scholarly journals One-sided reflected Brownian motions and the KPZ fixed point

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.

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Jay A. VonBank ◽  
Mitch D. Weegman ◽  
Paul T. Link ◽  
Stephanie A. Cunningham ◽  
Kevin J. Kraai ◽  
...  

Abstract Background Animal movement patterns are the result of both environmental and physiological effects, and the rates of movement and energy expenditure of given movement strategies are influenced by the physical environment an animal inhabits. Greater white-fronted geese in North America winter in ecologically distinct regions and have undergone a large-scale shift in wintering distribution over the past 20 years. White-fronts continue to winter in historical wintering areas in addition to contemporary areas, but the rates of movement among regions, and energetic consequences of those decisions, are unknown. Additionally, linkages between wintering and breeding regions are generally unknown, and may influence within-winter movement rates. Methods We used Global Positioning System and acceleration data from 97 white-fronts during two winters to elucidate movement characteristics, model regional transition probabilities using a multistate model in a Bayesian framework, estimate regional energy expenditure, and determine behavior time-allocation influences on energy expenditure using overall dynamic body acceleration and linear mixed-effects models. We assess the linkages between wintering and breeding regions by evaluating the winter distributions for each breeding region. Results White-fronts exhibited greater daily movement early in the winter period, and decreased movements as winter progressed. Transition probabilities were greatest towards contemporary winter regions and away from historical wintering regions. Energy expenditure was up to 55% greater, and white-fronts spent more time feeding and flying, in contemporary wintering regions compared to historical regions. White-fronts subsequently summered across their entire previously known breeding distribution, indicating substantial mixing of individuals of varying breeding provenance during winter. Conclusions White-fronts revealed extreme plasticity in their wintering strategy, including high immigration probability to contemporary wintering regions, high emigration from historical wintering regions, and high regional fidelity to western regions, but frequent movements among eastern regions. Given that movements of white-fronts trended toward contemporary wintering regions, we anticipate that a wintering distribution shift eastward will continue. Unexpectedly, greater energy expenditure in contemporary wintering regions revealed variable energetic consequences of choice in wintering region and shifting distribution. Because geese spent more time feeding in contemporary regions than historical regions, increased energy expenditure is likely balanced by increased energy acquisition in contemporary wintering areas.


Soft Matter ◽  
2021 ◽  
Author(s):  
Claudio Maggi ◽  
Matteo Paoluzzi ◽  
Andrea Crisanti ◽  
Emanuela Zaccarelli ◽  
Nicoletta Gnan

We perform large-scale computer simulations of an off-lattice two-dimensional model of active particles undergoing a motility-induced phase separation (MIPS) to investigate the systems critical behaviour close to the critical point...


1999 ◽  
Vol 10 (04) ◽  
pp. 517-529 ◽  
Author(s):  
SYNGE TODO

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.


2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Omid Askarisichani ◽  
Ambuj K. Singh ◽  
Francesco Bullo ◽  
Noah E. Friedkin

AbstractThere has been longstanding interest in the evolution of positive and negative relationships among countries. An interdisciplinary field of study, Structural Balance Theory, has developed on the dynamics of such appraisal systems. However, the advancement of research in the field has been impeded by the lack of longitudinal empirical data on large-scale networks. We construct the networks of international amicable and hostile relations occurring in specific time-periods in order to study the global evolution of the network of such international appraisals. Here we present an empirical evidence on the alignment of Structural Balance Theory with the evolution of the structure of this network, and a model of the probabilistic micro-dynamics of the alterations of international appraisals during the period 1995-2018. Also remarkably, we find that the trajectory of the Frobenius norm of sequential transition probabilities, which govern the evolution of international appraisals among nations, dramatically stabilizes.


