Universality of Persistence Exponents in Two-Dimensional Ostwald Ripening

Soriano, Jordi; Braslavsky, Ido; Xu, Di; Krichevsky, Oleg; Stavans, Joel

doi:10.1103/physrevlett.103.226101

Cited by 13 publications

(18 citation statements)

References 23 publications

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“…This constant γ d can be computed analytically, yielding in particular γ 2 = 0.39008 and γ 3 = 0.50945 (the authors also obtained a large d expansion of γ d ). Remarkably, this exponent θ (164) was measured in an experiment on two-dimensional Ostwald ripening [40] and a very good agreement was found with this theoretical prediction in the limit of small volume fraction. The low temperature coarsening dynamics of the one-dimensional Ising ferromagnet with conserved Kawasaki-like dynamics was also studied in Ref.…”

Section: Coarsening With a Conserved Order Parametersupporting

confidence: 73%

“…In these experiments, the persistence probability Q(t) that the local order parameter has not switched its state by the time t was found to decay algebraically Q(t) ∼ t −θ with a measured persistence exponent θ = 0.190 (31), in good agreement with analytical approximation [27] and numerical simulations [10,11]. These first results have been followed by a large numbers of other experimental measurements of the persistence probability in a variety of physical systems including NMR measurement of persistence in 1-d diffusion in Xenon gases [36], fluctuating step edges on crystals [37,38], advancing combustion fronts [39], two-dimensional Ostwald ripening [40], reactive-wetting interfaces [41] and liquid crystal turbulence [42]-some of these results will be discussed later in appropriate sections.…”

Section: (March 2013)supporting

confidence: 69%

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Persistence and first-passage properties in nonequilibrium systems

Bray

Majumdar

Schehr

2013

Advances in Physics

548

669

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In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration problems, we progressively discuss the persistence properties in systems with many degrees of freedom. These systems include spins models undergoing phase ordering dynamics, diffusion equation, fluctuating interfaces etc. Persistence properties are nontrivial in these systems as the effective underlying stochastic process is non-Markovian. Several exact and approximate methods have been developed to compute the persistence of such non-Markov processes over the last two decades, as reviewed in this article. We also discuss various generalisations of the local site persistence probability. Persistence in systems with quenched disorder is discussed briefly. Although the main emphasis of this review is on the theoretical developments on persistence, we briefly touch upon various experimental systems as well.

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Section: Coarsening With a Conserved Order Parametersupporting

confidence: 73%

Section: (March 2013)supporting

confidence: 69%

Persistence and first-passage properties in nonequilibrium systems

Bray

Majumdar

Schehr

2013

Advances in Physics

548

669

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“…error and hypergeometric functions, see Eq. (10). To our knowledge, this is the first systematic (exact up to O(…”

Section: Introductionmentioning

confidence: 74%

“…On the other hand, the exponent θ is non-trivial whenever the process is non-Markovian, i.e., has a memory. In addition to theoretical studies (for a brief review see [3]), the exponent θ has been measured in a number of experiments [4][5][6][7][8][9][10]. Even for Gaussian non-Markovian processes, θ is non-trivial [11].…”

Section: Introductionmentioning

confidence: 99%

Perturbation theory for fractional Brownian motion in presence of absorbing boundaries

2011

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Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations x(t1)x(t2) = D t2H , where H, with 0 < H < 1 is called the Hurst exponent. For H = 1/2, x(t) is a Brownian motion, while for H = 1/2, x(t) is a non-Markovian process. Here we study x(t) in presence of an absorbing boundary at the origin and focus on the probability density P+(x, t) for the process to arrive at x at time t, starting near the origin at time 0, given that it has never crossed the origin. It has a scaling form P+(x, t) ∼ t −H R+(x/t H ). Our objective is to compute the scaling function R+(y), which up to now was only known for the Markov case H = 1/2. We develop a systematic perturbation theory around this limit, setting H = 1/2 + , to calculate the scaling function R+(y) to first order in . We find that R+(y) behaves as R+(y) ∼ y φ as y → 0 (near the absorbing boundary), while R+(y) ∼ y γ exp(−y 2 /2) as y → ∞, with φ = 1 − 4 + O( 2 ) and2 ). Our -expansion result confirms the scaling relation φ = (1 − H)/H proposed in Ref. [29]. We verify our findings via numerical simulations for H = 2/3. The tools developed here are versatile, powerful, and adaptable to different situations.

