Ordering kinetics in liquid crystals with long-ranged interactions

Singh, Amrita; Ahmad, Shaista; Puri, Sanjay; Singh, Shri

doi:10.1140/epje/i2014-14002-9

Cited by 11 publications

(6 citation statements)

References 29 publications

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“…We thus consider n < 4 cases for the long-ranged interaction. For each value of n , we cut-off the interaction at r c = (2.5) 6/ n to accelerate our simulation [ 41 ]. We stress that the simulations are numerically very demanding for larger cut-offs.…”

Section: Details Of Simulationmentioning

confidence: 99%

Ordering Dynamics in Neuron Activity Pattern Model: An Insight to Brain Functionality

Gundh

Singh

2015

PLoS ONE

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We study the domain ordering kinetics in d = 2 ferromagnets which corresponds to populated neuron activities with both long-ranged interactions, V(r) ∼ r −n and short-ranged interactions. We present the results from comprehensive Monte Carlo (MC) simulations for the nonconserved Ising model with n ≥ 2, interaction range considering near and far neighbors. Our model results could represent the long-ranged neuron kinetics (n ≤ 4) in consistent with the same dynamical behaviour of short-ranged case (n ≥ 4) at far below and near criticality. We found that emergence of fast and slow kinetics of long and short ranged case could imitate the formation of connections among near and distant neurons. The calculated characteristic length scale in long-ranged interaction is found to be n independent (L(t) ∼ t 1/(n−2)), whereas short-ranged interaction follows L(t) ∼ t 1/2 law and approximately preserve universality in domain kinetics. Further, we did the comparative study of phase ordering near the critical temperature which follows different behaviours of domain ordering near and far critical temperature but follows universal scaling law.

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Section: Details Of Simulationmentioning

confidence: 99%

Ordering Dynamics in Neuron Activity Pattern Model: An Insight to Brain Functionality

Gundh

Singh

2015

PLoS ONE

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“…The generic simple feature of the method shall ensure its facile adoptions to nonequilibrium simulations of other models, viz., q-state Potts and clock models. In view of the delicate cut-off dependence, it would also be interesting to revisit the ordering phenomenon in long-range liquid crystals [41]. Although originally designed for simulating dynamics, our method should be proven to be handy for equilibrium simulations of systems with long-range interactions, for which there (currently) exist no cluster algorithms, e.g.,…”

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confidence: 99%

Phase ordering kinetics of the long-range Ising model

2019

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We use an efficient method that eases the daunting task of simulating dynamics in spin systems with long-range interaction. Our Monte Carlo simulations of the long-range Ising model for the nonequilibrium phase ordering dynamics in two spatial dimensions perform significantly faster than the standard Metropolis approach and considerably more efficiently than the kinetic Monte Carlo method. Importantly, this enables us to establish agreement with the theoretical prediction for the time dependence of domain growth, in contrast to previous numerical studies. This method can easily be generalized to applications in other systems.Generic models of statistical physics exhibiting a transition from disordered to ordered states have been proved to be instrumental for understanding the dynamics in diverse fields, from species evolution [1] to traffic flow [1], from economic dynamics [2] to rainfall dynamics [3]. An extensively used paradigm is the Ising model with nearest-neighbor (NNIM) interaction [4,5]. Even the complex neural dynamics of brain depends on similar underlying mechanisms [6]. The maximum entropy models obtained from experimental data upon mapping the spiking activities of the neurons onto spin variables are equivalent to Ising models [7]. However, it is believed that the neuron activities are effectively modelled by longdistance communications [6]. In nature, also many other intermolecular interactions are evidently long-range, e.g., electrostatic forces, polarization forces, etc. Hence, a more complete picture calls for employing models that consider long-range interactions.The simplest generic model system is the long-range Ising model (LRIM), which on a d-dimensional lattice is described by the Hamiltonian

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“…We thus consider n < 4 cases for the longranged interaction. For each value of n, we cut-off the interaction at r c = (2.5) 6/n to accelerate our simulation [29]. We stress that the simulations are numerically very demanding for larger cut-offs.…”

Section: Details Of Simulationmentioning

confidence: 99%

Ordering Dynamics in Neuron Activity Pattern Model: An insight to Brain Functionality

Singh¹,

Gundh²,

Singh³

2015

Preprint

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We study the ordering kinetics in d = 2 ferromagnets which corresponds to populated neuron activities with long-ranged interactions, V (r) ∼ r −n associated with short-ranged interaction. We present the results from comprehensive Monte Carlo (MC) simulations for the nonconserved Ising model with n ≥ 2. Our results of long-ranged neuron kinetics are consistent with the same dynamical behavior of short-ranged case (n > 4). The calculated characteristic length scale in long-ranged interaction is found to be n dependent (L(t) ∼ t 1/(n−2) ), whereas short-ranged interaction follows L(t) ∼ t 1/2 law and approximately preserve universality in domain kinetics. Further, we did the comparative study of phase ordering near the critical temperature which follows different behaviours of domain ordering near and far critical temperature but follows universal scaling law.

show abstract

Ordering kinetics in liquid crystals with long-ranged interactions

Cited by 11 publications

References 29 publications

Ordering Dynamics in Neuron Activity Pattern Model: An Insight to Brain Functionality

Ordering Dynamics in Neuron Activity Pattern Model: An Insight to Brain Functionality

Phase ordering kinetics of the long-range Ising model

Ordering Dynamics in Neuron Activity Pattern Model: An insight to Brain Functionality

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