scholarly journals Multiple asymptotics of kinetic equations with internal states

2020 ◽  
Vol 30 (06) ◽  
pp. 1041-1073
Author(s):  
Benoit Perthame ◽  
Weiran Sun ◽  
Min Tang ◽  
Shugo Yasuda
Keyword(s):  
Kinetic Equation ◽  
Equilibrium Equation ◽  
Internal State ◽  
Kinetic Equations ◽  
Chemical Stimulus ◽  
Adaptation Time ◽  
Macroscopic Models ◽  
Internal States ◽  
New Type ◽  
Run And Tumble

The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However, the relation between the tumbling rate and the internal state of bacteria is poorly understood. This study aims at deriving macroscopic models as limits of the mesoscopic kinetic equation in different regimes. In particular, we are interested in the roles of the stiffness of the response and the adaptation time in the kinetic equation. Depending on the asymptotics chosen both the standard Keller–Segel equation and the flux-limited Keller–Segel (FLKS) equation can appear. An interesting mathematical issue arises with a new type of equilibrium equation leading to solution with singularities.

Impaired discrimination of a subanesthetic dose of ketamine in a maternal immune activation model of schizophrenia risk

2021 ◽  
pp. 026988112110297
Author(s):  
Wayne Meighan ◽  
Thomas W Elston ◽  
David Bilkey ◽  
Ryan D Ward
Keyword(s):  
Animal Models ◽  
Drug Discrimination ◽  
Immune Activation ◽  
Internal State ◽  
Nmda Receptor Antagonist ◽  
Activation Model ◽  
Data Link ◽  
Maternal Immune Activation ◽  
Internal States ◽  
Reliable Methods

Background: Animal models of psychiatric diseases suffer from a lack of reliable methods for accurate assessment of subjective internal states in nonhumans. This gap makes translation of results from animal models to patients particularly challenging. Aims/methods: Here, we used the drug-discrimination paradigm to allow rats that model a risk factor for schizophrenia (maternal immune activation, MIA) to report on the subjective internal state produced by a subanesthetic dose of the N-methyl-D-aspartate (NMDA) receptor antagonist ketamine. Results/outcomes: The MIA rats’ discrimination of ketamine was impaired relative to controls, both in the total number of rats that acquired and the asymptotic level of discrimination accuracy. This deficit was not due to a general inability to learn to discriminate an internal drug cue or internal state generally, as MIA rats were unimpaired in the learning and acquisition of a morphine drug discrimination and were as sensitive to the internal state of satiety as controls. Furthermore, the deficit was not due to a decreased sensitivity to the physiological effects of ketamine, as MIA rats showed increased ketamine-induced locomotor activity. Finally, impaired discrimination of ketamine was only seen at subanesthetic doses which functionally correspond to psychotomimetic doses in humans. Conclusion: These data link changes in NMDA responses to the MIA model. Furthermore, they confirm the utility of the drug-discrimination paradigm for future inquiries into the subjective internal state produced in models of schizophrenia and other developmental diseases.

Kinetic equations for plasmas subjected to a strong time-dependent extenal field. Part 2. The weak-interaction approximation

1974 ◽  
Vol 11 (3) ◽  
pp. 377-387 ◽  
Author(s):  
R. Balescu ◽  
J. H. Misguich
Keyword(s):  
Kinetic Equation ◽  
General Theory ◽  
Weak Interaction ◽  
Weak Coupling ◽  
Kinetic Equations ◽  
Time Dependent ◽  
External Fields ◽  
Interaction Approximation

The general theory developed in part 1 is illustrated for a plasma described by the weak-coupling (Landau) approximation. The kinetic equation, valid for arbitrarily strong external fields, is written out explicitly.

scholarly journals Autonomous Decision-Making While Drilling

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 969
Author(s):  
Eric Cayeux ◽  
Benoît Daireaux ◽  
Adrian Ambrus ◽  
Rodica Mihai ◽  
Liv Carlsen
Keyword(s):  
Decision Making ◽  
Internal State ◽  
Drilling Process ◽  
Autonomous Decision ◽  
Internal States ◽  
Markov Decision ◽  
Drilling Operations ◽  
Drilling System ◽  
Drilling Conditions ◽  
Erratic Behavior

The drilling process is complex because unexpected situations may occur at any time. Furthermore, the drilling system is extremely long and slender, therefore prone to vibrations and often being dominated by long transient periods. Adding the fact that measurements are not well distributed along the drilling system, with the majority of real-time measurements only available at the top side and having only access to very sparse data from downhole, the drilling process is poorly observed therefore making it difficult to use standard control methods. Therefore, to achieve completely autonomous drilling operations, it is necessary to utilize a method that is capable of estimating the internal state of the drilling system from parsimonious information while being able to make decisions that will keep the operation safe but effective. A solution enabling autonomous decision-making while drilling has been developed. It relies on an optimization of the time to reach the section total depth (TD). The estimated time to reach the section TD is decomposed into the effective time spent in conducting the drilling operation and the likely time lost to solve unexpected drilling events. This optimization problem is solved by using a Markov decision process method. Several example scenarios have been run in a virtual rig environment to test the validity of the concept. It is found that the system is capable to adapt itself to various drilling conditions, as for example being aggressive when the operation runs smoothly and the estimated uncertainty of the internal states is low, but also more cautious when the downhole drilling conditions deteriorate or when observations tend to indicate more erratic behavior, which is often observed prior to a drilling event.

