scholarly journals Stochastic Model for Energy Propagation in Disordered Granular Chains

Materials ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1815
Author(s):  
Kianoosh Taghizadeh ◽  
Rohit Shrivastava ◽  
Stefan Luding
Keyword(s):  
Energy Transfer ◽  
Stochastic Model ◽  
Initial Conditions ◽  
Energy Levels ◽  
Model Systems ◽  
Energy Localization ◽  
Ensemble Averaging ◽  
Energy Propagation ◽  
Granular Chains ◽  
Repulsive Forces

Energy transfer is one of the essentials of mechanical wave propagation (along with momentum transport). Here, it is studied in disordered one-dimensional model systems mimicking force-chains in real systems. The pre-stressed random masses (other types of disorder lead to qualitatively similar behavior) interact through (linearized) Hertzian repulsive forces, which allows solving the deterministic problem analytically. The main goal, a simpler, faster stochastic model for energy propagation, is presented in the second part, after the basic equations are re-visited and the phenomenology of pulse propagation in disordered granular chains is reviewed. First, the propagation of energy in space is studied. With increasing disorder (quantified by the standard deviation of the random mass distribution), the attenuation of pulsed signals increases, transiting from ballistic propagation (in ordered systems) towards diffusive-like characteristics, due to energy localization at the source. Second, the evolution of energy in time by transfer across wavenumbers is examined, using the standing wave initial conditions of all wavenumbers. Again, the decay of energy (both the rate and amount) increases with disorder, as well as with the wavenumber. The dispersive ballistic transport in ordered systems transits to low-pass filtering, due to disorder, where localization of energy occurs at the lowest masses in the chain. Instead of dealing with the too many degrees of freedom or only with the lowest of all the many eigenmodes of the system, we propose a stochastic master equation approach with reduced complexity, where all frequencies/energies are grouped into bands. The mean field stochastic model, the matrix of energy-transfer probabilities between bands, is calibrated from the deterministic analytical solutions by ensemble averaging various band-to-band transfer situations for short times, as well as considering the basis energy levels (decaying with the wavenumber increasing) that are not transferred. Finally, the propagation of energy in the wavenumber space at transient times validates the stochastic model, suggesting applications in wave analysis for non-destructive testing, underground resource exploration, etc.

scholarly journals Energy propagation in 1D granular soft-stiff chain

2021 ◽  
Vol 249 ◽  
pp. 02002
Author(s):  
K. Taghizadeh ◽  
H. Steeb ◽  
S. Luding
Keyword(s):  
Energy Transfer ◽  
Total Energy ◽  
Initial Condition ◽  
Sinusoidal Wave ◽  
Energy Propagation ◽  
Rapid Loss ◽  
Mechanical Wave ◽  
One Dimensional ◽  
Repulsive Forces ◽  
Stiff Chain

When a mechanical wave travels through a medium, its intensity diminishes with distance. The research focuses on the energy transfer with distance as well as across different wavenumbers, as the mechanical wave propagates. The diffusive characteristic of energy propagation has been discussed for one-dimensional chains composed of random, pre-stressed soft and stiff particles interacting through Hertzian repulsive forces, which can be solved analytically after linearization. The effect of soft-stiff ratio (disorder in property) on energy transfer across wavenumbers is examined using a standing sinusoidal wave initial condition (with a specific wavenumber). From the total energy signals in wavenumber space, as function of time, it is observed that stronger disorder leads to more rapid loss of energy of the signal and faster transfer of energy to other wavenumbers.

Thermodynamics, static properties and transport behaviour of fluids with competing interactions

2022 ◽  
Author(s):  
Roman Perdomo-Pérez ◽  
Jaime Martínez Rivera ◽  
Norma Caridad Palmero Cruz ◽  
Miguel Angel Sandoval Puentes ◽  
Javier Alejandro Sánchez Gallegos ◽  
...  
Keyword(s):  
Phase Behaviour ◽  
Model Systems ◽  
Static Properties ◽  
Competing Interactions ◽  
Intermediate Range Order ◽  
System Of Particles ◽  
Transport Behaviour ◽  
Square Well ◽  
Competing Interaction ◽  
Repulsive Forces

Abstract Competing interaction fluids have become ideal model systems to study a large number of phenomena, for example, the formation of intermediate range order structures, condensed phases not seen in fluids driven by purely attractive or repulsive forces, the onset of particle aggregation under in- and out-of-equilibrium conditions, which results in the birth of reversible and irreversible aggregates or clusters whose topology and morphology depend additionally on the thermodynamic constrictions, and a particle dynamics that has a strong influence on the transport behaviour and rheological properties of the fluid. In this contribution, we study a system of particles interacting through a potential composed by a continuous succession of a short-ranged square-well, an intermediate-ranged square-shoulder and a long-ranged square-well. This potential model is chosen to systematically analyse the contribution of every component of the interaction potential on the phase behaviour, the microstructure, the morphology of the resulting aggregates and the transport phenomena of fluids described by competing interactions. Our results indicate that the inclusion of a barrier and a second well leads to new and interesting effects, which in addition result in variations of the physical properties associated to the competition among interactions.

