scholarly journals Theoretical Analysis for Bending of Single-Stranded DNA Adsorption on Microcantilever Sensors

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 2812 ◽  
Author(s):  
Zou-Qing Tan ◽  
Yang-Chun Chen ◽  
Neng-Hui Zhang
Keyword(s):  
Mechanical Energy ◽  
Minimum Principle ◽  
Mean Field Theory ◽  
Mean Field ◽  
Radius Of Curvature ◽  
Label Free ◽  
Dna Adsorption ◽  
Single Stranded Dna ◽  
Microcantilever Sensors ◽  
Volume Energy

An energy-based model is presented to establish the bending deformation of microcantilever beams induced by single-stranded DNA (ssDNA) adsorption. The total free energy of the DNA-microcantilever sensor was obtained by considering the excluded-volume energy and the polymer stretching energy of DNA chains from mean-field theory, and the mechanical energy of three non-biological layers. The radius of curvature and deflection of the cantilever were determined through the minimum principle of energy. The efficiency of the present model was confirmed through comparison with experimental data. The effects of length, grafting density, salt concentration, thickness, and elastic modulus of substrate on tip deflections are also discussed in this paper. These factors can significantly affect the deflections of the biosensor. This work demonstrates that it is useful to develop a theoretical model for the label-free nanomechanical detection technique.

scholarly journals Linker-mediated self-assembly of mobile DNA-coated colloids

2020 ◽  
Vol 6 (21) ◽  
pp. eaaz6921 ◽  
Author(s):  
Xiuyang Xia ◽  
Hao Hu ◽  
Massimo Pica Ciamarra ◽  
Ran Ni
Keyword(s):  
Self Assembly ◽  
Effective Interaction ◽  
Mean Field Theory ◽  
Mean Field ◽  
Mobile Dna ◽  
Complementary Sequence ◽  
Single Stranded Dna ◽  
Construction Methods ◽  
Free Dna ◽  
Innovative System

Developing construction methods of materials tailored for given applications with absolute control over building block placement poses an immense challenge. DNA-coated colloids offer the possibility of realising programmable self-assembly, which, in principle, can assemble almost any structure in equilibrium, but remains challenging experimentally. Here, we propose an innovative system of linker-mediated mobile DNA-coated colloids (mDNACCs), in which mDNACCs are bridged by the free DNA linkers in solution, whose two single-stranded DNA tails can bind with specific single-stranded DNA receptors of complementary sequence coated on colloids. We formulate a mean-field theory efficiently calculating the effective interaction between mDNACCs, where the entropy of DNA linkers plays a nontrivial role. Particularly, when the binding between free DNA linkers in solution and the corresponding receptors on mDNACCs is strong, the linker-mediated colloidal interaction is determined by the linker entropy depending on the linker concentration.

Optimal control of a rumor model with group propagation over complex networks

2020 ◽  
pp. 2150035
Author(s):  
Kalaiselvi Myilsamy ◽  
Muthukrishnan Senthil Kumar ◽  
Athira Satheesh Kumar
Keyword(s):  
Optimal Control ◽  
Mobile Networks ◽  
Social Life ◽  
Minimum Principle ◽  
Mean Field Theory ◽  
Mean Field ◽  
Real Life ◽  
Heterogeneous Model ◽  
The People ◽  
Spreading Dynamics

Rumor is an unauthenticated statement that gives significant changes in the social life of the people, financial markets (stocks and trades), etc. By incorporating the dissemination of rumor through groups in social, mobile networks and by considering the people’s cognitive factor (hesitate and forget), a new model on the rumor spreading process is presented in this paper. The spreading dynamics of rumor in homogeneous and heterogeneous networks is analyzed by using mean-field theory. The reproduction number is obtained by using the next-generation matrix. The global stability of the rumor-free equilibrium for the homogeneous and heterogeneous model is proved elaborately. An optimal control problem is developed to minimize the hesitators and infected persons and the existence of optimality is shown using Pontryagin’s Minimum Principle. The hesitating and forgetting mechanism has a great impact on the model and is similar to the real-life. Further, the control parameters work superior in controlling the spreading of rumors. Finally, the numerical results are verified by the analytical results.

scholarly journals Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Zhongxue Chang ◽  
Haijun Jiang ◽  
Shuzhen Yu ◽  
Shanshan Chen
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Complex Networks ◽  
Minimum Principle ◽  
Mean Field Theory ◽  
Mean Field ◽  
Propagation Model ◽  
Nonlinear Incidence ◽  
Rumor Propagation ◽  
Spreading Dynamics

An Innocents-Spreaders-Calmness-Removes (ISCR) rumor propagation model is established with nonlinear incidence and time delay on complex networks in this paper. Based on the mean-field theory, the spreading dynamics of the ISCR model are discussed in detail. Firstly, the basic reproduction number R 0 is obtained by the next generation matrix method to ensure the existence of rumor-prevailing equilibrium. Secondly, by utilizing the Routh–Hurwitz criterion and LaSalle’s invariance principle, the local stability and global stability of rumor equilibria are proved. Moreover, the optimal control is presented via Pontryagin’s minimum principle, which is to effectively restrain rumor diffusion. Finally, the theoretical results are verified by numerical simulations.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals Swarm shedding in networks of self-propelled agents

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jason Hindes ◽  
Victoria Edwards ◽  
Klimka Szwaykowska Kasraie ◽  
George Stantchev ◽  
Ira B. Schwartz
Keyword(s):  
Network Topology ◽  
Collective Motion ◽  
Mean Field Theory ◽  
Mean Field ◽  
Interaction Strength ◽  
Central Question ◽  
Agent Interaction ◽  
Sparse Networks ◽  
Swarm Pattern ◽  
Limited Sensing

AbstractUnderstanding swarm pattern formation is of great interest because it occurs naturally in many physical and biological systems, and has artificial applications in robotics. In both natural and engineered swarms, agent communication is typically local and sparse. This is because, over a limited sensing or communication range, the number of interactions an agent has is much smaller than the total possible number. A central question for self-organizing swarms interacting through sparse networks is whether or not collective motion states can emerge where all agents have coherent and stable dynamics. In this work we introduce the phenomenon of swarm shedding in which weakly-connected agents are ejected from stable milling patterns in self-propelled swarming networks with finite-range interactions. We show that swarm shedding can be localized around a few agents, or delocalized, and entail a simultaneous ejection of all agents in a network. Despite the complexity of milling motion in complex networks, we successfully build mean-field theory that accurately predicts both milling state dynamics and shedding transitions. The latter are described in terms of saddle-node bifurcations that depend on the range of communication, the inter-agent interaction strength, and the network topology.

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