scholarly journals Investigation on the Self-synchronization of Dual Steady States for a Vibrating System with Four Unbalanced Rotors

2021 ◽  
Author(s):  
Zhao Chunyu ◽  
Mengchao Jiang ◽  
Chunyu Zhao ◽  
Yuanhao Wang ◽  
Weihai Duan
Keyword(s):  
Steady State ◽  
Design Method ◽  
Steady States ◽  
The Self ◽  
Parameter Determination ◽  
Parameter Method ◽  
Crushed Material ◽  
Rigid Frame ◽  
Coupling Equations ◽  
Cone Crusher

Abstract In the field of vibration utilization engineering, to achieve the maximum degree or the highest efficiency use of the excitation force is still a hotspot among researchers. Based on this, this paper has carried out a series of synchronous theoretical analysis on the four identical unbalanced rotors (IURs) symmetrically and circularly mounted on a rigid frame (RF) model, which is used to drive a cone crusher. The dimensionless coupling equations of the four IURs are established using the improved small parameter method. The analysis of the coupling dynamics characteristics of the system shows that the four motors of the system adjust the speed through the synchronous torque to achieve synchronization, and a parameter determination method for realizing offset self-synchronization to eccentric force was put forward under the steady state of ultra-resonance. Furthermore, the relationship between the equivalent stiffness of the crushed material and crushing force and compression coefficient is discussed, and the design method of the full-load crusher working under the steady state of sub-resonance is proposed. Finally, through a series of computer simulations, the correctness of the self-synchronization of dual steady states is verified.

POVERTY TRAPS AND INFERIOR GOODS IN A DYNAMIC HECKSCHER–OHLIN MODEL

2012 ◽  
Vol 17 (6) ◽  
pp. 1227-1251 ◽  
Author(s):  
Eric W. Bond ◽  
Kazumichi Iwasa ◽  
Kazuo Nishimura
Keyword(s):  
Economic Theory ◽  
Steady State ◽  
World Economy ◽  
Steady States ◽  
The Other ◽  
Poverty Traps ◽  
Poverty Trap ◽  
Multiple Steady States ◽  
The World ◽  
State Capital

We extend the dynamic Heckscher–Ohlin model in Bond et al. [Economic Theory(48, 171–204, 2011)] and show that if the labor-intensive good is inferior, then there may exist multiple steady states in autarky and poverty traps can arise. Poverty traps for the world economy, in the form of Pareto-dominated steady states, are also shown to exist. We show that the opening of trade can have the effect of pulling the initially poorer country out of a poverty trap, with both countries having steady state capital stocks exceeding the autarky level. However, trade can also pull an initially richer country into a poverty trap. These possibilities are a sharp contrast with dynamic Heckscher–Ohlin models with normality in consumption, where the country with the larger (smaller) capital stock than the other will reach a steady state where the level of welfare is higher (lower) than in the autarkic steady state.

scholarly journals Zero Eigenvalue Analysis for the Determination of Multiple Steady States in Reaction Networks

1998 ◽  
Vol 53 (3-4) ◽  
pp. 171-177
Author(s):  
Hsing-Ya Li
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Reaction Network ◽  
Steady States ◽  
Eigenvalue Analysis ◽  
Zero Eigenvalue ◽  
Positive Steady State ◽  
Positive Steady States ◽  
Positive Rate ◽  
System Of Inequalities

Abstract A chemical reaction network can admit multiple positive steady states if and only if there exists a positive steady state having a zero eigenvalue with its eigenvector in the stoichiometric subspace. A zero eigenvalue analysis is proposed which provides a necessary and sufficient condition to determine the possibility of the existence of such a steady state. The condition forms a system of inequalities and equations. If a set of solutions for the system is found, then the network under study is able to admit multiple positive steady states for some positive rate constants. Otherwise, the network can exhibit at most one steady state, no matter what positive rate constants the system might have. The construction of a zero-eigenvalue positive steady state and a set of positive rate constants is also presented. The analysis is demonstrated by two examples.