scholarly journals Ultrabroadband two-dimensional electronic spectroscopy reveals energy flow pathways in LHCII across the visible spectrum

2019 ◽  
Vol 205 ◽  
pp. 09034
Author(s):  
Minjung Son ◽  
Alberta Pinnola ◽  
Roberto Bassi ◽  
Gabriela S. Schlau-Cohen
Keyword(s):  
Energy Transfer ◽  
Excited States ◽  
Energy Flow ◽  
Energy Levels ◽  
Electronic Spectroscopy ◽  
Visible Region ◽  
Visible Spectrum ◽  
Energy Relaxation ◽  
Two Dimensional ◽  
Flow Pathways

We utilise ultrabroadband two-dimensional electronic spectroscopy to map out pathways of energy flow in LHCII across the entire visible region. In addition to the well-established, low-lying chlorophyll Qy bands, our results reveal additional pathways of energy relaxation on the higher-lying excited states involving the S2 energy levels of carotenoids, including ultrafast carotenoid-to-chlorophyll energy transfer on 90-150 fs timescales.

scholarly journals Advancing from Convection-Allowing NWP to Warn-on-Forecast: Evidence of Progress

2018 ◽  
Vol 33 (2) ◽  
pp. 599-607 ◽  
Author(s):  
John R. Lawson ◽  
John S. Kain ◽  
Nusrat Yussouf ◽  
David C. Dowell ◽  
Dustan M. Wheatley ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Real Time ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Weather Prediction ◽  
Radar Data ◽  
Model Systems ◽  
Deterministic Systems ◽  
Forecast Lead Time ◽  
The Impact

Abstract The Warn-on-Forecast (WoF) program, driven by advanced data assimilation and ensemble design of numerical weather prediction (NWP) systems, seeks to advance 0–3-h NWP to aid National Weather Service warnings for thunderstorm-induced hazards. An early prototype of the WoF prediction system is the National Severe Storms Laboratory (NSSL) Experimental WoF System for ensembles (NEWSe), which comprises 36 ensemble members with varied initial conditions and parameterization suites. In the present study, real-time 3-h quantitative precipitation forecasts (QPFs) during spring 2016 from NEWSe members are compared against those from two real-time deterministic systems: the operational High Resolution Rapid Refresh (HRRR, version 1) and an upgraded, experimental configuration of the HRRR. All three model systems were run at 3-km horizontal grid spacing and differ in initialization, particularly in the radar data assimilation methods. It is the impact of this difference that is evaluated herein using both traditional and scale-aware verification schemes. NEWSe, evaluated deterministically for each member, shows marked improvement over the two HRRR versions for 0–3-h QPFs, especially at higher thresholds and smaller spatial scales. This improvement diminishes with forecast lead time. The experimental HRRR model, which became operational as HRRR version 2 in August 2016, also provides added skill over HRRR version 1.

Experimental and Numerical Investigation of Early Phase of Laser Ignition Under Stoichiometric and Lean Conditions

2018 ◽  
Author(s):  
Deshawn M. Coombs ◽  
Nathan D. Peters ◽  
Ben Akih-Kumgeh
Keyword(s):  
Shock Wave ◽  
Heat Release ◽  
Blast Wave ◽  
Early Phase ◽  
Initial Conditions ◽  
Energy Levels ◽  
Wave Theory ◽  
Laser Ignition ◽  
Ignition Process ◽  
Successful Operation

Forced ignition, the initiation of combustion processes by rapid and localized introduction of energy, is central to the successful operation of many combustion systems. It is therefore of interest to investigate this process, starting from the introduction of energy to the emergence of self-sustained flame or the quenching of an otherwise initialized flame kernel. Since the process is highly non-equilibrium and involves various complex kinetic phenomena, it is important to understand the key aspects that control failed or successful ignition. Detailed studies of the early phases of the ignition process can lead to knowledge of more general characteristics of the problem so that reduced models of the ignition process can be developed. These reduced versions can be used in less costly computational studies to assess various ignition events. This paper reports an experimental and numerical investigations of the early phase of laser ignition. The gas mixtures, air, methane/N2 and methane/air are considered to bring out the effect of heat release on the early flow field. The mixtures are studied at three different energy levels and the Jones blast wave theory is used to deduce the energy responsible for the development of the attendant shock waves. This energy is also used to specify initial conditions for the simulations of air and methane/air processes. Additionally, interferometry is used to resolve the density field within the plasma kernel. For the methane/air simulation two chemical models are used, a global reaction model supplemented by an ignition model and a two-step mechanism. The sensitivity of the simulations to the initial geometry of the laser spark is also investigated. The blast wave and interferometry results show that in the reacting methane/air mixture the resulting shock wave is strengthened by early heat release. It is also shown that the shock wave trajectory is not strongly affected by the initial spark geometry, but it has an impact on the velocity field and on the distribution of thermodynamic properties.

