arXiv subjects

Ofer Biham

Publications and source records attributed to Ofer Biham.

At least 55 records · Page 3Linked to original sources

arXiv2009

Accurate rate coefficients for models of interstellar gas-grain chemistry

The methodology for modeling grain-surface chemistry has been greatly improved by taking into account the grain size and fluctuation effects. However, the reaction rate coefficients currently used in all practical models of gas-grain chemistry are inaccurate by a significant amount. We provide expressions for these crucial rate coefficients that are both accurate and easy to incorporate into gas-grain models. We use exact results obtained in earlier work, where the reaction rate coefficient was defined by a first-passage problem, which was solved using random walk theory. The approximate reaction rate coefficient presented here is easy to include in all models of interstellar gas-grain chemistry. In contrast to the commonly used expression, the results that it provides are in perfect agreement with detailed kinetic Monte Carlo simulations. We also show the rate coefficient for reactions involving multiple species.

astro-ph.GA↗

arXiv2009

Stochastic Analysis of Dimerization Systems

The process of dimerization, in which two monomers bind to each other and form a dimer, is common in nature. This process can be modeled using rate equations, from which the average copy numbers of the reacting monomers and of the product dimers can then be obtained. However, the rate equations apply only when these copy numbers are large. In the limit of small copy numbers the system becomes dominated by fluctuations, which are not accounted for by the rate equations. In this limit one must use stochastic methods such as direct integration of the master equation or Monte Carlo simulations. These methods are computationally intensive and rarely succumb to analytical solutions. Here we use the recently introduced moment equations which provide a highly simplified stochastic treatment of the dimerization process. Using this approach, we obtain an analytical solution for the copy numbers and reaction rates both under steady state conditions and in the time-dependent case. We analyze three different dimerization processes: dimerization without dissociation, dimerization with dissociation and hetero-dimer formation. To validate the results we compare them with the results obtained from the master equation in the stochastic limit and with those obtained from the rate equations in the deterministic limit. Potential applications of the results in different physical contexts are discussed.

physics.comp-ph↗

arXiv2009

Quantifying the connectivity of a network: The network correlation function method

Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as social networks. Lately, it was found that many of these networks display some common topological features, such as high clustering, small average path length (small world networks) and a power-law degree distribution (scale free networks). The topological features of a network are commonly related to the network's functionality. However, the topology alone does not account for the nature of the interactions in the network and their strength. Here we introduce a method for evaluating the correlations between pairs of nodes in the network. These correlations depend both on the topology and on the functionality of the network. A network with high connectivity displays strong correlations between its interacting nodes and thus features small-world functionality. We quantify the correlations between all pairs of nodes in the network, and express them as matrix elements in the correlation matrix. From this information one can plot the correlation function for the network and to extract the correlation length. The connectivity of a network is then defined as the ratio between this correlation length and the average path length of the network. Using this method we distinguish between a topological small world and a functional small world, where the latter is characterized by long range correlations and high connectivity. Clearly, networks which share the same topology, may have different connectivities, based on the nature and strength of their interactions. The method is demonstrated on metabolic networks, but can be readily generalized to other types of networks.

physics.comp-ph↗

arXiv2007

Evaluation of the Multiplane Method for Efficient Simulations of Reaction Networks

Reaction networks in the bulk and on surfaces are widespread in physical, chemical and biological systems. In macroscopic systems, which include large populations of reactive species, stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations. However, many physical systems are partitioned into microscopic domains, where the number of molecules in each domain is small and fluctuations are strong. Under these conditions, the simulation of reaction networks requires stochastic methods such as direct integration of the master equation. However, direct integration of the master equation is infeasible for complex networks, because the number of equations proliferates as the number of reactive species increases. Recently, the multiplane method, which provides a dramatic reduction in the number of equations, was introduced [A. Lipshtat and O. Biham, Phys. Rev. Lett. 93, 170601 (2004)]. The reduction is achieved by breaking the network into a set of maximal fully connected sub-networks (maximal cliques). Lower-dimensional master equations are constructed for the marginal probability distributions associated with the cliques, with suitable couplings between them. In this paper we test the multiplane method and examine its applicability. We show that the method is accurate in the limit of small domains, where fluctuations are strong. It thus provides an efficient framework for the stochastic simulation of complex reaction networks with strong fluctuations, for which rate equations fail and direct integration of the master equation is infeasible. The method also applies in the case of large domains, where it converges to the rate equation results.

