Speed of reaction-transport processes

We present an approach to determining the speed of wave-front solutions to reaction-transport processes. This method is more accurate than previous ones. This is explicitly shown for several cases of practical interest: (i) the anomalous diffusion reaction, (ii) reaction diffusion in an advective field, and (iii) time-delayed reaction diffusion. There is good agreement with the results of numerical simulations

Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Time-delayed reaction-diffusion fronts

A time-delayed second-order approximation for the front speed in reaction-dispersion systems was obtained by Fort and Méndez [Phys. Rev. Lett. 82, 867 (1999)]. Here we show that taking proper care of the effect of the time delay on the reactive process yields a different evolution equation and, therefore, an alternate equation for the front speed. We apply the new equation to the Neolithic transition. For this application the new equation yields speeds about 10% slower than the previous one

Reaction-diffusion waves of advance in the transition to agricultural economics

In a previous paper [J.Fort and V.Méndez, Phys. Rev. Lett. 82, 867 (1999)], the possible importance of higher-order terms in a human population wave of advance has been studied. However, only a few such terms were considered. Here we develop a theory including all higher-order terms. Results are in good agreement with the experimental evidence involving the expansion of agriculture in Europe

Characterization and evolution of the novel gene family FAM90A in primates originated by multiple duplication and rearrangement events

Genomic plasticity of human chromosome 8p23.1 region is highly influenced by two groups of complex segmental duplications (SDs), termed REPD and REPP, that mediate different kinds of rearrangements. Part of the difficulty to explain the wide range of phenotypes associated with 8p23.1 rearrangements is that REPP and REPD are not yet well characterized, probably due to their polymorphic status. Here, we describe a novel primate-specific gene family, named FAM90A (family with sequence similarity 90), found within these SDs. According to the current human reference sequence assembly, the FAM90A family includes 24 members along 8p23.1 region plus a single member on chromosome 12p13.31, showing copy number variation (CNV) between individuals. These genes can be classified into subfamilies I and II, which differ in their upstream and 5′-untranslated region sequences, but both share the same open reading frame and are ubiquitously expressed. Sequence analysis and comparative fluorescence in situ hybridization studies showed that FAM90A subfamily II suffered a big expansion in the hominoid lineage, whereas subfamily I members were likely generated sometime around the divergence of orangutan and African great apes by a fusion process. In addition, the analysis of the Ka/Ks ratios provides evidence of functional constraint of some FAM90A genes in all species. The characterization of the FAM90A gene family contributes to a better understanding of the structural polymorphism of the human 8p23.1 region and constitutes a good example of how SDs, CNVs and rearrangements within themselves can promote the formation of new gene sequences with potential functional consequences.

Array-CGH in patients with a clinical diagnosis of Kabuki syndrome: identification of two cases with terminal 2q37 deletion and no other recurrent rearrangement

Background: Kabuki syndrome (KS) is a multiple congenital anomaly syndrome characterized by specific facial features, mild to moderate mental retardation, postnatal growth delay, skeletal abnormalities, and unusual dermatoglyphic patterns with prominent fingertip pads. A 3.5 Mb duplication at 8p23.1-p22 was once reported as a specific alteration in KS but has not been confirmed in other patients. The molecular basis of KS remains unknown. Methods: We have studied 16 Spanish patients with a clinical diagnosis of KS or KS-like to search for genomic imbalances using genome-wide array technologies. All putative rearrangements were confirmed by FISH, microsatellite markers and/or MLPA assays, which also determined whether the imbalance was de novo or inherited. Results: No duplication at 8p23.1-p22 was observed in our patients. We detected complex rearrangements involving 2q in two patients with Kabuki-like features: 1) a de novo inverted duplication of 11 Mb with a 4.5 Mb terminal deletion, and 2) a de novo 7.2 Mb-terminal deletion in a patient with an additional de novo 0.5 Mb interstitial deletion in 16p. Additional copy number variations (CNV), either inherited or reported in normal controls, were identified and interpreted as polymorphic variants. No specific CNV was significantly increased in the KS group. Conclusion: Our results further confirmed that genomic duplications of 8p23 region are not a common cause of KS and failed to detect other recurrent rearrangement causing this disorder. The detection of two patients with 2q37 deletions suggests that there is a phenotypic overlap between the two conditions, and screening this region in the Kabuki-like patients should be considered.

Barrier for the reaction X20+ + X20+ -> X402+ in alkali-metal clusters related to electron density at the bond midpoint of the supermolecule (X20+)2

Using the extended Thomas-Fermi version of density-functional theory (DFT), calculations are presented for the barrier for the reaction Na20++Na20+¿Na402+. The deviation from the simple Coulomb barrier is shown to be proportional to the electron density at the bond midpoint of the supermolecule (Na20+)2. An extension of conventional quantum-chemical studies of homonuclear diatomic molecular ions is then effected to apply to the supermolecular ions of the alkali metals. This then allows the Na results to be utilized to make semiquantitative predictions of position and height of the maximum of the fusion barrier for other alkali clusters. These predictions are confirmed by means of similar DFT calculations for the K clusters.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

Semiclassical back reaction in the formation of a straight cosmic string

We derive the back reaction on the gravitational field of a straight cosmic string during its formation due to the gravitational coupling of the string to quantum matter fields. A very simple model of string formation is considered. The gravitational field of the string is computed in the linear approximation. The vacuum expectation value of the stress tensor of a massless scalar quantum field coupled to the string gravitational field is computed to one loop order. Finally, the back-reaction effect is obtained by solving perturbatively the semiclassical Einsteins equations.

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.