scholarly journals Faraday wave–droplet dynamics: discrete-time analysis

2017 ◽  
Vol 821 ◽  
pp. 296-329 ◽  
Author(s):  
Matthew Durey ◽  
Paul A. Milewski
Keyword(s):  
Statistical Analysis ◽  
Fixed Points ◽  
Discrete Time ◽  
First Principles ◽  
Fluid Model ◽  
Wave System ◽  
Time Analysis ◽  
Droplet Dynamics ◽  
Pilot Wave ◽  
The Stability

A droplet may ‘walk’ across the surface of a vertically vibrating bath of the same fluid, due to the propulsive interaction with its wave field. This hydrodynamic pilot-wave system exhibits many dynamics previously believed to exist only in the quantum realm. Starting from first principles, we derive a discrete-time fluid model, whereby the bath–droplet interactions are modelled as instantaneous. By analysing the stability of the fixed points of the system, we explain the dynamics of a walking droplet and capture the quantisations for multiple-droplet interactions. Circular orbits in a harmonic potential are studied, and a double quantisation of chaotic trajectories is obtained through systematic statistical analysis.

scholarly journals Faraday pilot-wave dynamics: modelling and computation

2015 ◽  
Vol 778 ◽  
pp. 361-388 ◽  
Author(s):  
Paul A. Milewski ◽  
Carlos A. Galeano-Rios ◽  
André Nachbin ◽  
John W. M. Bush
Keyword(s):  
Fluid Model ◽  
Wave Theory ◽  
Realistic Model ◽  
Resonant Interaction ◽  
Wave System ◽  
Transient Wave ◽  
Wave Dynamics ◽  
Pilot Wave ◽  
Dynamics Modelling ◽  
Pilot Wave Theory

A millimetric droplet bouncing on the surface of a vibrating fluid bath can self-propel by virtue of a resonant interaction with its own wave field. This system represents the first known example of a pilot-wave system of the form envisaged by Louis de Broglie in his double-solution pilot-wave theory. We here develop a fluid model of pilot-wave hydrodynamics by coupling recent models of the droplet’s bouncing dynamics with a more realistic model of weakly viscous quasi-potential wave generation and evolution. The resulting model is the first to capture a number of features reported in experiment, including the rapid transient wave generated during impact, the Doppler effect and walker–walker interactions.

Thermodynamic Stability of Hexagonal and Rhombohedral Bn at Cvd Conditions from Van der Waals Corrected First Principles Calculations

2019 ◽  
Author(s):  
Henrik Pedersen ◽  
Björn Alling ◽  
Hans Högberg ◽  
Annop Ektarawong
Keyword(s):  
Thin Films ◽  
Thermodynamic Stability ◽  
First Principles ◽  
Thermal Equilibrium ◽  
Density Functional ◽  
Van Der Waals ◽  
Chemical Vapor ◽  
First Principles Calculations ◽  
Functional Theory ◽  
The Stability

Thin films of boron nitride (BN), particularly the sp<sup>2</sup>-hybridized polytypes hexagonal BN (h-BN) and rhombohedral BN (r-BN) are interesting for several electronic applications given band gaps in the UV. They are typically deposited close to thermal equilibrium by chemical vapor deposition (CVD) at temperatures and pressures in the regions 1400-1800 K and 1000-10000 Pa, respectively. In this letter, we use van der Waals corrected density functional theory and thermodynamic stability calculations to determine the stability of r-BN and compare it to that of h-BN as well as to cubic BN and wurtzitic BN. We find that r-BN is the stable sp<sup>2</sup>-hybridized phase at CVD conditions, while h-BN is metastable. Thus, our calculations suggest that thin films of h-BN must be deposited far from thermal equilibrium.

Site preference and atomic ordering in the ternary Rh5Ga2As: first-principles calculations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nilanjan Roy ◽  
Sucharita Giri ◽  
Harshit ◽  
Partha P. Jana
Keyword(s):  
Total Energy ◽  
First Principles ◽  
Density Functional ◽  
Structure Type ◽  
Site Preference ◽  
X Ray Diffraction ◽  
Atomic Ordering ◽  
Functional Theory ◽  
The Stability ◽  
Bonding Characteristics