cond-mat.stat-mech↗

arXiv2007

Stochastic Simulations of the Repressilator Circuit

The genetic repressilator circuit consists of three transcription factors, or repressors, which negatively regulate each other in a cyclic manner. This circuit was synthetically constructed on plasmids in {\it Escherichia coli} and was found to exhibit oscillations in the concentrations of the three repressors. Since the repressors and their binding sites often appear in low copy numbers, the oscillations are noisy and irregular. Therefore, the repressilator circuit cannot be fully analyzed using deterministic methods such as rate-equations. Here we perform stochastic analysis of the repressilator circuit using the master equation and Monte Carlo simulations. It is found that fluctuations modify the range of conditions in which oscillations appear as well as their amplitude and period, compared to the deterministic equations. The deterministic and stochastic approaches coincide only in the limit in which all the relevant components, including free proteins, plasmids and bound proteins, appear in high copy numbers. We also find that subtle features such as cooperative binding and bound-repressor degradation strongly affect the existence and properties of the oscillations.

q-bio.MN↗

arXiv2007

Temperature fluctuations of interstellar dust grains

The temperatures of interstellar dust grains are analyzed using stochastic simulations, taking into account the grain composition and size and the discreteness of the photon flux. [...] The distribution of grain temperatures is calculated for a broad range of grain sizes and for different intensities of the interstellar radiation field, relevant to diffuse clouds and to PDRs. The dependence of the average grain temperature on its size is shown for different irradiation intensities. It is found that the average temperatures of grains with radii smaller than about 0.02 $μ$m are reduced due to the fluctuations. The average temperatures of grains of radii larger than about 0.35 $μ$m are also slightly reduced due to their more efficient emission of infrared radiation, particularly when exposed to high irradiation intensities. The average temperatures of silicate and carbonaceous grains are found to depend on the radiation field intensity X_MMP according to ~X_MMP^gamma, where the exponent gamma depends on the grain size and composition. This fitting formula is expected to be useful in simulations of interstellar processes, and can replace commonly used approximations which do not account for the grain temperature fluctuations and for the detailed properties of interstellar dust particles. The implications of the results on molecular hydrogen formation are also discussed. It is concluded that grain-temperature fluctuations tend to reduce the formation rate of molecular hydrogen, and cannot account for the observations of H_2 in photon dominated regions, even in the presence of chemisorption sites.

astro-ph↗

arXiv2007

Formation of molecular hydrogen on amorphous silicate surfaces

Experimental results on the formation of molecular hydrogen on amorphous silicate surfaces are presented and analyzed using a rate equation model. The energy barriers for the relevant diffusion and desorption processes are obtained. They turn out to be significantly higher than those obtained for polycrystalline silicates, demonstrating the importance of grain morphology. Using these barriers we evaluate the efficiency of molecular hydrogen formation on amorphous silicate grains under interstellar conditions. It is found that unlike polycrystalline silicates, amorphous silicate grains are efficient catalysts of H_2 formation in diffuse interstellar clouds.

astro-ph↗

arXiv2007

Formation of Multipartite Entanglement Using Random Quantum Gates

The formation of multipartite quantum entanglement by repeated operation of one and two qubit gates is examined. The resulting entanglement is evaluated using two measures: the average bipartite entanglement and the Groverian measure. A comparison is made between two geometries of the quantum register: a one dimensional chain in which two-qubit gates apply only locally between nearest neighbors and a non-local geometry in which such gates may apply between any pair of qubits. More specifically, we use a combination of random single qubit rotations and a fixed two-qubit gate such as the controlled-phase gate. It is found that in the non-local geometry the entanglement is generated at a higher rate. In both geometries, the Groverian measure converges to its asymptotic value more slowly than the average bipartite entanglement. These results are expected to have implications on different proposed geometries of future quantum computers with local and non-local interactions between the qubits.