FRACTIONAL KINETIC EQUATIONS INVOLVING GENERALIZED V-FUNCTION VIA LAPLACE TRANSFORM

2021 ◽  
Vol 10 (5) ◽  
pp. 2593-2610
Author(s):  
Wagdi F.S. Ahmed ◽  
D.D. Pawar ◽  
W.D. Patil
Keyword(s):  
Kinetic Equation ◽  
Laplace Transform ◽  
Kinetic Equations ◽  
Graphical Interpretation ◽  
Fractional Kinetic Equation ◽  
Fractional Kinetic Equations

In this study, a new and further generalized form of the fractional kinetic equation involving the generalized V$-$function has been developed. We have discussed the manifold generality of the generalized V$-$function in terms of the solution of the fractional kinetic equation. Also, the graphical interpretation of the solutions by employing MATLAB is given. The results are very general in nature, and they can be used to generate a large number of known and novel results.

KINETIC EQUATION FOR A GAS WITH LONG-RANGE ATTRACTION

1967 ◽  
Vol 45 (11) ◽  
pp. 3555-3567 ◽  
Author(s):  
R. A. Elliott ◽  
Luis de Sobrino
Keyword(s):  
Kinetic Equation ◽  
Long Range ◽  
Short Range ◽  
Kinetic Equations ◽  
Perturbation Expansion ◽  
Interparticle Distance ◽  
Range Interaction ◽  
Short Range Repulsion ◽  
Self Consistent Field ◽  
Range Force

A classical gas whose particles interact through a weak long-range attraction and a strong short-range repulsion is studied. The Liouville equation is solved as an infinite-order perturbation expansion. The terms in this series are classified by Prigogine-type diagrams according to their order in the ratio of the range of the interaction to the average interparticle distance. It is shown that, provided the range of the short-range force is much less than the average interparticle distance which, in turn, is much less than the range of the long-range force, the terms can be grouped into two classes. The one class, represented by chain diagrams, constitutes the significant contributions of the short-range interaction; the other, represented by ring diagrams, makes up, apart from a self-consistent field term, the significant contributions from the long-range force. These contributions are summed to yield a kinetic equation. The orders of magnitude of the terms in this equation are compared for various ranges of the parameters of the system. Retaining only the dominant terms then produces a set of eight kinetic equations, each of which is valid for a definite range of the parameters of the system.

Long-term evolution of directional spectra of wind waves modelled by DNS and kinetic equations, and comparison with airborne measurements

2021 ◽  
Author(s):  
Sergei Annenkov ◽  
Victor Shrira ◽  
Leonel Romero ◽  
Ken Melville
Keyword(s):  
Angular Distribution ◽  
Kinetic Equation ◽  
Kinetic Theory ◽  
Wind Waves ◽  
Kinetic Equations ◽  
Spectral Peak ◽  
Angular Width ◽  
Angular Structure ◽  
Airborne Measurements ◽  
Steady Growth

<p>We consider the evolution of directional spectra of waves generated by constant and changing wind, modelling it by direct numerical simulation (DNS), based on the Zakharov equation. Results are compared with numerical simulations performed with the Hasselmann kinetic equation and the generalised kinetic equation, and with airborne measurements of waves generated by offshore wind, collected during the GOTEX experiment off the coast of Mexico. Modelling is performed with wind measured during the experiment, and the initial conditions are taken as the observed spectrum at the moment when wind waves prevail over swell after the initial part of the evolution.</p><p>Directional spreading is characterised by the second moment of the normalised angular distribution function, taken at selected wavenumbers relative to the spectral peak. We show that for scales longer than the spectral peak the angular spread predicted by the DNS is close to that predicted by both kinetic equations, but it underestimates the corresponding measured value, apparently due to the presence of swell. For the spectral peak and shorter waves, the DNS shows good agreement with the data. A notable feature is the steady growth of angular width at the spectral peak with time/fetch, in contrast to nearly constant width in the kinetic equations modelling. Dependence of angular width on wavenumber is shown to be much weaker than predicted by the kinetic equations. A more detailed consideration of the angular structure at the spectral peak at large fetches shows that the kinetic equations predict an angular distribution with a well-defined peak at the central angle, while the DNS reproduces the observed angular structure, with a flat peak over a range of angles.</p><p>In order to study in detail the differences between the predictions of the DNS and the kinetic equations modelling under idealised conditions, we also perform numerical simulations for the case of constant wind forcing. As in the previous case of forcing by real wind, the most striking difference between the kinetic equations and the DNS is the steady growth with time of angular width at the spectral peak, which is demonstrated by the DNS, but is not present in the modelling with the kinetic equations. We show that while the kinetic theory, both in the case of the Hasselmann equation and the generalised kinetic equation, predicts a relatively simple shape of the spectral peak, the DNS shows a more complicated structure, with a flat top and dependence of the peak position on angle. We discuss the approximations employed in the derivation of the kinetic theory and the possible causes of the found differences of directional structure.</p>

