scholarly journals Universally bistable shells with nonzero Gaussian curvature for two-way transition waves

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Nikolaos Vasios ◽  
Bolei Deng ◽  
Benjamin Gorissen ◽  
Katia Bertoldi
Keyword(s):  
Gaussian Curvature ◽  
Energy Landscape ◽  
Propagation Distance ◽  
Energy Landscapes ◽  
Bending Energy ◽  
Nonlinear Dynamic Response ◽  
One Dimensional ◽  
Doubly Curved Shells ◽  
Doubly Curved ◽  
The Waves

AbstractMulti-welled energy landscapes arising in shells with nonzero Gaussian curvature typically fade away as their thickness becomes larger because of the increased bending energy required for inversion. Motivated by this limitation, we propose a strategy to realize doubly curved shells that are bistable for any thickness. We then study the nonlinear dynamic response of one-dimensional (1D) arrays of our universally bistable shells when coupled by compressible fluid cavities. We find that the system supports the propagation of bidirectional transition waves whose characteristics can be tuned by varying both geometric parameters as well as the amount of energy supplied to initiate the waves. However, since our bistable shells have equal energy minima, the distance traveled by such waves is limited by dissipation. To overcome this limitation, we identify a strategy to realize thick bistable shells with tunable energy landscape and show that their strategic placement within the 1D array can extend the propagation distance of the supported bidirectional transition waves.

scholarly journals BAR-Based Multi-Dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape

2019 ◽  
Author(s):  
Xiaohui Wang ◽  
Qiaole He ◽  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Thermodynamic Cycle ◽  
Simulation Method ◽  
Collective Variable ◽  
Energy Simulation ◽  
Energy Landscapes ◽  
One Dimensional ◽  
Free Energy Landscapes ◽  
Energy Simulations

<p>Construction of free energy landscapes at Quantum mechanics (QM) level is computationally demanding. As shown in previous studies, by employing an indirect scheme (i.e. constructing a thermodynamic cycle connecting QM states via an alchemical pathway), simulations are converged with much less computational burden. The indirect scheme makes QM/ molecular mechanics (MM) free energy simulation orders of magnitude faster than the direct QM/MM schemes. However, the indirect QM/MM simulations were mostly equilibrium sampling based and the nonequilibrium methods were merely exploited in one-dimensional alchemical QM/MM end-state correction at two end states. In this work, we represent a multi-dimensional nonequilibrium pulling scheme for indirect QM/MM free energy simulations, where the whole free energy simulation is performed only with nonequilibrium methods. The collective variable (CV) space we explore is a combination of one alchemical CV and one physically meaningful CV. The current nonequilibrium indirect QM/MM simulation method can be seen as the generalization of equilibrium perturbation based indirect QM/MM methods. The test systems include one backbone dihedral case and one distance case. The two cases are significantly different in size, enabling us to investigate the dependence of the speedup of the indirect scheme on the size of the system. It is shown that the speedup becomes larger when the size of the system becomes larger, which is consistent with the scaling behavior of QM Hamiltonians. </p>

scholarly journals BAR-Based Multi-Dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape

2019 ◽  
Author(s):  
Xiaohui Wang ◽  
Qiaole He ◽  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Thermodynamic Cycle ◽  
Simulation Method ◽  
Collective Variable ◽  
Energy Simulation ◽  
Energy Landscapes ◽  
One Dimensional ◽  
Free Energy Landscapes ◽  
Energy Simulations

<p>Construction of free energy landscapes at Quantum mechanics (QM) level is computationally demanding. As shown in previous studies, by employing an indirect scheme (i.e. constructing a thermodynamic cycle connecting QM states via an alchemical pathway), simulations are converged with much less computational burden. The indirect scheme makes QM/ molecular mechanics (MM) free energy simulation orders of magnitude faster than the direct QM/MM schemes. However, the indirect QM/MM simulations were mostly equilibrium sampling based and the nonequilibrium methods were merely exploited in one-dimensional alchemical QM/MM end-state correction at two end states. In this work, we represent a multi-dimensional nonequilibrium pulling scheme for indirect QM/MM free energy simulations, where the whole free energy simulation is performed only with nonequilibrium methods. The collective variable (CV) space we explore is a combination of one alchemical CV and one physically meaningful CV. The current nonequilibrium indirect QM/MM simulation method can be seen as the generalization of equilibrium perturbation based indirect QM/MM methods. The test systems include one backbone dihedral case and one distance case. The two cases are significantly different in size, enabling us to investigate the dependence of the speedup of the indirect scheme on the size of the system. It is shown that the speedup becomes larger when the size of the system becomes larger, which is consistent with the scaling behavior of QM Hamiltonians. </p>