scholarly journals Evaluating Approximations and Heuristic Measures of Integrated Information

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 525 ◽  
Author(s):  
André Sevenius Nilsen ◽  
Bjørn Erik Juel ◽  
William Marshall
Keyword(s):  
Binary Systems ◽  
Initial Conditions ◽  
Transition Probability ◽  
Ground Truth ◽  
Transition Probability Matrix ◽  
Efficient Estimation ◽  
Model Systems ◽  
Practical Applications ◽  
Linear Threshold ◽  
Integrated Information

Integrated information theory (IIT) proposes a measure of integrated information, termed Phi (Φ), to capture the level of consciousness of a physical system in a given state. Unfortunately, calculating Φ itself is currently possible only for very small model systems and far from computable for the kinds of system typically associated with consciousness (brains). Here, we considered several proposed heuristic measures and computational approximations, some of which can be applied to larger systems, and tested if they correlate well with Φ. While these measures and approximations capture intuitions underlying IIT and some have had success in practical applications, it has not been shown that they actually quantify the type of integrated information specified by the latest version of IIT and, thus, whether they can be used to test the theory. In this study, we evaluated these approximations and heuristic measures considering how well they estimated the Φ values of model systems and not on the basis of practical or clinical considerations. To do this, we simulated networks consisting of 3–6 binary linear threshold nodes randomly connected with excitatory and inhibitory connections. For each system, we then constructed the system’s state transition probability matrix (TPM) and generated observed data over time from all possible initial conditions. We then calculated Φ, approximations to Φ, and measures based on state differentiation, coalition entropy, state uniqueness, and integrated information. Our findings suggest that Φ can be approximated closely in small binary systems by using one or more of the readily available approximations (r > 0.95) but without major reductions in computational demands. Furthermore, the maximum value of Φ across states (a state-independent quantity) correlated strongly with measures of signal complexity (LZ, rs = 0.722), decoder-based integrated information (Φ*, rs = 0.816), and state differentiation (D1, rs = 0.827). These measures could allow for the efficient estimation of a system’s capacity for high Φ or function as accurate predictors of low- (but not high-)Φ systems. While it is uncertain whether the results extend to larger systems or systems with other dynamics, we stress the importance that measures aimed at being practical alternatives to Φ be, at a minimum, rigorously tested in an environment where the ground truth can be established.

scholarly journals Mechanisms of triplet energy transfer across the inorganic nanocrystal/organic molecule interface

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Xiao Luo ◽  
Yaoyao Han ◽  
Zongwei Chen ◽  
Yulu Li ◽  
Guijie Liang ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Charge Transfer ◽  
Organic Molecule ◽  
Transient Absorption ◽  
High Energy ◽  
Model Systems ◽  
Trap States ◽  
Triplet Energy ◽  
Surface Trap ◽  
Triplet Energy Transfer

AbstractThe mechanisms of triplet energy transfer across the inorganic nanocrystal/organic molecule interface remain poorly understood. Many seemingly contradictory results have been reported, mainly because of the complicated trap states characteristic of inorganic semiconductors and the ill-defined relative energetics between semiconductors and molecules used in these studies. Here we clarify the transfer mechanisms by performing combined transient absorption and photoluminescence measurements, both with sub-picosecond time resolution, on model systems comprising lead halide perovskite nanocrystals with very low surface trap densities as the triplet donor and polyacenes which either favour or prohibit charge transfer as the triplet acceptors. Hole transfer from nanocrystals to tetracene is energetically favoured, and hence triplet transfer proceeds via a charge separated state. In contrast, charge transfer to naphthalene is energetically unfavourable and spectroscopy shows direct triplet transfer from nanocrystals to naphthalene; nonetheless, this “direct” process could also be mediated by a high-energy, virtual charge-transfer state.

Energy Transfer between the Low-Lying Energy Levels ofPr3+andNd3+in LaCl3

1973 ◽  
Vol 8 (3) ◽  
pp. 1010-1020 ◽  
Author(s):  
N. Krasutsky ◽  
H. W. Moos
Keyword(s):  
Energy Transfer ◽  
Energy Levels
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