The static response of axisymmetric conical shells exhibiting bistable behavior

Belleville springs are widely used in variety of mechanical systems. Recent advances in the field of multi-stable structures suggest that these conical axisymmetric washers may be extremely useful as bistable building-blocks for multi-stable architected metamaterials. In this paper, we examine the ability of existing analytical models to accurately predict the bistable behavior of Belleville springs, namely a non-monotonous force-displacement relation with two branches of positive stiffness separated by a branch of negative stiffness. By comparing to results of finite-element simulations, we find that current analytical models may suffer from significant inaccuracies associated with the assumption of rigid rotation. According to this assumption, adopted by all analytical models of Belleville springs, the cross-section of the spring rotates without bending, i.e. maintains zero curvature as the spring deforms. Motivated by this insight, we relax the rigid-rotation assumption and approximate the radial displacement field by a linear relation in terms of the distance from the spring axis. We find, based on extensive finite-element simulations, that the functional dependence of the radial displacement on the geometry of the springs is indifferent to the stage of deformation and can be expressed in terms of three geometrical parameters. These findings enable us to derive closed-form expressions that are simple and straight-forward to use, yet are significantly more accurate than existing analytical models.

Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements

In Veliz-Cuba and Stigler 2011, Boolean models were proposed for the lac operon in Escherichia coli capable of reproducing the operon being OFF, ON and bistable for three (low, medium and high) and two (low and high) parameters, representing the concentration ranges of lactose and glucose, respectively. Of these 6 possible combinations of parameters, 5 produce results that match with the biological experiments of Ozbudak et al., 2004. In the remaining one, the models predict the operon being OFF while biological experiments show a bistable behavior. In this paper, we first explore the robustness of two such models in the sense of how much its attractors change against any deterministic update schedule. We prove mathematically that, in cases where there is no bistability, all the dynamics in both models lack limit cycles while, when bistability appears, one model presents 30% of its dynamics with limit cycles while the other only 23%. Secondly, we propose two alternative improvements consisting of biologically supported modifications; one in which both models match with Ozbudak et al., 2004 in all 6 combinations of parameters and, the other one, where we increase the number of parameters to 9, matching in all these cases with the biological experiments of Ozbudak et al., 2004.

Optical Bistability in an Optomechanical System with N-Type Atoms under Nonresonant Conditions

In this paper, the phenomenon of the optical bistability of a cavity field is theoretically investigated in an optomechanical system containing an N-type atomic ensemble. In this hybrid optomechanical system, the atoms are coupled with two controlling light fields besides coupling with the cavity field. Under the nonresonant condition, we analyze the influences of the coupling strength between cavity and atoms, Rabi frequencies of the controlling light field, the detuning between the controlling light field and atoms, and pump field power on the optical bistable behavior of mean intracavity photon number. The nonlinear distribution of the mean intracavity photon number has a potential application in field optical switches and optical bistable devices.

Fabrication of a 3D Bistable Composite

Bistable composites have created much attention in engineering applications because of its ability to sustain two stable shapes. A systematic layup of carbon fiber reinforced polymer (CFRP) causes bistability in a lamina. The transition from one stable shape to another is occurred by snap-through and snap-back process. Due to their adaptive nature a lot of study has been conducted on a 2D laminate for over the past 30 years. However, fabrication of a 3D model that exhibits bistability is yet to be explored. In this research we fabricated a 3D bistable composite structure having two parallel cross-ply square laminates connected by a rigid tab at one edge. The entire structure exhibits bistability when the two laminates are actuated simultaneously. The parallel laminates are also independent when actuated individually, making the model achieve four independent stable shapes. Our goal is to understand the bistable behavior and predict the degree of curvature and the snap through response of the solid structure. This paper discusses the fabrication of a solid composite structure that can be further analyzed numerically by creating an FEA model using ABAQUS. The simulation results could be validated experimentally. In this research we also aim to put together an analytical model of this 3D laminate structure. Successful fabrication and mathematical analysis of our 3D laminate using carbon fiber reinforced polymer will hopefully inspire additive manufacturing of bistable composite structure that will lead to more complicated design of bistable materials with more morphing characteristics.

A Bar and Hinge Model for Simulating Bistability in Origami Structures With Compliant Creases

Active origami structures usually have creases made with soft and compliant plates because it is difficult to fabricate real hinges and actuate them. However, most conventional origami modeling techniques fail to capture these compliant creases and simplify them as concentrated rotational springs, which neglects torsional and extensional deformations of the creases. In this paper, an improved formulation of a bar and hinge model is proposed to explicitly capture the geometry and the flexibility of compliant creases with nonnegligible width in an origami, and the model is verified against finite element simulations. The verification shows that the model performs relatively well despite being simple and computationally inexpensive. Moreover, simulation examples demonstrate that the proposed model can capture the bistable behavior of the compliant crease origami with nonnegligible crease width because it explicitly includes the extensional stretching energy into the simulation framework and allows torsional crease deformations.

Bistable behavior of the nitrogen impurity in SiC nanoclusters

Bistable behavior and coexistence of effective mass, small bound polaron and DX-like states of the nitrogen impurity in SiC nanoclusters.

Bifurcation phenomenon and multi-stable behavior in vortex-induced vibration of top tension riser in shear flow

Top tension riser is one of the most frequently used and vulnerable equipment in deep-sea petroleum engineering. With experiments and CFD simulations, researchers have found some hysteresis phenomenon and bistable behavior in vortex-induced vibration of the cylinders. However, there is still insufficient research on the bifurcation phenomenon and the multi-stable behavior of the riser vortex-induced vibration. In this study, based on the Van der Pol wake oscillator model, the vortex-induced vibration cross-flow governing equations of the riser fluid structure–coupled system in linear shear flow are established. Then the simplified multi-degrees-of-freedom model with 15-order modes is derived by the Galerkin method. Poincare map is utilized to obtain bifurcation diagram and identify the dynamic property of the top tension riser in a wide flow velocity range. Nonlinear dynamic behavior such as bistable behavior and even tristable behavior are discovered from the bifurcation diagram. Combined with the riser coupled system’s eigen analysis and the three-dimensional spectrum contour, it is found that there are various phenomena of mode interaction in the riser system, including 1:3 internal resonance phenomenon. Such study can provide reference and guide the design and optimization of riser structural parameters.

Dynamical analysis of tumor-immune-help T cells system

In this paper, we construct a mathematical model to investigate the interaction between the tumor cells, the immune cells and the helper T cells (HTCs). We perform mathematical analysis to reveal the stability of the equilibria of the model. In our model, the HTCs are stimulated by the identification of the presence of tumor antigens. Our investigation implies that the presence of tumor antigens may inhibit the existence of high steady state of tumor cells, which leads to the elimination of the bistable behavior of the tumor-immune system, i.e. the equilibrium corresponding to the high steady state of tumor cells is destabilized. Choosing immune intensity [Formula: see text] as bifurcation parameter, there exists saddle-node bifurcation. Besides, there exists a critical value [Formula: see text], at which a Hopf bifurcation occurs. The stability and direction of Hopf bifurcation are discussed.