Abstract The site preference and atomic ordering of the ternary Rh5Ga2As have been investigated using first-principles density functional theory (DFT). An interesting atomic ordering of two neighboring elements Ga and As reported in the structure of Rh5Ga2As by X-ray diffraction data only is confirmed by first-principles total-energy calculations. The previously reported experimental model with Ga/As ordering is indeed the most stable in the structure of Rh5Ga2As. The calculation detected that there is an obvious trend concerning the influence of the heteroatomic Rh–Ga/As contacts on the calculated total energy. Interestingly, the orderly distribution of As and Ga that is found in the binary GaAs (Zinc-blende structure type), retained to ternary Rh5Ga2As. The density of states (DOS) and Crystal Orbital Hamiltonian Population (COHP) are calculated to enlighten the stability and bonding characteristics in the structure of Rh5Ga2As. The bonding analysis also confirms that Rh–Ga/As short contacts are the major driving force towards the overall stability of the compound.

scholarly journals On the Stability of the Endemic Equilibrium of A Discrete-Time Networked Epidemic Model

2020 ◽  
Vol 53 (2) ◽  
pp. 2576-2581
Author(s):  
Fangzhou Liu ◽  
Shaoxuan CUI ◽  
Xianwei Li ◽  
Martin Buss
Keyword(s):  
Discrete Time ◽  
Epidemic Model ◽  
Endemic Equilibrium ◽  
The Stability

scholarly journals Anion ordering and vacancy defects in niobium perovskite oxynitrides

2021 ◽  
Vol 2 (7) ◽  
pp. 2398-2407
Author(s):  
Joshua J. Brown ◽  
Youxiang Shao ◽  
Zhuofeng Ke ◽  
Alister J. Page
Keyword(s):  
First Principles ◽  
First Principles Calculations ◽  
Defect Engineering ◽  
Vacancy Defects ◽  
The Stability

First-principles calculations predict the stability and mobility of vacancy defects in niobium perovskite oxynitrides, aiding defect engineering for enhanced photocatalysis.

scholarly journals Emergent chiral symmetry in a three-dimensional interacting Dirac liquid

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
András L. Szabó ◽  
Bitan Roy
Keyword(s):  
Fixed Points ◽  
Chiral Symmetry ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Spatial Dimension ◽  
Dirac Fermions ◽  
Electronic Interactions ◽  
Emergent Phenomena ◽  
Ordered Phases ◽  
The Stability

Abstract We compute the effects of strong Hubbardlike local electronic interactions on three-dimensional four-component massless Dirac fermions, which in a noninteracting system possess a microscopic global U(1) ⊗ SU(2) chiral symmetry. A concrete lattice realization of such chiral Dirac excitations is presented, and the role of electron-electron interactions is studied by performing a field theoretic renormalization group (RG) analysis, controlled by a small parameter ϵ with ϵ = d−1, about the lower-critical one spatial dimension. Besides the noninteracting Gaussian fixed point, the system supports four quantum critical and four bicritical points at nonvanishing interaction couplings ∼ ϵ. Even though the chiral symmetry is absent in the interacting model, it gets restored (either partially or fully) at various RG fixed points as emergent phenomena. A representative cut of the global phase diagram displays a confluence of scalar and pseudoscalar excitonic and superconducting (such as the s-wave and p-wave) mass ordered phases, manifesting restoration of (a) chiral U(1) symmetry between two excitonic masses for repulsive interactions and (b) pseudospin SU(2) symmetry between scalar or pseudoscalar excitonic and superconducting masses for attractive interactions. Finally, we perturbatively study the effects of weak rotational symmetry breaking on the stability of various RG fixed points.

scholarly journals The stability and electronic and photocatalytic properties of the ZnWO4 (010) surface determined from first-principles and thermodynamic calculations

RSC Advances ◽  
2021 ◽  
Vol 11 (38) ◽  
pp. 23477-23490
Author(s):  
Yonggang Wu ◽  
Jihua Zhang ◽  
Bingwei Long ◽  
Hong Zhang
Keyword(s):  
Phase Diagram ◽  
Density Functional Theory ◽  
First Principles ◽  
Density Functional ◽  
Thermodynamic Calculations ◽  
Photocatalytic Properties ◽  
Thermodynamic Approach ◽  
Functional Theory ◽  
Stability Phase Diagram ◽  
The Stability

The ZnWO4 (010) surface termination stability is studied using a density functional theory-based thermodynamic approach. The stability phase diagram shows that O-Zn, DL-W, and DL-Zn terminations of ZnWO4 (010) can be stabilized.

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