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Juan Perez-Mercader

Publications and source records attributed to Juan Perez-Mercader.

At least 19 recordsLinked to original sources
arXiv2020

Renormalization of stochastic differential equations with multiplicative noise using effective potential methods

We present a new method to renormalize stochastic differential equations subjected to multiplicative noise. The method is based on the widely used concept of effective potential in high energy physics, and has already been successfully applied to the renormalization of stochastic differential equations subjected to additive noise. We derive a general formula for the one-loop effective potential of a single ordinary stochastic differential equation (with arbitrary interaction terms) subjected to multiplicative Gaussian noise (provided the noise satisfies a certain normalization condition). To illustrate the usefulness (and limitations) of the method, we use the effective potential to renormalize a toy chemical model based on a simplified Gray-Scott reaction. In particular, we use it to compute the scale dependence of the toy model's parameters (in perturbation theory) when subjected to a Gaussian power-law noise with short time correlations.

cond-mat.stat-mech↗
arXiv2019

From chemical soup to computing circuit: Transforming a contiguous chemical medium into a logic gate network by modulating its external conditions

It has been shown that it is possible to transform a well-stirred chemical medium into a logic-gate simply by varying the chemistry's external conditions (feed rates, lighting conditions, etc). We extend this work, showing that the same method can be generalized to spatially-extended systems. We vary the external conditions of a well-known chemical medium (a cubic autocatalytic reaction diffusion model), so that different regions of the simulated chemistry are operating under particular conditions at particular times. In so doing, we are able to transform the initially uniform chemistry, not just into a single logic gate, but into a functionally integrated network of diverse logic gates that operate as a basic computational circuit known as a full-adder.

physics.chem-ph↗
arXiv2019

Growth Model Interpretation of Planet Size Distribution

The radii and orbital periods of 4000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. Yet an important question about the composition of planets ranging from 2 to 4 Earth radii still remains. They may either have a rocky core enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant amount of multi-component, H2O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 Earth masses, if half-ice and half-rock by mass, have radii of 2.5 Earth radii, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2-4 Earth radii range requires a gas envelope of at most a few mass percentage points, regardless of the core composition. To resolve the ambiguity of internal compositions, we use a growth model and conduct Monte Carlo simulations to demonstrate that many intermediate-size planets are water worlds.

astro-ph.EP↗
arXiv2019

Native Chemical Automata and the Thermodynamic Interpretation of Their Experimental Accept/Reject Responses

The theory of computation is based on abstract computing automata which can be classified into a three-class hierarchy: Finite Automata (FA), Push-down Automata (PDA) and the Turing Machines (TM). Each class corresponds to grammar/language classes. The function of the automata consists on recognizing words in a language generated by some grammar and expressed with letters from an alphabet. Such automata are, in principle, abstract entities and with suitable combinations of them we can represent any computation, no matter how complex. Their physical implementations are possible in any information carrying and recognition contexts and media, such as electrons in semiconductors, certain biomolecules in biology or even non-biological molecules. Here we describe and build non-biochemistry (inorganic chemistry) examples of a FA, PDA and TM computations carried out by specific laboratory realizations of the automata. For each of the three realizations we find a thermodynamic metric, based on enthalpy for the FA and PDA, and on the Gibbs free energy for the TM, to both assess the results of computation and as a first step towards quantifying the energetic cost of such computations.

cs.ET↗
arXiv2018

Selection and control of pathways by using externally adjustable noise on a stochastic cubic autocatalytic chemical system

We investigate the effect of noisy feed rates on the behavior of a cubic autocatalytic chemical reaction model. By combining the renormalization group and stoichiometric network analysis, we demonstrate how externally adjustable random perturbations (extrinsic noise) can be used to select reaction pathways and therefore control reaction yields. This method is general and provides the means to explore the impact that changing statistical parameters in a noisy external environment (such as noisy feed rates, fluctuating reaction rates induced by noisy light, etc) has on chemical fluxes and pathways, thus demonstrating how external noise may be used to control, promote, direct and optimize chemical progress through a given reaction pathway.