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“…Excellent control over the temperature profile in these experiments significantly improved the TH measurements. The nanoliter osmometer additionally allowed us to test the recrystallization inhibition of IBPs 5,13 . In general, recrystallization is a phenomenon in which large crystals grow larger at the expense of small crystals.…”

mentioning

confidence: 99%

LabVIEW-operated Novel Nanoliter Osmometer for Ice Binding Protein Investigations

Braslavsky

Drori

2013

JoVE

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Ice-binding proteins (IBPs), including antifreeze proteins, ice structuring proteins, thermal hysteresis proteins, and ice recrystallization inhibition proteins, are found in cold-adapted organisms and protect them from freeze injuries by interacting with ice crystals. IBPs are found in a variety of organism, including fish 1 , plants 2, 3 , arthropods 4,5 , fungi 6 , and bacteria 7. IBPs adsorb to the surfaces of ice crystals and prevent water molecules from joining the ice lattice at the IBP adsorption location. Ice that grows on the crystal surface between the adsorbed IBPs develops a high curvature that lowers the temperature at which the ice crystals grow, a phenomenon referred to as the Gibbs-Thomson effect. This depression creates a gap (thermal hysteresis, TH) between the melting point and the nonequilibrium freezing point, within which ice growth is arrested [8][9][10] , see Figure 1. One of the main tools used in IBP research is the nanoliter osmometer, which facilitates measurements of the TH activities of IBP solutions. Nanoliter osmometers, such as the Clifton instrument (Clifton Technical Physics, Hartford, NY,) and Otago instrument (Otago Osmometers, Dunedin, New Zealand), were designed to measure the osmolarity of a solution by measuring the melting point depression of droplets with nanoliter volumes. These devices were used to measure the osmolarities of biological samples, such as tears 11 , and were found to be useful in IBP research. Manual control over these nanoliter osmometers limited the experimental possibilities. Temperature rate changes could not be controlled reliably, the temperature range of the Clifton instrument was limited to 4,000 mOsmol (about -7.5 °C), and temperature recordings as a function of time were not an available option for these instruments.We designed a custom-made computer-controlled nanoliter osmometer system using a LabVIEW platform (National Instruments). The cold stage, described previously 9,10 , contains a metal block through which water circulates, thereby functioning as a heat sink, see Figure 2. Attached to this block are thermoelectric coolers that may be driven using a commercial temperature controller that can be controlled via LabVIEW modules, see Figure 3. Further details are provided below. The major advantage of this system is its sensitive temperature control, see Figure 4. Automated temperature control permits the coordination of a fixed temperature ramp with a video microscopy output containing additional experimental details.To study the time dependence of the TH activity, we tested a 58 kDa hyperactive IBP from the Antarctic bacterium Marinomonas primoryensis (MpIBP) 12 . This protein was tagged with enhanced green fluorescence proteins (eGFP) in a construct developed by Peter Davies' group (Queens University) 10 . We showed that the temperature change profile affected the TH activity. Excellent control over the temperature profile in these experiments significantly improved the TH measurements. The nanoliter osmometer additionally a...

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Universality of Persistence Exponents in Two-Dimensional Ostwald Ripening

Cited by 13 publications

References 23 publications

Persistence and first-passage properties in nonequilibrium systems

Persistence and first-passage properties in nonequilibrium systems

Perturbation theory for fractional Brownian motion in presence of absorbing boundaries

LabVIEW-operated Novel Nanoliter Osmometer for Ice Binding Protein Investigations

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