scholarly journals Velocity distribution in active particles systems

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Umberto Marini Bettolo Marconi ◽  
Nicoletta Gnan ◽  
Matteo Paoluzzi ◽  
Claudio Maggi ◽  
Roberto Di Leonardo

Abstract We derive an analytic expression for the distribution of velocities of multiple interacting active particles which we test by numerical simulations. In clear contrast with equilibrium we find that the velocities are coupled to positions. Our model shows that, even for two particles only, the individual velocities display a variance depending on the interparticle separation and the emergence of correlations between the velocities of the particles. When considering systems composed of many particles we find an analytic expression connecting the overall velocity variance to density, at the mean-field level, and to the pair distribution function valid in the limit of small noise correlation times. Finally we discuss the intriguing analogies and main differences between our effective free energy functional and the theoretical scenario proposed so far for phase-separating active particles.


1995 ◽  
Vol 02 (06) ◽  
pp. 773-785 ◽  
Author(s):  
L. WOJTCZAK ◽  
J.H. RUTKOWSKI

The thermodynamic potential governing the surface-melting, considered in terms of the crystallinity and its profile is related to the Gibbs free-energy functional, leads to van der Waals equation of state. The presented construction allows us to determine the mean-field coefficients by their reference to material constants. The model is applied to the surface-melting discussion within the Landau-type mean-field theory of phase-transitions. In particular, the surface-melting temperature is estimated and temperature dependence of the surface liquid-like layer thickness profile is obtained.



2007 ◽  
Vol 16 (02) ◽  
pp. 222-236 ◽  
Author(s):  
M. BENDER ◽  
T. DUGUET

We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in the spirit of a naive generalized density functional theory.



2014 ◽  
Vol 14 (19) ◽  
pp. 27195-27231
Author(s):  
C. R. MacIntosh ◽  
K. P. Shine ◽  
W. J. Collins

Abstract. Multi-model ensembles are frequently used to assess understanding of the response of ozone and methane lifetime to changes in emissions of ozone precursors such as NOx, VOC and CO. When these ozone changes are used to calculate radiative forcing (RF) (and climate metrics such as the global warming potential (GWP) and global temperature potential (GTP)) there is a methodological choice, determined partly by the available computing resources, as to whether the mean ozone (and methane lifetime) changes are input to the radiation code, or whether each model's ozone and methane changes are used as input, with the average RF computed from the individual model RFs. We use data from the Task Force on Hemispheric Transport of Air Pollution Source-Receptor global chemical transport model ensemble to assess the impact of this choice for emission changes in 4 regions (East Asia, Europe, North America and South Asia). We conclude that using the multi-model mean ozone and methane responses is accurate for calculating the mean RF, with differences up to 0.6% for CO, 0.7% for VOC and 2% for NOx. Differences of up to 60% for NOx 7% for VOC and 3% for CO are introduced into the 20 year GWP as a result of the exponential decay terms, with similar values for the 20 years GTP. However, estimates of the SD calculated from the ensemble-mean input fields (where the SD at each point on the model grid is added to or subtracted from the mean field) are almost always substantially larger in RF, GWP and GTP metrics than the true SD, and can be larger than the model range for short-lived ozone RF, and for the 20 and 100 year GWP and 100 year GTP. We find that the effect is generally most marked for the case of NOx emissions, where the net effect is a smaller residual of terms of opposing signs. For example, the SD for the 20 year GWP is two to three times larger using the ensemble-mean fields than using the individual models to calculate the RF. Hence, while the average of multi-model fields are appropriate for calculating mean RF, GWP and GTP, they are not a reliable method for calculating the uncertainty in these fields, and in general overestimate the uncertainty.



2019 ◽  
Author(s):  
Mohammadreza Bahadorian ◽  
Christoph Zechner ◽  
Carl Modes

Many systems in biology and beyond employ collaborative, collective communication strategies for improved efficiency and adaptive benefit. One such paradigm of particular interest is the community estimation of a dynamic signal, when, for example, an epithelial tissue of cells must decide whether to react to a given dynamic external concentration of stress signaling molecules. At the level of dynamic cellular communication, however, it remains unknown what effect, if any, arises from communication beyond the mean field level. What are the limits and benefits to communication across a network of neighbor interactions? What is the role of Poissonian vs. super Poissonian dynamics in such a setting? How does the particular topology of connections impact the collective estimation and that of the individual participating cells? In this letter we construct a robust and general framework of signal estimation over continuous time Markov chains in order to address and answer these questions. Our results show that in the case of Possonian estimators, the communication solely enhances convergence speed of the Mean Squared Error (MSE) of the estimators to their steady-state values while leaving these values unchanged. However, in the super-Poissonian regime, MSE of estimators significantly decreases by increasing the number of neighbors. Surprisingly, in this case, the clustering coefficient of an estimator does not enhance its MSE while reducing total MSE of the population.