quant-ph↗

arXiv2007

Molecular Hydrogen Formation on Amorphous Silicates Under Interstellar Conditions

Experimental results on the formation of molecular hydrogen on amorphous silicate surfaces are presented for the first time and analyzed using a rate equation model. The energy barriers for the relevant diffusion and desorption processes are obtained. They turn out to be significantly higher than those obtained earlier for polycrystalline silicates, demonstrating the importance of grain morphology. Using these barriers we evaluate the efficiency of molecular hydrogen formation on amorphous silicate grains under interstellar conditions. It is found that unlike polycrystalline silicates, amorphous silicate grains are efficient catalysts of H$_{2}$ formation within a temperature range which is relevant to diffuse interstellar clouds. The results also indicate that the hydrogen molecules are thermalized with the surface and desorb with low kinetic energy. Thus, they are unlikely to occupy highly excited states.

astro-ph↗

arXiv2007

Deterministic and Stochastic Simulations of Simple Genetic Circuits

We analyze three simple genetic circuits which involve transcriptional regulation and feedback: the autorepressor, the switch and the repressilator, that consist of one, two and three genes, respectively. Such systems are commonly simulated using rate equations, that account for the concentrations of the mRNAs and proteins produced by these genes. Rate equations are suitable when the concentrations of the relevant molecules in a cell are large and fluctuations are negligible. However, when some of the proteins in the circuit appear in low copy numbers, fluctuations become important and the rate equations fail. In this case stochastic methods, such as direct numerical integration of the master equation or Monte Carlo simulations are required. Here we present deterministic and stochastic simulations of the autorepressor, the switch and the repressilator. We show that fluctuations give rise to quantitative and qualitative changes in the dynamics of these systems. In particular, we demonstrate a fluctuations-induced bistability in a variant of the genetic switch and and noisy oscillations obtained in the repressilator circuit.

q-bio.MN↗

arXiv2007

Groverian Entanglement Measure of Pure Quantum States with Arbitrary Partitions

The Groverian entanglement measure of pure quantum states of $n$ qubits is generalized to the case in which the qubits are divided into any $m \le n$ parties and the entanglement between these parties is evaluated. To demonstrate this measure we apply it to general states of three qubits and to symmetric states with any number of qubits such as the Greenberg-Horne-Zeiliner state and the W state.

quant-ph↗

arXiv2007

Stochastic Simulations of Genetic Switch Systems

Genetic switch systems with mutual repression of two transcription factors are studied using deterministic methods (rate equations) and stochastic methods (the master equation and Monte Carlo simulations). These systems exhibit bistability, namely two stable states such that spontaneous transitions between them are rare. Induced transitions may take place as a result of an external stimulus. We study several variants of the genetic switch and examine the effects of cooperative binding, exclusive binding, protein-protein interactions and degradation of bound repressors. We identify the range of parameters in which bistability takes place, enabling the system to function as a switch. Numerous studies have concluded that cooperative binding is a necessary condition for the emergence of bistability in these systems. We show that a suitable combination of network structure and stochastic effects gives rise to bistability even without cooperative binding. The average time between spontaneous transitions is evaluated as a function of the biological parameters.

q-bio.MN↗

arXiv2006

Genetic Toggle Switch Without Cooperative Binding

Genetic switch systems with mutual repression of two transcription factors are studied using deterministic and stochastic methods. Numerous studies have concluded that cooperative binding is a necessary condition for the emergence of bistability in these systems. Here we show that for a range of biologically relevant conditions, a suitable combination of network structure and stochastic effects gives rise to bistability even without cooperative binding.

