Purpose The fibers are loaded by the cosine component of the external load, when a fiber fails, and due to the local load-sharing nature, its force is shared by surviving neighboring fibers. The results show that the system presents a greater resistance and toughness toward the applied load compared to the classical one. Design/methodology/approach In this paper, the authors adopt the dynamics of a local load-sharing fiber bundle model in two dimensions under an external load to study scaling law in failure process of composite materials with randomly oriented fibers. The model is based on the fiber bundle model where the fibers are randomly oriented. The system is different to the classical one where the fibers are arranged in parallel with the applied load direction. Findings The evolution time of the fraction of broken fiber is described by an exponential law with two characteristic times. The latter decrease linearly and exponentially respectively with both applied load and temperature. Originality/value Scaling behavior of the broken fiber numbers with the size system shows that the system exhibits a scaling law of Family–Vicsek model with universal exponents.
Purpose The aim of the present paper is to investigate the behavior of collective motion of living biological organisms in the two-dimensional (2D) plane by adopting a new approach based on the use of Langevin dynamics. Langevin dynamics is a powerful tool to study these systems because they present a stochastic process due to collisions between their constituents. Design/methodology/approach In this paper, the dynamical properties and scaling behavior of self-propelled particles were studied numerically by using Langevin dynamics. These dynamics have been affected by the use of only the alignment zone of radius R . Findings The results indicated that the system’s velocity increases with time and reaches to finite value at the equilibrium phase. Research limitations/implications This result is more consistent with that of Vicsek’s model. However, the system’s velocity decreases exponentially with the applied noise without taking the zero value for the highest noise value. Practical implications As well as, the crossover time of the growth kinetic system decreases exponentially with noise. Social implications Scaling behavior has been checked for this system and the corresponding results prove that behavior scales with the same law of the one in Vicsek’s model but with different scaling exponents. Originality/value The phase transition observed in Vicsek’s model cannot be reproduced by the Langevin dynamics model, which describes more about the dynamical properties of self-propelled systems.
Fluid transport phenomena in porous media exhibit different properties with scaling law behavior according to different universal components, which describe the corresponding universal classes exactly. A numerical study of the fluid intrusion process in a porous medium under the effect of a static pressing force is introduced. Investigations are developed by using Langevin dynamic based on the competition between the stochastic and the dissipation processes. The mean flow rate is studied with an energetic study, then the temporal profiles are shown. The results show that the time evolution of these two magnitudes exhibits exponential profiles with two different regimes; transient and permanent, characterized by their cross-over time. They also exhibit a decreasing behavior versus the friction coefficient, but an increasing behavior versus both the static pressure and the medium porosity. Scaling laws with universal exponents of the mean flow rate are checked for different parameters, namely the static pressure and the friction coefficient. The system mean energy follows a scaling law with universal exponents, independently of the parameters (static pressure, friction coefficient, medium porosity, and system size), which proves their universal character.
In nature, living organisms move in a collective state of aggregation, this collective motion is influenced by the nature of the environment, the obstacles refocused during the movement and the local interaction between individuals, this interaction is responsible for avoiding collision between each individual. In this paper, we study numerically the collective motion of self-organized organisms by expanding the Langevin dynamics, in which we have modeled the interaction between individuals by an elastic force. Modeling the interaction between individuals using an elastic force gives remarkable results. This interaction has an important effect if the individuals are dispersed a lot in space, but if a certain number of particles N is exceeded, this force is of no importance and the saturation velocity becomes constant. The results of the numerical simulation show that the average velocity of the individuals goes through a transient regime before reaching the permanent regime. Moreover, the results show that the system represents a transition from a nonequilibrium state to an equilibrium state, which is similar to a second-phase transition (paramagnetic/ferromagnetic) in the absence of the magnetic field; this phase transition is observable if the distance between two individuals is greater than a critical radius noted [Formula: see text].
To understand and improve the performance of membrane separation surface used in the water desalination water process, we have studied the effect of friction coefficient on the morphological properties of retentate deposits particles on the surface membrane separation. The investigation is made in the framework of the Langevin equation model based on the competition between stochastic and particle dissipation mechanisms. The noise coefficient, the friction coefficient, and the constant flow rate are remarkable parameters that influence the average velocity and the average distance between the particles. The results show that the temporal evolution of the mean velocity of retentate deposits particles presents an exponential profile with two different regimes. However, the scaling dynamic studies show that the studied system is governed by scaling exponents more consistent with the Family–Vicsek model.
Abstract Collective motion of self-propelled particles is one of basic phenomenon observed in large spectra of biological system behavior due to the correlated process evolution in space and time. In this manuscript, we study numerically the kinetic properties and the correlation process in complex systems evolves out equilibrium phase by employing the Langevin dynamics. In this model, we have adopted one zone of orientation where the system evolves spontaneously in presence of quenched stochastic noise. The results show that the system evolves to its equilibrium phase by reaching one orientation. Hence, this evolution is characterized by a correlation process increasing in time but with decelerate profile. However the obtained profile of the correlation function per time unity shows that the collective motion in complex system, can be characterized by a characteristic time when the system change the acceleration of the correlation process. Our result shows that this characteristic time decreases exponentially with the quenched noise. In the additional crossover time at when the system reaches its equilibrium phase, scales with quenched noise as power law. This result is more consisting with the one of Vicsek model
This study numerically examines the fluid flow in porous media used in desalination. This topic is of significant current interest in the fields of science, engineering and technology, particularly in the process of water filtration. Moreover, in this work, we are attracted to correlation and diffusion process of the porous medium below the effect of permeability, dynamic pressure and friction coefficient. These parameters characterized the fluid flow in porous medium. To study numerically this phenomenon, many models have been proposed. However, we developed our investigation by using the Langevin dynamics model. Furthermore, this dynamic framework is based on Newton’s second law and Darcy’s law. Hence, we modeled the medium as a set of random diameters pores, which are dispersed randomly. The obtained results indicate that the average velocity time evolution presents an exponential profile with two different states: the first is transient and the second is permanent. The two regimes are separated by a cross-over time. Furthermore, time evolution exhibits an increasing profile versus the permeability, then it presents a decreasing profile versus the friction coefficient. Likewise, the diffusion process and correlation are tested for different parameters, especially the permeability and the dynamic pressure. We remark that the effective diffusion coefficient decreases exponentially with permeability and increases linearly with dynamic pressure. Hence, the fluid flow correlation in porous media presents a Gaussian function profile, with standard deviation function which increases exponentially with permeability.
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