Nonlinear Mechanical Properties of Prestressed Branched Fibrous Networks

Hatami-Marbini, Hamed; Rohanifar, Milad

doi:10.1016/j.bpj.2020.10.050

Cited by 11 publications

(3 citation statements)

References 69 publications

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“…Literature 2 conducted symbolic calculations on a three-coupled variable-coefficient nonlinear Schrödinger system for the attenuation/amplification of picosecond-pulses in multi-component inhomogeneous optical fiber with different polarizations/frequencies [2]. Reference 3 studied the mechanical properties of diluted hexagonal lattice under prestress, which better explained the nonlinear mechanical response of biological branching networks such as Actin and collagen networks [3]. Reference 4 studied the nonlinear dynamics of changes in microcirculation blood flow signals in the symmetrical region of the human upper limb during resting and disturbance states [4].…”

Section: Introductionmentioning

confidence: 99%

Weierstrass elliptic function solutions and degenerate solutions of a variable coefficient higher-order Schrödinger equation

Fan,

Bao

2023

Phys. Scr.

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In this paper, the auxiliary equation method is used to study the Weierstrass elliptic function solutions and degenerate solutions of the variable coefficient higher order Schrödinger equation, including Jacobian elliptic function solutions, trigonometric function solutions and hyperbolic function solutions. The types of solutions of the variable coefficient higher-order Schrödinger equation are enriched, and the method of seeking precise and accurate solutions is extended. It is concluded that the types of degenerate solutions are related to the coefficients of the equation itself when the degenerate solutions are obtained from the solutions of the Weierstrass elliptic functions. In addition, the solutions form of the equation is extended from the power series expansion form to the Laurent series expansion form, and the corresponding solutions are obtained. After the conversion formula between the Weierstrass elliptic function solutions and the Jacobian elliptic function solutions is constructed, the Jacobian elliptic function solutions of the higher order Schrödinger equation with variable coefficients are also obtained. These have not been previously studied.

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Section: Introductionmentioning

confidence: 99%

Weierstrass elliptic function solutions and degenerate solutions of a variable coefficient higher-order Schrödinger equation

Fan,

Bao

2023

Phys. Scr.

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“…In addition to mathematics, nonlinear phenomena are involved in many fields, such as atmospheric physics, optical fiber communication, biophysics, hydrodynamics and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Because of its important application value, the research of nonlinear phenomena has become a hot spot.…”

Section: Introductionmentioning

confidence: 99%

Superposition solutions to a (3+1)-dimensional variable-coefficient Sharma-Tasso-Olver-Like equation

Fan¹,

Bao²

2022

Phys. Scr.

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In this paper, the superposition solutions of (3+1)-dimensional variable-coefficient Sharma-Tasso-Olver-Like(vcSTOL) equation are studied. The equation can illustrate various difficult sciences areas. Due to the wide application, it is very important to find the exact solutions of it. By introducing transformation, the equation is transformed into bilinear form. We use variable separation method and trial function method to obtain the superposition solutions of the equation containing different functions and forms. The images are drawn with the help of symbolic computing system Mathematica, and the properties of the solutions are analyzed. The analysis shows that different functions will affect the overall shape of waves, including the interaction between waves, the size, the direction and the number of waves, which can get more new phenomena. To our knowledge, those types of superposition solutions of (3+1)-dimensional vcSTOL equation mentioned in our work by variable separation method have not been reported before. Furthermore, we add the square terms to the expansion function, so that the obtained solutions have the characteristics of Lump solution, which has not been done in the previous literatures.

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“…[16] Furthermore, many complex biological networks, such as the ECM and cytoskeleton, do not possess the regularity of these common CAD models. [17,18] Taken together, a question arises as to how complex network architecture should be incorporated into scaffold CAD models for 2PP DLW.…”

mentioning

confidence: 99%

Bioinspired 3D microprinted cell scaffolds: Integration of graph theory to recapitulate complex network wiring in lymph nodes

Chin,

Reid,

Lachina

et al. 2023

Biotechnology Journal

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Physical networks are ubiquitous in nature, but many of them possess a complex organizational structure that is difficult to recapitulate in artificial systems. This is especially the case in biomedical and tissue engineering, where the microstructural details of 3D cell scaffolds are important. Studies of biological networks—such as fibroblastic reticular cell (FRC) networks—have revealed the crucial role of network topology in a range of biological functions. However, cell scaffolds are rarely analyzed, or designed, using graph theory. To understand how networks affect adhered cells, 3D culture platforms capturing the complex topological properties of biologically relevant networks would be needed. In this work, we took inspiration from the small‐world organization (high clustering and low path length) of FRC networks to design cell scaffolds. An algorithmic toolset was created to generate the networks and process them to improve their 3D printability. We employed tools from graph theory to show that the networks were small‐world (omega factor, ω = ‐0.10 ± 0.02; small‐world propensity, SWP = 0.74 ± 0.01). 3D microprinting was employed to physicalize networks as scaffolds, which supported the survival of FRCs. This work, therefore, represents a bioinspired, graph theory‐driven approach to control the networks of microscale cell niches.

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Nonlinear Mechanical Properties of Prestressed Branched Fibrous Networks

Cited by 11 publications

References 69 publications

Weierstrass elliptic function solutions and degenerate solutions of a variable coefficient higher-order Schrödinger equation

Weierstrass elliptic function solutions and degenerate solutions of a variable coefficient higher-order Schrödinger equation

Superposition solutions to a (3+1)-dimensional variable-coefficient Sharma-Tasso-Olver-Like equation

Bioinspired 3D microprinted cell scaffolds: Integration of graph theory to recapitulate complex network wiring in lymph nodes

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