toluene ◽

Double Well Potential ◽

Ethyl Cation

Diethylchloronium (C2H5)2Cl+) has been formed in a high pressure (2–4 Torr) ion source using a C2H5Cl/CH4 mixture. (C2H5)2Cl+ reacts with C2H5Cl (Ea = 22 ± 2 kcal mol−1) at temperatures above 500 K to give [Formula: see text]. The reaction of (C2H5)2Cl+ with B (B = benzene, toluene, isopropylbenzene, mesitylene) yields mainly C2H5B+ at temperatures below 500 K but BH+ is also formed at higher temperatures. The further reactions of C2H5B+ include proton transfer to B yielding BH+ (mesitylene), hydride transfer from B (isopropylbenzene), and reaction with C2H5Cl+ (C2H5)2B+ (toluene and benzene) and (C2H5)3B+ (benzene). The rate constants for the reaction (C2H5)2Cl+ + B → C2H5B+ + C2H5B+ + C2H5Cl increase in the order of increasing reaction exothermicity (mesitylene > isopropylbenzene > toluene > benzene). Mesitylene has a negative temperature coefficient, isopropylbenzene has no temperature coefficient, and toluene and benzene show positive temperature coefficients of reaction rate constants consistent with the double well potential theory for gas phase SN2 reactions.

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Searching for a one-dimensional random walker

Journal of Applied Probability ◽

10.1017/s0021900200036421 ◽

1974 ◽

Vol 11 (01) ◽

pp. 86-93 ◽

Cited By ~ 4

Author(s):

Bernard J. McCabe

Keyword(s):

Random Walk ◽

Wiener Process ◽

One Dimensional ◽

Random Walker ◽

Search Plan ◽

Crossing Time ◽

Definition Of ◽

First Crossing Time ◽

Finite Moments ◽

Bernoulli Random Walk

Let {xk } k ≧ − r be a simple Bernoulli random walk with x –r = 0. An integer valued threshold ϕ = {ϕ k } k≧1 is called a search plan if |ϕ k+1−ϕ k |≦1 for all k ≧ 1. If ϕ is a search plan let τϕ be the smallest integer k such that x and ϕ cross or touch at k. We show the existence of a search plan ϕ such that ϕ 1 = 0, the definition of ϕ does not depend on r, and the first crossing time τϕ has finite mean (and in fact finite moments of all orders). The analogous problem for the Wiener process is also solved.

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Searching for a one-dimensional random walker

Journal of Applied Probability ◽

10.2307/3212585 ◽

1974 ◽

Vol 11 (1) ◽

pp. 86-93 ◽

Cited By ~ 11

Author(s):

Bernard J. McCabe

Keyword(s):

Random Walk ◽

Wiener Process ◽

One Dimensional ◽

Random Walker ◽

Search Plan ◽

Crossing Time ◽

Definition Of ◽

First Crossing Time ◽

Finite Moments ◽

Bernoulli Random Walk

Let {xk}k ≧ − r be a simple Bernoulli random walk with x–r = 0. An integer valued threshold ϕ = {ϕk}k≧1 is called a search plan if |ϕk+1−ϕk|≦1 for all k ≧ 1. If ϕ is a search plan let τϕ be the smallest integer k such that x and ϕ cross or touch at k. We show the existence of a search plan ϕ such that ϕ1 = 0, the definition of ϕ does not depend on r, and the first crossing time τϕ has finite mean (and in fact finite moments of all orders). The analogous problem for the Wiener process is also solved.

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Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation

Science Advances ◽

10.1126/sciadv.abf1966 ◽

2021 ◽

Vol 7 (9) ◽

pp. eabf1966

Author(s):

Hang Zhang ◽

Jun Wu ◽

Daining Fang ◽

Yihui Zhang

Keyword(s):

Structural Diversity ◽

Cell Number ◽

Structural Elements ◽

Ternary Logic ◽

Stable States ◽

One Dimensional ◽

Logic Operation ◽

Artificial Materials ◽

Mechanical Metamaterials ◽

Unit Cells

Multistable mechanical metamaterials are artificial materials whose microarchitectures offer more than two different stable configurations. Existing multistable mechanical metamaterials mainly rely on origami/kirigami-inspired designs, snap-through instability, and microstructured soft mechanisms, with mostly bistable fundamental unit cells. Scalable, tristable structural elements that can be built up to form mechanical metamaterials with an extremely large number of programmable stable configurations remains illusive. Here, we harness the elastic tensile/compressive asymmetry of kirigami microstructures to design a class of scalable X-shaped tristable structures. Using these structure as building block elements, hierarchical mechanical metamaterials with one-dimensional (1D) cylindrical geometries, 2D square lattices, and 3D cubic/octahedral lattices are designed and demonstrated, with capabilities of torsional multistability or independent controlled multidirectional multistability. The number of stable states increases exponentially with the cell number of mechanical metamaterials. The versatile multistability and structural diversity allow demonstrative applications in mechanical ternary logic operators and amplitude modulators with unusual functionalities.

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Equivalent Scalar Stress Formulation Taking into Account Non-Resolved Turbulent Scales

Cardiovascular Engineering and Technology ◽

10.1007/s13239-021-00526-x ◽

2021 ◽

Author(s):

Lucas Konnigk ◽

Benjamin Torner ◽

Martin Bruschewski ◽

Sven Grundmann ◽

Frank-Hendrik Wurm

Keyword(s):

Mechanical Stress ◽

Turbulence Models ◽

Turbulent Channel Flow ◽

Simulation Method ◽

Blood Damage ◽

Stress Calculation ◽

High Risk Factors ◽

Cardiovascular Engineering ◽

Scalar Stress ◽

Definition Of

Abstract Purpose Cardiovascular engineering includes flows with fluid-dynamical stresses as a parameter of interest. Mechanical stresses are high-risk factors for blood damage and can be assessed by computational fluid dynamics. By now, it is not described how to calculate an adequate scalar stress out of turbulent flow regimes when the whole share of turbulence is not resolved by the simulation method and how this impacts the stress calculation. Methods We conducted direct numerical simulations (DNS) of test cases (a turbulent channel flow and the FDA nozzle) in order to access all scales of flow movement. After validation of both DNS with literature und experimental data using magnetic resonance imaging, the mechanical stress is calculated as a baseline. Afterwards, same flows are calculated using state-of-the-art turbulence models. The stresses are computed for every result using our definition of an equivalent scalar stress, which includes the influence from respective turbulence model, by using the parameter dissipation. Afterwards, the results are compared with the baseline data. Results The results show a good agreement regarding the computed stress. Even when no turbulence is resolved by the simulation method, the results agree well with DNS data. When the influence of non-resolved motion is neglected in the stress calculation, it is underpredicted in all cases. Conclusion With the used scalar stress formulation, it is possible to include information about the turbulence of the flow into the mechanical stress calculation even when the used simulation method does not resolve any turbulence.

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