scholarly journals Fluid models with phase transition for kinetic equations in swarming

2020 ◽  
Vol 30 (10) ◽  
pp. 2023-2065 ◽  
Author(s):  
Mihaï Bostan ◽  
José Antonio Carrillo
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Kinetic Equation ◽  
Free Parameter ◽  
Kinetic Equations ◽  
Interaction Frequency ◽  
Fluid Models ◽  
Mean Velocity ◽  
Friction Forces ◽  
The Mean

We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case, the equilibria depend on the density and the orientation of the mean velocity, whereas the mean speed is not anymore a free parameter and a phase transition occurs in the homogeneous kinetic equation. We analyze the profile of equilibria for general potentials identifying a family of potentials leading to phase transitions. Finally, we derive the fluid equations when the interaction frequency becomes very large.

Collisional transport for a superthermal ion species in magnetized plasma

1986 ◽  
Vol 36 (3) ◽  
pp. 313-328 ◽  
Author(s):  
F. Cozzani ◽  
W. Horton
Keyword(s):  
Kinetic Equation ◽  
Transport Theory ◽  
A Priori ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
High Energy ◽  
Magnetized Plasma ◽  
Fractional Density ◽  
Background Ions ◽  
Ion Species

The transport theory of a high-energy ion species injected isotropically in a magnetized plasma is considered for arbitrary ratios of the high-energy ion cyclotron frequency to the collisional slowing down time. The assumptions of (i) low fractional density of the high-energy species and (ii) average ion speed faster than the thermal ions and slower than the electrons are used to decouple the kinetic equation for the high-energy species from the kinetic equations for background ions and electrons. The kinetic equation is solved by a Chapman–Enskog expansion in the strength of the gradients; an equation for the first correction to the lowest-order distribution function is obtained without scaling a priori the collision frequency with respect to the gyrofrequency. Various transport coefficients are explicitly calculated for the two cases of a weakly and a strongly magnetized plasma.

Constrained representation learning for recurrent policy optimisation under uncertainty

2019 ◽  
pp. 105971231989164
Author(s):  
Viet-Hung Dang ◽  
Ngo Anh Vien ◽  
TaeChoong Chung
Keyword(s):  
Short Term Memory ◽  
Internal State ◽  
Representation Learning ◽  
Linear Mapping ◽  
State Representation ◽  
Future Observation ◽  
Non Linear ◽  
Internal States ◽  
Markov Decision ◽  
Partially Observable

Learning to make decisions in partially observable environments is a notorious problem that requires a complex representation of controllers. In most work, the controllers are designed as a non-linear mapping from a sequence of temporal observations to actions. These problems can, in principle, be formulated as a partially observable Markov decision process whose policy can be parameterised through the use of recurrent neural networks. In this paper, we will propose an alternative framework that (a) uses the Long-Short-Term-Memory (LSTM) Encoder-Decoder framework to learn an internal state representation for historical observations and then (b) integrates it into existing recurrent policy models to improve the task performance. The LSTM Encoder encodes a history of observations as input into a representation of internal states. The LSTM Decoder can perform two alternative decoding tasks: predicting the same input observation sequence or predicting future observation sequences. The first proposed decoder acts like an auto-encoder that will guide and constrain the learning of a useful internal state for the policy optimisation task. The second proposed decoder decodes the learnt internal state by the encoder to predict future observation sequences. This idea makes the network act like a non-linear predictive state representation model. Both these decoding parts, which introduce constraints to policy representation, will help guide both the policy optimisation problem and latent state representation learning. The integration of representation learning and policy optimisation aims to help learn more complex policies and improve the performance of policy learning tasks.

Spectral functions for gases: Test of approximations employing model kinetic equations

1976 ◽  
Vol 54 (2) ◽  
pp. 137-141
Author(s):  
Norbert Müller ◽  
Siegfried Hess
Keyword(s):  
Kinetic Equation ◽  
Kinetic Equations ◽  
Spectral Functions ◽  
Model Kinetic Equations ◽  
Effective Collision

Approximations to spectral functions obtained from model kinetic equations with two effective collision frequencies are tested for a special kinetic equation which can be solved exactly.

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