cond-mat.stat-mech↗
arXiv2018

Dynamic modulation of external conditions can transform chemistry into logic gates

We introduce a new method for transforming chemical systems into desired logical operators (e.g. NAND-gates) or similar signal-manipulation components. The method is based upon open-loop dynamic regulation, where external conditions such as feed-rate, lighting conditions, etc. are modulated according to a prescribed temporal sequence that is independent of the input to the network. The method is first introduced using a simple didactic model. We then show its application in transforming a well-stirred cubic autocatalytic reaction (often referred to as the Selkov-Gray-Scott model) into a logical NAND-gate. We also comment on the applicability of the method to biological and other systems.

physics.chem-ph↗
arXiv2016

Effects of spatial and temporal noise on a cubic-autocatalytic reaction-diffusion model

We characterize the influence that external noise, with both spatial and temporal correlations, has on the scale dependence of the reaction parameters of a cubic autocatalytic reaction diffusion (CARD) system. Interpreting the CARD model as a primitive reaction scheme for a living system, the results indicate that power-law correlations in environmental fluctuations can either decrease or increase the rates of nutrient decay and the rate of autocatalysis (replication) on small spatial and temporal scales.

cond-mat.other↗
arXiv2015

Small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion model

We investigate the small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion (CARD) model using renormalization techniques. We renormalize noise-induced ultraviolet divergences and obtain beta functions for the decay rate and coupling at one-loop. Assuming colored (power law) noise, our results show that the behavior of both decay rate and coupling with scale depends crucially on the noise exponent. Interpreting the CARD model as a proxy for a (very simple) living system, our results suggest that power law correlations in environmental fluctuations can both decrease or increase the growth of structures at smaller scales.

cond-mat.stat-mech↗
arXiv2015

Clues on chemical mechanisms from renormalizability: The example of a noisy cubic autocatalytic model

We study the effect of noise on the renormalizability of a specific reaction-diffusion system of equations describing a cubic autocatalytic chemical reaction. The noise we are using is gaussian with power-law correlations in space, characterized by an amplitude $A$ and a noise exponent $y$. We show that changing the noise exponent is equivalent to the substitution $d_{s} \rightarrow d_{\rm eff} = d_{s} - y$ and thus modifies the divergence structure of loop integrals ($d_{s}$ is the dimension of space). The model is renormalizable at one-loop for $d_{\rm eff} < 6$ and nonrenormalizable for $d_{\rm eff} \geq 6$. The effects of noise-generated higher order interactions are discussed. In particular, we show how noise induces new interaction terms that can be interpreted as a manifestation of some (internal) "chemical mechanism". We also show how ideas of effective field theory can be applied to construct a more fundamental chemical model for this system.

cond-mat.stat-mech↗
arXiv2009

Large scale emergent properties of an autocatalytic reaction-diffusion model subject to noise

The non-equilibrium dynamic fluctuations of a stochastic version of the Gray-Scott (GS) model are studied analytically in leading order in perturbation theory by means of the dynamic renormalization group. There is an attracting stable fixed point at one-loop order, and the asymptotic scaling of the correlation functions is predicted for both spatial and temporally correlated noise sources. New effective three-body reaction terms, not present in the original GS model, are induced by the combined interplay of the fluctuations and nonlinearities.

cond-mat.stat-mech↗
arXiv2000

Effective potential for classical field theories subject to stochastic noise

Classical field theories coupled to stochastic noise provide an extremely powerful tool for modeling phenomena as diverse as turbulence, pattern-formation, and the structural development of the universe itself. In this Letter we sketch a general formalism that maps such systems into a field theory language, and demonstrate how to extract the one-loop physics for an arbitrary classical field theory coupled to Gaussian noise. The amplitude of the noise two-point function serves as the loop-counting parameter and is the analog of Planck's constant hbar in quantum field theory. We define the effective action and the effective potential, and derive a general formula for the one-loop effective potential of a classical field theory coupled to translation-invariant Gaussian noise.

