scholarly journals Scaling limit of two-component interacting Brownian motions

2018 ◽  
Vol 46 (4) ◽  
pp. 2038-2063 ◽  
Author(s):  
Insuk Seo
2006 ◽  
Vol 06 (02) ◽  
pp. 213-228
Author(s):  
LUIZ RENATO FONTES ◽  
CHARLES M. NEWMAN

In this paper we construct an object which we call the full Brownian web (FBW) and prove that the collection of all spacetime trajectories of a class of one-dimensional stochastic flows converges weakly, under diffusive rescaling, to the FBW. The (forward) paths of the FBW include the coalescing Brownian motions of the ordinary Brownian web along with bifurcating paths. Convergence of rescaled stochastic flows to the FBW follows from general characterization and convergence theorems that we present here combined with earlier results of Piterbarg.


2017 ◽  
Vol 354 (2) ◽  
pp. 549-589 ◽  
Author(s):  
Joscha Diehl ◽  
Massimiliano Gubinelli ◽  
Nicolas Perkowski

2015 ◽  
Vol 25 (3) ◽  
pp. 1349-1382 ◽  
Author(s):  
Patrik L. Ferrari ◽  
Herbert Spohn ◽  
Thomas Weiss

2005 ◽  
Vol 05 (03) ◽  
pp. 343-384 ◽  
Author(s):  
PETER M. KOTELENEZ

Two types of point particles, large and small, with state space ℝd are considered, where d ≥ 2 and "large" and "small" refer to different masses. The small particles move deterministically with very large initial velocities. They transfer their momenta to the large particles through a smooth mean field interaction which completely determines the motion of the large particles. The joint dynamics is described in a spacetime lattice by an Euler scheme for coupled oscillators with a friction term for the large particles. This lattice defines the mesoscale for the system. A scaling limit leads to a replacement of the mesoscale by the macroscale as follows: The very large initial velocities are assumed to be independent and they let a small particle interact with a large particle only for a short time, after which the particle escapes to infinity and new particles start interacting with the large particles. Thus, the initial spatial independence of the small particles causes independence in the time increments of the velocities of the large particles. Therefore, as the friction of the large particles and the speed of the small particles tend to infinity in this scaling limit, the positions of the large particles become the positions of spatially correlated Brownian motions whose correlations can be computed from the interaction force. A similar result holds for a system without friction, where the velocities of the large particles become spatially correlated Brownian motions.


2020 ◽  
Vol 8 ◽  
Author(s):  
Mihai Nica ◽  
Jeremy Quastel ◽  
Daniel Remenik

Abstract We consider the system of one-sided reflected Brownian motions that is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and hitting times of exponential random walks, and that it converges in the 1:2:3 scaling limit to the KPZ fixed point, the scaling-invariant Markov process defined in [MQR17] and believed to govern the long-time, large-scale fluctuations for all models in the KPZ universality class. Brownian last-passage percolation was shown recently in [DOV18] to converge to the Airy sheet (or directed landscape), defined there as a strong limit of a functional of the Airy line ensemble. This establishes the variational formula for the KPZ fixed point in terms of the Airy sheet.


1965 ◽  
Vol 5 ◽  
pp. 109-111
Author(s):  
Frederick R. West

There are certain visual double stars which, when close to a node of their relative orbit, should have enough radial velocity difference (10-20 km/s) that the spectra of the two component stars will appear resolved on high-dispersion spectrograms (5 Å/mm or less) obtainable by use of modern coudé and solar spectrographs on bright stars. Both star images are then recorded simultaneously on the spectrograph slit, so that two stellar components will appear on each spectrogram.


Author(s):  
R.J. Mount ◽  
R.V. Harrison

The sensory end organ of the ear, the organ of Corti, rests on a thin basilar membrane which lies between the bone of the central modiolus and the bony wall of the cochlea. In vivo, the organ of Corti is protected by the bony wall which totally surrounds it. In order to examine the sensory epithelium by scanning electron microscopy it is necessary to dissect away the protective bone and expose the region of interest (Fig. 1). This leaves the fragile organ of Corti susceptible to physical damage during subsequent handling. In our laboratory cochlear specimens, after dissection, are routinely prepared by the O-T- O-T-O technique, critical point dried and then lightly sputter coated with gold. This processing involves considerable specimen handling including several hours on a rotator during which the organ of Corti is at risk of being physically damaged. The following procedure uses low cost, readily available materials to hold the specimen during processing ,preventing physical damage while allowing an unhindered exchange of fluids.Following fixation, the cochlea is dehydrated to 70% ethanol then dissected under ethanol to prevent air drying. The holder is prepared by punching a hole in the flexible snap cap of a Wheaton vial with a paper hole punch. A small amount of two component epoxy putty is well mixed then pushed through the hole in the cap. The putty on the inner cap is formed into a “cup” to hold the specimen (Fig. 2), the putty on the outside is smoothed into a “button” to give good attachment even when the cap is flexed during handling (Fig. 3). The cap is submerged in the 70% ethanol, the bone at the base of the cochlea is seated into the cup and the sides of the cup squeezed with forceps to grip it (Fig.4). Several types of epoxy putty have been tried, most are either soluble in ethanol to some degree or do not set in ethanol. The only putty we find successful is “DUROtm MASTERMENDtm Epoxy Extra Strength Ribbon” (Loctite Corp., Cleveland, Ohio), this is a blue and yellow ribbon which is kneaded to form a green putty, it is available at many hardware stores.


1997 ◽  
Vol 90 (4) ◽  
pp. 679-681
Author(s):  
F. SAIJA ◽  
G. FIUMARA ◽  
P.V. GIAQUINTA

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