Multidimensional Vibrations of Cable-Harnessed Beam Structures with Periodic Pattern: Modeling and Experiment

The dynamics of space structures is significantly impacted by the presence of power and electronic cables. Robust physical model is essential to investigate how the host structure dynamics is influenced by cable harnessing. All the developed models only considered the decoupled bending motion. Initial studies by authors point out the importance of coordinate coupling in structures with straight longitudinal cable patterns. In this article, an experimentally validated mathematical model is developed to analyze the fully coupled dynamics of beam with a more complex cable wrapping pattern which is periodic in nature. The effects of cable wrapping pattern and geometry on the system dynamics are investigated through the proposed coupled model. Homogenization-based mathematical modeling is developed to obtain an analogous solid beam that represents the cable wrapped system. The energy expressions obtained for fundamental repeating segment are transferred into the global coordinates consisting of several periodic elements. The coupled partial differential equations (PDE) are obtained for an analogous solid structure. The advantage of the proposed analytical model over the existing models to analyze the vibratory motion of beam with complex cable wrapping pattern has been shown through experimental validation.

A Keller-Segel model for C elegans L1 aggregation

We describe a mathematical model for the aggregation of starved first-stage C elegans larvae (L1s). We propose that starved L1s produce and respond chemotactically to two labile diffusible chemical signals, a short-range attractant and a longer range repellent. This model takes the mathematical form of three coupled partial differential equations, one that describes the movement of the worms and one for each of the chemical signals. Numerical solution of these equations produced a pattern of aggregates that resembled that of worm aggregates observed in experiments. We also describe the identification of a sensory receptor gene, srh–2, whose expression is induced under conditions that promote L1 aggregation. Worms whose srh–2 gene has been knocked out form irregularly shaped aggregates. Our model suggests this phenotype may be explained by the mutant worms slowing their movement more quickly than the wild type.

A Keller-Segel model for C elegans L1 aggregation

We describe a mathematical model for the aggregation of starved first-stage C elegans larvae (L1s). We propose that starved L1s produce and respond chemotactically to two labile diffusible chemical signals, a short-range attractant and a longer range repellent. This model takes the mathematical form of three coupled partial differential equations, one that describes the movement of the worms and one for each of the chemical signals. Numerical solution of these equations produced a pattern of aggregates that resembled that of worm aggregates observed in experiments. We also describe the identification of a sensory receptor gene, srh-2 , whose expression is induced under conditions that promote L1 aggregation. Worms whose srh-2 gene has been knocked out form irregularly shaped aggregates. Our model suggests this phenotype may be explained by the mutant worms slowing their movement more quickly than the wild type.

Improved IMPES Scheme for the Simulation of Incompressible Three-Phase Flows in Subsurface Porous Media

In this work, an improved IMplicit Pressure and Explicit Saturation (IMPES) scheme is proposed to solve the coupled partial differential equations to simulate the three-phase flows in subsurface porous media. This scheme is the first IMPES algorithm for the three-phase flow problem that is locally mass conservative for all phases. The key technique of this novel scheme relies on a new formulation of the discrete pressure equation. Different from the conventional scheme, the discrete pressure equation in this work is obtained by adding together the discrete conservation equations of all phases, thus ensuring the consistency of the pressure equation with the three saturation equations at the discrete level. This consistency is important, but unfortunately it is not satisfied in the conventional IMPES schemes. In this paper, we address and fix an undesired and well-known consequence of this inconsistency in the conventional IMPES in that the computed saturations are conservative only for two phases in three-phase flows, but not for all three phases. Compared with the standard IMPES scheme, the improved IMPES scheme has the following advantages: firstly, the mass conservation of all the phases is preserved both locally and globally; secondly, it is unbiased toward all phases, i.e., no reference phases need to be chosen; thirdly, the upwind scheme is applied to the saturation of all phases instead of only the referenced phases; fourthly, numerical stability is greatly improved because of phase-wise conservation and unbiased treatment. Numerical experiments are also carried out to demonstrate the strength of the improved IMPES scheme.

Analytical soliton solutions and modulation instability for a generalized (3 + 1)-dimensional coupled variable-coefficient nonlinear Schrödinger equations in nonlinear optics

In this work, the soliton solutions of a (3 + 1)-dimensional coupled nonlinear Schrödinger system with time-dependent coefficients arising in optical fiber has been studied analytically. A complex traveling wave ansatz is used to transform the proposed coupled partial differential equations into ordinary differential equations (ODEs). Then, we solved the obtained nonlinear ODEs for the envelope function in the traveling wave parameter. The obtained waves envelope have the forms of bright and dark soliton-like solutions which are considered as new solutions of the studied system. As a kind of completing the analysis, the modulation instability is discussed based on the linear stability analysis.

Modeling of Symbiotic Bacterial Biofilm Growth with an Example of the Streptococcus–Veillonella sp. System

We present a multi-dimensional continuum mathematical model for modeling the growth of a symbiotic biofilm system. We take a dual-species namely, the Streptococcus–Veillonella sp. biofilm system as an example for numerical investigations. The presented model describes both the cooperation and competition between these species of bacteria. The coupled partial differential equations are solved by using an integrative finite element numerical strategy. Numerical examples are carried out for studying the evolution and distribution of the bio-components. The results demonstrate that the presented model is capable of describing the symbiotic behavior of the biofilm system. However, homogenized numerical solutions are observed locally. To study the homogenization behavior of the model, numerical investigations regarding on how random initial biomass distribution influences the homogenization process are carried out. We found that a smaller correlation length of the initial biomass distribution leads to faster homogenization of the solution globally, however, shows more fluctuated biomass profiles along the biofilm thickness direction. More realistic scenarios with bacteria in patches are also investigated numerically in this study.

Modeling of symbiotic bacterial biofilm growth with an example of the Streptococcus-Veillonella sp. system

We present a multi-dimensional continuum mathematical model for modeling the growth of a symbiotic biofilm system. We take a dual-species namely, the Streptococcus - Veillonella sp. biofilm system as an example for numerical investigations. The presented model describes both the cooperation and competition between these species of bacteria. The coupled partial differential equations are solved by using an integrative finite element numerical strategy. Numerical examples are carried out for studying the evolution and distribution of the bio-components. The results demonstrate that the presented model is capable of describing the symbiotic behavior of the biofilm system. However, homogenized numerical solutions are observed locally. To study the homogenization behavior of the model, numerical investigations regarding on how random initial biomass distribution influences the homogenization process are carried out. We found that a smaller correlation length of the initial biomass distribution leads to faster homogenization of the solution globally, however, shows more fluctuated biomass profiles along the biofilm thickness direction. More realistic scenarios with bacteria in patches are also investigated numerically in this study.