Author(s):  
Martin Schreiber ◽  
Pedro S Peixoto ◽  
Terry Haut ◽  
Beth Wingate

This paper presents, discusses and analyses a massively parallel-in-time solver for linear oscillatory partial differential equations, which is a key numerical component for evolving weather, ocean, climate and seismic models. The time parallelization in this solver allows us to significantly exceed the computing resources used by parallelization-in-space methods and results in a correspondingly significantly reduced wall-clock time. One of the major difficulties of achieving Exascale performance for weather prediction is that the strong scaling limit – the parallel performance for a fixed problem size with an increasing number of processors – saturates. A main avenue to circumvent this problem is to introduce new numerical techniques that take advantage of time parallelism. In this paper, we use a time-parallel approximation that retains the frequency information of oscillatory problems. This approximation is based on (a) reformulating the original problem into a large set of independent terms and (b) solving each of these terms independently of each other which can now be accomplished on a large number of high-performance computing resources. Our results are conducted on up to 3586 cores for problem sizes with the parallelization-in-space scalability limited already on a single node. We gain significant reductions in the time-to-solution of 118.3× for spectral methods and 1503.0× for finite-difference methods with the parallelization-in-time approach. A developed and calibrated performance model gives the scalability limitations a priori for this new approach and allows us to extrapolate the performance of the method towards large-scale systems. This work has the potential to contribute as a basic building block of parallelization-in-time approaches, with possible major implications in applied areas modelling oscillatory dominated problems.


2021 ◽  
Vol 66 (4) ◽  
pp. 293
Author(s):  
A.A. Al-Sammarraie ◽  
F.A. Ahmed ◽  
A.A. Okhunov

The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.


Author(s):  
Walter Boscheri ◽  
Giacomo Dimarco ◽  
Lorenzo Pareschi

In this paper, we propose a novel space-dependent multiscale model for the spread of infectious diseases in a two-dimensional spatial context on realistic geographical scenarios. The model couples a system of kinetic transport equations describing a population of commuters moving on a large scale (extra-urban) with a system of diffusion equations characterizing the non-commuting population acting over a small scale (urban). The modeling approach permits to avoid unrealistic effects of traditional diffusion models in epidemiology, like infinite propagation speed on large scales and mass migration dynamics. A construction based on the transport formalism of kinetic theory allows to give a clear model interpretation to the interactions between infected and susceptible in compartmental space-dependent models. In addition, in a suitable scaling limit, our approach permits to couple the two populations through a consistent diffusion model acting at the urban scale. A discretization of the system based on finite volumes on unstructured grids, combined with an asymptotic preserving method in time, shows that the model is able to describe correctly the main features of the spatial expansion of an epidemic. An application to the initial spread of COVID-19 is finally presented.


2001 ◽  
Vol 38 (A) ◽  
pp. 142-157 ◽  
Author(s):  
John Sansom ◽  
Peter Thomson

The paper proposes a hidden semi-Markov model for breakpoint rainfall data that consist of both the times at which rain-rate changes and the steady rates between such changes. The model builds on and extends the seminal work of Ferguson (1980) on variable duration models for speech. For the rainfall data the observations are modelled as mixtures of log-normal distributions within unobserved states where the states evolve in time according to a semi-Markov process. For the latter, parametric forms need to be specified for the state transition probabilities and dwell-time distributions.Recursions for constructing the likelihood are developed and the EM algorithm used to fit the parameters of the model. The choice of dwell-time distribution is discussed with a mixture of distributions over disjoint domains providing a flexible alternative. The methods are also extended to deal with censored data. An application of the model to a large-scale bivariate dataset of breakpoint rainfall measurements at Wellington, New Zealand, is discussed.


1993 ◽  
Vol 08 (18) ◽  
pp. 3107-3137 ◽  
Author(s):  
A. MIRONOV ◽  
S. PAKULIAK

The double scaling limit of a new class of the multi-matrix models proposed in Ref. 1, which possess the W-symmetry at the discrete level, is investigated in detail. These models are demonstrated to fall into the same universality class as the standard multi-matrix models. In particular, the transformation of the W-algebra at the discrete level into the continuum one of the papers2 is proposed and the corresponding partition functions compared. All calculations are demonstrated in full in the first nontrivial case of W(3)-constraints.


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