Equilibrium dynamics in a model of growth and spatial agglomeration

We present a multiregional endogenous growth model in which forward-looking agents choose their regions to live in, in addition to consumption and capital accumulation paths. The spatial distribution of economic activity is determined by the interplay between production spillover effects and urban congestion effects. We characterize the global stability of the spatial equilibrium states in terms of economic primitives such as agents’ time preference and intra- and interregional spillovers. We also study how macroeconomic variables at the stable equilibrium state behave according to the structure of the spillover network.

P53-Mdm2 Loop Stability and Oscillatory Dynamics with Mdm2-Induced Delay Effect in P53

In this paper, we consider P53-Mdm2 negative feedback loop supposed to be the core circuit of genome. We study stability and the oscillatory dynamics of the loop. Many of the studies modeled this loop by delay-differential equations with P53-induced transcrip- tional delay in the production of Mdm2. We, however, highlight the importance of Mdm2- induced delay in the degradation of P53 protein. We consider two forms of P53 protein i.e., plain P53 and active P53 along with its principal antagonist protein Mdm2 to formulate a minimal model. Active P53 finds its inclusion in the loop in the presence of DNA damage represented by a Boolean variable ‘s’. The analysis of the model provides thresholds on delays using Nyquist criterion such that delays in the degradation of P53 lower than these thresholds guarantee stability of the loop in that all proteins plain P53, active P53 and Mdm2 approach to stable equilibrium state. The oscillatory dynamics in proteins, if any, would exist beyond these thresholds.

Numerical Studies on the Design of Self-Resetting Active Bistable Cross-Shaped Structure for Morphing Applications

Multistable structures that possess more than one elastically stable equilibrium state are highly attractive for advanced shape-changing (morphing) applications due to the nominal control effort required to maintain the structure in any of its specific stable shapes. The aim of the paper is to develop a bistable cross-shaped structure consisting of symmetric and unsymmetric laminate actuated using Macro Fibre Composite (MFC) actuators. The critical snap-through voltages required to change the shapes are investigated in a commercially available finite element package. The use of MFC actuators to snap the bistable laminate from one equilibrium shape to another and back again (self-resetting) is demonstrated. A new cross-shaped design of active bistable laminate with MFC actuators is proposed where the cross-shape consist of four rectangles on the four legs and a square on the middle portion. All the rectangles are made up of unsymmetric laminates, and the central portion is designed with a symmetric laminate. MFC actuators are bonded on both sides of the four legs to trigger snap-through and snap-back actions. An attempt is made to address the possible design difficulties arising from the additional stiffness contribution by MFC layers on the naturally cured equilibrium shapes of cross-shaped bistable laminates.

Research on evolution of collaboration mechanism of stakeholders in mining enterprises’ implementation of social responsibility

Multiple stakeholders are involved when mining enterprises assume their social responsibility, so a tripartite game pattern among local government, mining enterprises and local community is formed after supervision is introduced. By combining evolutionary game model with system dynamics for simulation analysis, this paper studies the dynamic game process among the three parties and we find out that: (1) local government, mining enterprises and local community will eventually reach a stable equilibrium state (supervision, participation, performance), and it will simplify the evolutionary path of the stable equilibrium state when local government chooses supervision at the early stage; (2) local government plays a leading role in supervision, and the strategy choices of mining enterprises and local community depend on local government's strategy and the relationship between the size of exogenous; (3) the formation of the eventual stabilization strategy is decided by the joint action of multiple variables, although every single variable will affect the strategy choice of all parties, so local government should deal with the relationship between various stakeholders properly.

Finite-dimensional maps describing the dynamics of a logistic equation with delay

This article discusses a family of maps that are used in the numerical simulation of a logistic equation with delay. This equation and presented maps are widely used in problems of mathematical ecology as models of the dynamics of populations. The paper compares the dynamic properties of the trajectories of these mappings and the original equation with delay. It is shown that the behavior of the solutions of maps can be quite complicated, while the logistic equation with delay has only a stable equilibrium state or cycle.

Haematopoietic stem cells: entropic landscapes of differentiation

The metaphor of a potential epigenetic differentiation landscape broadly suggests that during differentiation a stem cell approaches a stable equilibrium state from a higher free energy towards a stable equilibrium state which represents the final cell type. It has been conjectured that there is an analogy to the concept of entropy in statistical mechanics. In this context, in the undifferentiated state, the entropy would be large since fewer constraints exist on the gene expression programmes of the cell. As differentiation progresses, gene expression programmes become more and more constrained and thus the entropy would be expected to decrease. In order to assess these predictions, we compute the Shannon entropy for time-resolved single-cell gene expression data in two different experimental set-ups of haematopoietic differentiation. We find that the behaviour of this entropy measure is in contrast to these predictions. In particular, we find that the Shannon entropy is not a decreasing function of developmental pseudo-time but instead it increases towards the time point of commitment before decreasing again. This behaviour is consistent with an increase in gene expression disorder observed in populations sampled at the time point of commitment. Single cells in these populations exhibit different combinations of regulator activity that suggest the presence of multiple configurations of a potential differentiation network as a result of multiple entry points into the committed state.

Magnetic Belt Conveyor Running Stability Analysis

Magnetic suspension type belt conveyor used magnetic machinery technology design can solve the belt conveyor of roller support parts number, large energy consumption and high maintenance cost, limited tape speed, large noise and other issues. Magnetic belt conveyor design is the key to stability analysis of the operation of conveyor belt. Papers from a mechanical point of view to study the structural stability calculation. The results show that small interfering in the external magnetic conveyor belt, the permanent support system can be adjusted to spontaneously stable equilibrium state.

A Bi-Stable von-Mises Truss for Morphing Applications Actuated Using Shape Memory Alloys

The present study focuses on a bi-stable von-Mises truss (VMT), with integrated Shape Memory Alloy (SMA) wires which are resistively heated to provide the actuation force to transition the VMT from one stable equilibrium condition to the other, and back. This coupled VMT-SMA system can potentially be used in structural morphing applications. The paper considers in detail the design of the system, equilibrium between the VMT and the SMA wires, the initial pre-stress required in the two SMA wires, explains how the active (heated) SMA wire drives the VMT beyond the unstable equilibrium state, and the VMT in moving to the second stable equilibrium state pre-stresses the passive (unheated) SMA wire. The two SMA wires switch roles in moving the VMT back from the second to the first stable equilibrium state. A prototype is designed and fabricated and the transition of the VMT from one equilibrium state to the other, and back, is experimentally demonstrated. The governing differential equation representing the VMT behavior is coupled with equations representing the SMA behavior based on the Brinson thermo-mechanical model. The numerical predictions of system displacements versus temperature and time show good correlation with experimental results.

Analysis to Stress Relaxation Phenomena of Viscoelastic Materials by Means of Irreversible Thermodynamics (Ⅰ)

Through defining a piece of viscoelastic medium as a thermodynamic system described by the generalized coordinates in the stress relaxation process, the evolution equation is derived by making use of the 1st law of thermodynamics, the 2nd law of thermodynamics and the Onsager’s principle. Based on the general solutions of the evolution, the constitutive expressions of uniaxial stress relaxation are obtained for both ideal viscoelastic solid materials and ideal viscoelastic fluid one respectively, in terms of the situation whether the coordinates participating in the entropy production are in stable or neutrally stable equilibrium state. As the result, whether the stress relaxes to a constant or zero depends on whether the free energy in viscoelastic medium is left or not.