A Tribute to Marian Smoluchowski's Legacy on Soft Grains Assembly and Hydrogel Formation

Gadomski, Adam; Kruszewska, Natalia; Bełdowski, Piotr; Lent, Bogdan; Ausloos, Marcel

doi:10.5506/aphyspolb.49.993

Cited by 3 publications

(4 citation statements)

References 20 publications

(61 reference statements)

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“…Here P (v , δt, v) is the transition probability between two states with different velocities. The second one, a fundamental cornerstone of molecular physical chemistry and of cellular biochemistry [22,25] is "Smoluchowski's theory of diffusion limited coagulation of two colloidal particles." Unfortunately, due to his premature death, the Nobel prize was not awarded to Smoluchowski.…”

Section: B the Tale Of The Three Giantsmentioning

confidence: 99%

“…Consequently, we may have different classes of diffusion for distinct memories. Now, we can study the asymptotic behavior of Equation (25) or of its second moment, Equation ( 18), to characterize the type of diffusion presented by the system for any memory Π(t). Much information about the system's relaxation properties can be obtained by studying the correlation function…”

Section: The Generalized Langevin Equation Approachmentioning

confidence: 99%

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Anomalous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems

et al. 2019

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In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be given to some methods applied in the analysis and characterization of diffusive regimes through the memory function, the mixing condition (or irreversibility), and ergodicity. Those methods can be used in the study of small-scale systems, ranging in size from single-molecule to particle clusters and including among others polymers, proteins, ion channels and biological cells, whose diffusive properties have received much attention lately.

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Section: B the Tale Of The Three Giantsmentioning

confidence: 99%

Section: The Generalized Langevin Equation Approachmentioning

confidence: 99%

Anomalous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems

et al. 2019

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“…Collisions between the emitted particles and the fluid molecules cause them to diffuse throughout the medium. It would be computationally infeasible to model each of these collisions individually, since the number of collisions between each particle and the fluid molecules is in the order of 10 20 per second [221]. Fortunately, the seemingly random movement of the suspended particles caused by collisions between the particles and the smaller fluid molecules can be mathematically modeled as Brownian motion.…”

Section: A32 Particle Modelmentioning

confidence: 99%

On the scalability limits of communication networks to the nanoscale

Martí¹

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Nanosystems, integrated systems with a total size of a few micrometers, are capable of interacting at the nanoscale, but their short operating range limits their usefulness in practical macro-scale scenarios. Nanonetworks, the interconnection of nanosystems, will extend their range of operation by allowing communication among nanosystems, thereby greatly enhancing their potential applications. In order to integrate communication capabilities into nanosystems, their communication subsystem needs to shrink to a size of a few micrometers. There are doubts about the feasibility of scaling down current metallic antennas to such a small size, mainly because their resonant frequency would be extremely high (in the optical domain) leading to a large free-space attenuation of the radiated EM waves. In consequence, as an alternative to implement wireless communications among nanosystems, two novel paradigms have emerged: molecular communication and graphene-enabled wireless communications. On the one hand, molecular communication is based on the exchange of molecules among nanosystems, inspired by communication among living cells. In Diffusion-based Molecular Communication (DMC), the emitted molecules propagate throughout the environment following a diffusion process until they reach the receiver. On the other hand, graphene, a one-atom-thick sheet of carbon atoms, has been proposed to implement graphene plasmonic RF antennas, or graphennas. Graphennas with a size in the order of a few micrometers show plasmonic effects which allow them to radiate EM waves in the terahertz band. Graphennas are the enabling technology of Graphene-enabled Wireless Communications (GWC). In order to answer the question of how communication networks will scale when their size shrinks, this thesis presents a scalability analysis of the performance metrics of communication networks to the nanoscale, following a general model with as few assumptions as possible. In the case of DMC, two detection schemes are proposed: amplitude detection and energy detection. Key performance metrics are identified and their scalability with respect to the transmission distance is found to differ significantly from the case of traditional wireless communications. These unique scaling trends present novel challenges which require the design of novel networking protocols specially adapted to DMC networks. The analysis of the propagation of plasmonic waves in graphennas allows determining their radiation performance. In particular, the resonant frequency of graphennas is not only lower than in metallic antennas, but it also increases more slowly as their length is reduced to the nanoscale. Moreover, the study of parameters such as the graphenna dimensions, the relaxation time of graphene and the applied chemical potential shows the tunability of graphennas in a wide frequency range. Furthermore, an experimental setup to measure graphennas based on feeding them by means of a photoconductive source is described. The effects of molecular absorption in the short-range terahertz channel, which corresponds to the expected operating scenario of graphennas, are analyzed. Molecular absorption is a process in which molecules present in the atmosphere absorb part of the energy of the terahertz EM waves radiated by graphennas, causing impairments in the performance of GWC. The study of molecular absorption allows quantifying this loss by deriving relevant performance metrics in this scenario, which show novel scalability trends as a function of the transmission distance with respect to the case of free-space propagation. Finally, the channel capacity of GWC is found to scale better as the antenna size is reduced than in traditional wireless communications. In consequence, GWC will require lower transmission power to achieve a given performance target. These results establish a general framework which may serve designers as a guide to implement wireless communication networks among nanosystems.

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“…Con tales resultados por parte de Einstein y Smoluchowski, aunado a los resultados experimentales de Jean Perrin (1870-1942) sobre la determinación del número de Avogadro predicho en el artículo de Einstein es como finalmente se formarían las bases de la teoría microscópica y su puente con el mundo macrosópico. En 1926 Jean Perrin recibiría el premio Nobel por [41]: "sus trabajos sobre la estructura discontinua de la materia. "…”

Section: Introducción Históricaunclassified

Difusión con dos puntos de reinicio y condición inicial variable

Julián Salgado

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A Tribute to Marian Smoluchowski's Legacy on Soft Grains Assembly and Hydrogel Formation

Cited by 3 publications

References 20 publications

Anomalous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems

Anomalous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems

On the scalability limits of communication networks to the nanoscale

Difusión con dos puntos de reinicio y condición inicial variable

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