q-bio.MN↗

arXiv2005

Molecular Hydrogen Formation on Porous Dust Grains

Recent laboratory experiments on interstellar dust analogues have shown that H_2 formation on dust grain surfaces is efficient in a range of grain temperatures below 20 K. These results indicate that surface processes may account for the observed H_2 abundance in cold diffuse and dense clouds. However, high abundances of H_2 have also been observed in warmer clouds, including photon-dominated regions (PDRs), where grain temperatures may reach 50 K, making the surface processes extremely inefficient. It was suggested that this apparent discrepancy can be resolved by chemisorption sites. However, recent experiments indicate that chemisorption processes may not be efficient at PDR temperatures. Here we consider the effect of grain porosity on H_2 formation. It is found that porosity extends the efficiency of the recombination process to higher temperatures. This is because H atoms that desorb from the internal surfaces of the pores may re-adsorb many times and thus stay longer on the surface. However, this porosity-driven extension may enable efficient H_2 formation in PDRs only if porosity also contributes to significant cooling of the grains, compared to non-porous grains.

astro-ph↗

arXiv2005

Entangled Quantum States Generated by Shor's Factoring Algorithm

The intermediate quantum states of multiple qubits, generated during the operation of Shor's factoring algorithm are analyzed. Their entanglement is evaluated using the Groverian measure. It is found that the entanglement is generated during the pre-processing stage of the algorithm and remains nearly constant during the quantum Fourier transform stage. The entanglement is found to be correlated with the speedup achieved by the quantum algorithm compared to classical algorithms.

quant-ph↗

arXiv2005

The formation of H_2 and HD with the master equation approach

The formation of H2 and HD molecules on interstellar dust grains is studied using rate equation and master equation models. Rate equations are used in the analysis of laboratory experiments which examine the formation of molecular hydrogen on astrophysically relevant surfaces. However, under interstellar conditions, rate equations are not suitable for the calculation of reaction rates on dust-grain surfaces. Due to the low flux and the sub-micron size of the grains, the populations of H and D atoms on a single grain are likely to be small. In this case the reaction rates are dominated by fluctuations and should be calculated using stochastic methods. The rate of molecular hydrogen formation in interstellar clouds is evaluated using the master equation, taking into account the distribution of grain sizes.

astro-ph↗

arXiv2005

The Groverian Measure of Entanglement for Mixed States

The Groverian entanglement measure introduced earlier for pure quantum states [O. Biham, M.A. Nielsen and T. Osborne, Phys. Rev. A 65, 062312 (2002)] is generalized to the case of mixed states, in a way that maintains its operational interpretation. The Groverian measure of a mixed state of n qubits is obtained by a purification procedure into a pure state of 2n qubits, followed by an optimization process based on Uhlmann's theorem, before the resulting state is fed into Grover's search algorithm. The Groverian measure, expressed in terms of the maximal success probability of the algorithm, provides an operational measure of entanglement of both pure and mixed quantum states of multiple qubits. These results may provide further insight into the role of entanglement in making quantum algorithms powerful.

quant-ph↗

arXiv2005

The effect of grain size distribution on H$_2$ formation rate in the interstellar medium

The formation of molecular hydrogen in the interstellar medium takes place on the surfaces of dust grains. Hydrogen molecules play a role in gas-phase reactions that produce other molecules, some of which serve as coolants during gravitational collapse and star formation. Thus, the evaluation of the roduction rate of hydrogen molecules and its dependence on the physical conditions in the cloud are of great importance. Interstellar dust grains exhibit a broad size distribution in which the small grains capture most of the surface area. Recent studies have shown that the production efficiency strongly depends on the grain composition and temperature as well as on its size. In this paper we present a formula which provides the total production rate of H$_2$ per unit volume in the cloud, taking into account the grain composition and temperature as well as the grain size distribution. The formula agrees very well with the master equation results. It shows that for a physically relevant range of grain temperatures, the production rate of H$_2$ is significantly enhanced due to their broad size distribution.

astro-ph↗