Instability in bacterial populations and the curvature tensor

Melgarejo, Augusto A.; Langoni, Laura; Ruscitti, Claudia

doi:10.1016/j.physa.2016.04.019

Cited by 3 publications

(13 citation statements)

References 11 publications

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“…ðÞ . An example of this behavior is the formation of density patterns in the populations of self-propelled bacteria whose mobility can be investigated in terms of the diffusion coefficient D [5]. We also observe from Eq.…”

Section: Optimal Trajectory and Entropymentioning

confidence: 64%

“…In equilibrium thermodynamics this information is contained in the scalar curvature of the manifold of equilibrium states [2]. For nonequilibrium problems, the instabilities are associated with the singularities or discontinuities of the curvature tensor [5,15]. In the case of diffusive problems, the instabilities can be found by studying the singularities of R 0 ðÞ 1212 μ, σ ðÞ .…”

Section: Discussion and Perspectivesmentioning

confidence: 99%

“…The affine connection, called the α-connection [4], is a generalization of the Levi-Civita connection in Riemannian geometry, and in the case α ¼ 0 the metric-affine manifold reduces to the so-called Riemannian manifold. A first element that appears for nonequilibrium systems is the visualization of the phase transitions through the curvature tensor [5]. A second issue is the study of temporal evolution of a statistical system in order to study the optimal evolution.…”

Section: Introductionmentioning

confidence: 99%

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Differential Geometry and Macroscopic Descriptions in Nonequilibrium Process

Ruscitti¹,

Langoni²,

Melgarejo³

2020

Advances on Tensor Analysis and Their Applications

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The method of Riemannian geometry is fruitful in equilibrium thermodynamics. From the theory of fluctuations it has been possible to construct a metric for the space of thermodynamic equilibrium states. Inspired by these geometric elements, we will discuss the geometric-differential approach of nonequilibrium systems. In particular we will study the geometric aspects from the knowledge of the macroscopic potential associated with the Uhlenbeck-Ornstein (UO) nonequilibrium process. Assuming the geodesic curve as an optimal path and using the affine connection, known as α-connection, we will study the conditions under which a diffusive process can be considered optimal. We will also analyze the impact of this behavior on the entropy of the system, relating these results with studies of instabilities in diffusive processes.

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Section: Optimal Trajectory and Entropymentioning

confidence: 64%

Section: Discussion and Perspectivesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Differential Geometry and Macroscopic Descriptions in Nonequilibrium Process

Ruscitti¹,

Langoni²,

Melgarejo³

2020

Advances on Tensor Analysis and Their Applications

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“…Moreover, keeping in mind the stochastic effects and considering that the diffusion coefficient is proportional to v 2 [8], we can study the bacterial mobility through the diffusion coefficient using (24). In this sense, the analysis of bacterial mobility as a function of θ 1 and θ 2 can be carried out based on the behavior of x 2 due to (24).…”

Section: Mobility and The Fokker-planck Equationmentioning

confidence: 99%

“…In this sense, the tensor R 1212 gives us information about the macroscopic behavior of the system so that we interpret the singularities of the tensor as a change in bacterial mobility [8].…”

Section: Geometric Perspectivementioning

confidence: 99%

Curvature tensor and collective behavior in a population of bacteria

Oleaga

Ruscitti²,

Langoni³

et al. 2022

Phys. Scr.

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In this work, from a geometric point of view, we analyze the SET model (Schweitzer, Ebeling and Tilch) of the mobility of a bacterium. Biological systems are out of thermodynamic equilibrium and they are subject to complex external or internal influences that can be modeled in the form of noise or fluctuations. In this sense, due to the stochasticity of the variables, we study the probability of finding a bacteria with a speed v in the interval (v; v +dv) or, from a population point of view, we can interpret the probability density function as associated with finding a bacterium with a speed v in the interval (v; v +dv). We carry out this study from the stationary probability density solution of the Fokker-Planck equation and using the structure of the statistical manifold related with the stationary probability density, we study the curvature tensor in terms of two coordinates associated with the state of mobility of the bacteria and the environmental conditions. Taking as reference the geometric interpretations found in the framework of equilibrium thermodynamics, our results suggest that bacteria have an effective repulsive interaction that increases with mobility. These results are compatible with the behavior of populations of bacteria that form biofilms when their mobility decreases.

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Description of instabilities in Uhlenbeck–Ornstein process

Ruscitti¹,

Langoni²,

Melgarejo³

2019

Phys. Scr.

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The method of Riemannian geometry has been successful in the context of equilibrium thermodynamics. In this work, we extend this approach to non-equilibrium processes. As a geometric-differential frame of non-equilibrium systems, we consider in our study the geometric properties of a manifold associated with simple but typical non-equilibrium models. We consider a Uhlenbeck-Ornstein process and the formal structure of the probability density function solution of the Fokker-Planck equation. We propose a general geometric strategy for the construction of macroscopic potentials in non-equilibrium problems. This macroscopic potential is a function of the transport coefficient and is associated with system instabilities.

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Instability in bacterial populations and the curvature tensor

Cited by 3 publications

References 11 publications

Differential Geometry and Macroscopic Descriptions in Nonequilibrium Process

Differential Geometry and Macroscopic Descriptions in Nonequilibrium Process

Curvature tensor and collective behavior in a population of bacteria

Description of instabilities in Uhlenbeck–Ornstein process

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