Density Functional Theory Study of the Energy Landscapes for the Channeling of Li in LiFePO4

2019 ◽  
Vol 288 ◽  
pp. 98-103
Author(s):  
Batsaikhan Tankhilsaikhan ◽  
Semen Gorfman ◽  
Naran Tungalag ◽  
Norovsambuu Tuvjargal ◽  
Jav Davaasambuu ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
First Principles ◽  
Density Functional ◽  
Energy Landscape ◽  
First Principles Calculation ◽  
Density Functional Theory Study ◽  
Energy Landscapes ◽  
Functional Theory ◽  
One Dimensional ◽  
Structure Relaxation

By adopting the first-principles calculation based on density functional theory (DFT), the diffuse pattern and the energy landscape for Li transfer in the LiFePO4 are investigated for the three different directions. The results of relaxed structure are compared with those of the non-relaxed structure and the energy barriers are significantly reduced and the effect of structure relaxation is most obvious for Li displacement along [100] direction. Energy barrier for the Li diffusion along [010] direction is lower than the other two direction in both calculation which indicates that the Li diffusion in LiFePO4 is one dimensional.

scholarly journals Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 443-452
Author(s):  
Tianshu Jiang ◽  
Anan Fang ◽  
Zhao-Qing Zhang ◽  
Che Ting Chan
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Waves ◽  
Anderson Localization ◽  
Random Media ◽  
Normal Incidence ◽  
Disordered Media ◽  
One Dimensional ◽  
Gain Loss ◽  
The Waves ◽  
Localization Behavior

AbstractIt has been shown recently that the backscattering of wave propagation in one-dimensional disordered media can be entirely suppressed for normal incidence by adding sample-specific gain and loss components to the medium. Here, we study the Anderson localization behaviors of electromagnetic waves in such gain-loss balanced random non-Hermitian systems when the waves are obliquely incident on the random media. We also study the case of normal incidence when the sample-specific gain-loss profile is slightly altered so that the Anderson localization occurs. Our results show that the Anderson localization in the non-Hermitian system behaves differently from random Hermitian systems in which the backscattering is suppressed.

scholarly journals Configurational and energy landscape in one-dimensional Coulomb systems

2017 ◽  
Vol 95 (2) ◽  
Author(s):  
Lucas Varela ◽  
Gabriel Téllez ◽  
Emmanuel Trizac
Keyword(s):  
Energy Landscape ◽  
Coulomb Systems ◽  
One Dimensional

Kompressionswellen in einer isothermen Atmosphäre mit vertikalem Magnetfeld

1966 ◽  
Vol 21 (7) ◽  
pp. 1098-1106 ◽  
Author(s):  
R. Lust ◽  
M. Scholer
Keyword(s):  
Magnetic Field ◽  
Strong Influence ◽  
Vertical Direction ◽  
Time Dependent ◽  
Solar Chromosphere ◽  
Magnetohydrodynamic Equation ◽  
One Dimensional ◽  
Spatial Dimensions ◽  
Propagation Of Waves ◽  
The Waves

The propagation of waves in the solar atmosphere is investigated with respect to the problem of the chromospheric spiculae and of the heating of the solar chromosphere and corona. In particular the influence of external magnetic fields is considered. Waves of finite amplitudes are numerically calculated by solving the time-dependent magnetohydrodynamic equation for two spatial dimensions by assuming axial symmetry. For the case without a magnetic field the comparison between one dimensional and two dimensional treatment shows the strong influence of the radial propagation on the steepening of waves in the vertical direction. In the presence of a magnetic field it is shown that the propagation is strongly guided along the lines of force. The steepening of the waves along the field is much larger as compared to the case where no field is present.

Pressure Stability of Orthotropic Prolate Spheroids

1968 ◽  
Vol 12 (03) ◽  
pp. 163-164
Author(s):  
Herbert Becker
Keyword(s):  
External Pressure ◽  
Stress Fields ◽  
Membrane Stress ◽  
Doubly Curved Shells ◽  
Instability Theory ◽  
Mathematical Relation ◽  
Prolate Spheroids ◽  
Pressure Stability ◽  
Doubly Curved ◽  
Orthotropic Shells

Through the use of general instability theory for doubly curved orthotropic shells, a mathematical relation was developed to predict external pressure buckling of stiffened prolate spheroids. The procedure was applied to two experiments which were found to be in fair agreement with theory. In general, the method is applicable to doubly curved shells with orthotropic material properties (composites) as well as geometric orthotropicity, and subject to arbitrary membrane stress fields. It is not limited to pressure alone. Furthermore, because of the closed form of the solutions to many problems, the procedure would be particularly useful for optimization purposes.

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