cond-mat.stat-mech↗
arXiv2000

Small-scale properties of the KPZ equation and dynamical symmetry breaking

A functional integral technique is used to study the ultraviolet or short distance properties of the Kardar-Parisi-Zhang (KPZ) equation with white Gaussian noise. We apply this technique to calculate the one-loop effective potential for the KPZ equation. The effective potential is (at least) one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, but non-renormalizable in 4 or higher space dimensions. This potential is intimately related to the probability distribution function (PDF) for the spacetime averaged field. For the restricted class of field configurations considered here, the KPZ equation exhibits dynamical symmetry breaking (DSB) via an analog of the Coleman-Weinberg mechanism in 1 and 2 space dimensions, but not in 3 space dimensions.

cond-mat.stat-mech↗
arXiv1999

Effective potential for the reaction-diffusion-decay system

In previous work [cond-mat/9904207,cond-mat/9904215] we have developed a general method for casting stochastic partial differential equations (SPDEs) into a functional integral formalism, and have derived the one-loop effective potential for these systems. In this paper we apply the same formalism to a specific field theory of considerable interest, the reaction-diffusion-decay system. When this field theory is subject to white noise we can calculate the one-loop effective potential (for arbitrary polynomial reaction kinetics) and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions. For specific choices of interaction terms the one-loop renormalizability can be extended to higher dimensions. We also show how to include the effects of fluctuations in the study of pattern formation away from equilibrium, and conclude that noise affects the stability of the system in a way which is calculable.

cond-mat.stat-mech↗
arXiv1999

Effective action for stochastic partial differential equations

Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. In this paper we set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these non-quantum field theories are fully interacting. Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues, and furthermore offers marked technical advantages: We can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the BRST formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ``direct approach'' is the SPDE analog of canonical quantization using physical fields.) We show how to define the effective action to all loops, and then focus on the one-loop effective action, and its specialization to constant fields: the effective potential. An important result is that the amplitude of the two-point function governing the noise acts as the loop-counting parameter and is the analog of Planck's constant hbar in this SPDE context. We derive a general expression for the one-loop effective potential of an arbitrary SPDE subject to translation-invariant Gaussian noise, and compare this with the one-loop potential for QFT.

cond-mat.stat-mech↗
arXiv1999

The fractal distribution of galaxies and the transition to homogeneity

There is an ongoing debate in cosmology about the value of the length scale at which ``homogeneity'' in the matter distribution is reached or even if such a scale exists. In the wake of this debate, we intend in this letter to clarify the meaning of the statement transition to homogeneity and of the concept of correlation length. We show that there are two scales each associated to the fractal and to the homogeneous regimes of the matter distribution, respectively. The distinction between both scales has deep consequences, for there can be a regime which despite having small fluctuations around the average density exhibits large clusters of galaxies.

astro-ph↗
arXiv1999

Extending the scope of models for large-scale structure formation in the Universe

We propose a phenomenological generalization of the models of large-scale structure formation in the Universe by gravitational instability in two ways: we include pressure forces to model multi-streaming, and noise to model fluctuations due to neglected short-scale physical processes. We show that pressure gives rise to a viscous-like force of the same character as that one introduced in the ``adhesion model'', while noise leads to a roughening of the density field yielding a scaling behavior of its correlations.

astro-ph↗
arXiv1999

Evidence Against the Sciama Model of Radiative Decay of Massive Neutrinos

We report on spectral observations of the night sky in the band around 900 angstroms where the emission line in the Sciama model of radiatively decaying massive neutrinos would be present. The data were obtained with a high resolution, high sensitivity spectrometer flown on the Spanish MINISAT satellite. The observed emission is far less intense than that expected in the Sciama model.

astro-ph↗