2021 ◽  
Author(s):  
Konstantinos Mazarakos ◽  
Huan-Xiang Zhou

We present a mean-field theory for the multiphase organization of multi-component biomolecular condensates and validate the theory by molecular dynamics simulations of model mixtures. A first phase transition results in the separation of the dense phase from the bulk phase. In a second phase transition, the components in the dense phase demix to localize in separate regions that attach to each other. The second phase transition occurs when the strength of cross- species attraction goes below the mean strength of the self-attraction of the individual species and reaches a critical value. At a given strength of cross-species attraction, both of the phase transitions can be observed by decreasing temperature, leading first to phase separation and then to demixing of the dense phase. The theory and simulations establish the disparity in strength between self and cross-species attraction as a main driver for the multiphase organization of multi-component biomolecular condensates.



2007 ◽  
Vol 16 (02) ◽  
pp. 533-540 ◽  
Author(s):  
K. ZBERECKI ◽  
P. MAGIERSKI ◽  
P.-H. HEENEN ◽  
N. SCHUNCK

The possible existence of stable axial octupole and tetrahedral deformations is investigated in 80 Zr and 98 Zr . HFBCS calculations with parity projection have been performed for various parametrizations of the Skyrme energy functional. The correlation and excitation energies of negative parity states associated with shape fluctuations have been obtained using the generator coordinate method (GCM). The results indicate that in these nuclei both the axial octupole and tetrahedral deformations are of dynamic character and possess similar characteristics. Various Skyrme forces give consistent results as a function of these two octupole degrees of freedom both at the mean-field level as well as for configuration mixing calculations.



2018 ◽  
Vol 856 ◽  
pp. 921-957 ◽  
Author(s):  
Maria Tătulea-Codrean ◽  
Eric Lauga

Phoretic swimmers are a class of artificial active particles that has received significant attention in recent years. By making use of self-generated gradients (e.g. in temperature, electric potential or some chemical product) phoretic swimmers are capable of self-propulsion without the complications of mobile body parts or a controlled external field. Focusing on diffusiophoresis, we quantify in this paper the mechanisms through which phoretic particles may achieve chemotaxis, both at the individual and the non-interacting population level. We first derive a fully analytical law for the instantaneous propulsion and orientation of a phoretic swimmer with general axisymmetric surface properties, in the limit of zero Péclet number and small Damköhler number. We then apply our results to the case of a Janus sphere, one of the most common designs of phoretic swimmers used in experimental studies. We next put forward a novel application of generalised Taylor dispersion theory in order to characterise the long-time behaviour of a population of non-interacting phoretic swimmers. We compare our theoretical results with numerical simulations for the mean drift and anisotropic diffusion of phoretic swimmers in chemical gradients. Our results will help inform the design of phoretic swimmers in future experimental applications.



1993 ◽  
Vol 08 (20) ◽  
pp. 1909-1915 ◽  
Author(s):  
DIDIER CAENEPEEL ◽  
RICHARD MACKENZIE

We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument.



1974 ◽  
Vol 13 (02) ◽  
pp. 193-206
Author(s):  
L. Conte ◽  
L. Mombelli ◽  
A. Vanoli

SummaryWe have put forward a method to be used in the field of nuclear medicine, for calculating internally absorbed doses in patients. The simplicity and flexibility of this method allow one to make a rapid estimation of risk both to the individual and to the population. In order to calculate the absorbed doses we based our procedure on the concept of the mean absorbed fraction, taking into account anatomical and functional variability which is highly important in the calculation of internal doses in children. With this aim in mind we prepared tables which take into consideration anatomical differences and which permit the calculation of the mean absorbed doses in the whole body, in the organs accumulating radioactivity, in the gonads and in the marrow; all this for those radionuclides most widely used in nuclear medicine. By comparing our results with dose obtained from the use of M.I.R.D.'s method it can be seen that when the errors inherent in these types of calculation are taken into account, the results of both methods are in close agreement.



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