Associative Behaviors of a Novel Series of Amphiphilic Statistical Tripolymers

2014 ◽  
Vol 472 ◽  
pp. 603-606
Author(s):  
Xu Wu ◽  
Hong Hua Xiao ◽  
Ji Juan Wang ◽  
Xiao Xuan Xie ◽  
Jia Wei Lin ◽  
...  
Keyword(s):  
Steady State ◽  
Self Assembly ◽  
Sulfonic Acid ◽  
The Self ◽  
Steady State Fluorescence

A novel series of brush-like amphiphilic statistical tripolymers were designed and prepared by polymerization of amphiphilic macromonomer 2-(acrylamido)-dodecane sulfonic acid (AMC12S, 10 to 90 mol %), with hindrance units sodium p-styrenesulfonate (SSS, 0 to 5 mol %), and 2-(acrylamido)- 2-methylpro-panesulfonic acid (AMPS). The self-assembly behaviors of these tripolymers were investigated using steady-state fluorescence, and the increase of amphiphilic units results in a decrease of microdomain polarity and polymer concentrations for assembly, while the increase of hindrance units leads little change of microdomain polarity.

scholarly journals Thermal Robustness of Entanglement in a Dissipative Two-Dimensional Spin System in an Inhomogeneous Magnetic Field

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1066
Author(s):  
Gehad Sadiek ◽  
Samaher Almalki
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Nearest Neighbor ◽  
Quantum Phase Transitions ◽  
Inhomogeneous Magnetic Field ◽  
Steady States ◽  
Inhomogeneous Field ◽  
Spin States ◽  
Two Dimensional ◽  
Spin Lattice

Recently new novel magnetic phases were shown to exist in the asymptotic steady states of spin systems coupled to dissipative environments at zero temperature. Tuning the different system parameters led to quantum phase transitions among those states. We study, here, a finite two-dimensional Heisenberg triangular spin lattice coupled to a dissipative Markovian Lindblad environment at finite temperature. We show how applying an inhomogeneous magnetic field to the system at different degrees of anisotropy may significantly affect the spin states, and the entanglement properties and distribution among the spins in the asymptotic steady state of the system. In particular, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustness against the thermal dissipative decay effect in the completely anisotropic (Ising) system, whereas the beyond nearest neighbor ones vanish entirely. The spins of the system in this case reach different steady states depending on their positions in the lattice. However, the inhomogeneity of the field shows no effect on the entanglement in the completely isotropic (XXX) system, which vanishes asymptotically under any system configuration and the spins relax to a separable (disentangled) steady state with all the spins reaching a common spin state. Interestingly, applying the same field to a partially anisotropic (XYZ) system does not just enhance the nearest neighbor entanglements and their thermal robustness but all the long-range ones as well, while the spins relax asymptotically to very distinguished spin states, which is a sign of a critical behavior taking place at this combination of system anisotropy and field inhomogeneity.

scholarly journals ESTABLISHING THE ROTATION SPEED VARIATION RANGE LIMITS FOR AUTO-EXCITATION OF SELF-OSCILLATING GRINDING IN A TUMBLING MILL

2020 ◽  
Vol 4 ◽  
pp. 32-35
Author(s):  
Kateryna Deineka ◽  
Yurii Naumenko
Keyword(s):  
Visual Analysis ◽  
Rotation Speed ◽  
Relative Size ◽  
Fine Fraction ◽  
Coarse Fraction ◽  
The Self ◽  
Cement Clinker ◽  
Crushed Material ◽  
Degree Of Filling ◽  
Tumbling Mill

The influence of the structure of a two-fraction polygranular feed of the chamber on the value of the drum rotation speed at auto-excitation of self-excited oscillations with a maximum swing is considered. Such a pulsating mode of movement of the charge is used in the self-oscillating process of grinding in a tumbling mill. The coarse fraction simulated the grinding bodies was steel bullets with a relative size ψdb=0.026. The fine fraction, simulated the particles of the crushed material, was a cement clinker with a relative particle size ψdm=0.00013. Variable factors of experimental studies were: the degree of filling the chamber in the state of rest κbr=0.25; 0.29; 0.33 and the degree of filling the gaps between the particles of the coarse fraction with particles of the fine fraction κmbgr=0.0625; 0.375; 0.6875; 1. The method of visual analysis of transient processes of self-oscillating modes of feed behavior in the cross section of the rotating drum chamber is applied. Measurements of the speed limits of the drum rotation were carried out with auto-excitation of self-oscillations of the filling. The magnitude of the self-oscillation swing was estimated by the increase in the difference between the maximum and minimum values of the filling dilatancy for one period of pulsations. An increase in the upper limit of the speed range ψω2 with a decrease in κbr and κmbgr was established. The growth rate of ψω2 increases at low values of κbr and κmbgr. Some increase in the lower limit of the ψω1 range with a decrease in κbr and κmbgr was revealed. An increase in the range of speeds of rotation was recorded at the maximum range of self-oscillations ψω1–ψω2 with a decrease in the connected interaction of the intra-mill filling. This coherent interaction is due to an increase in κbr and κmbgr. The value of the ψω1–ψω2 range varies from 1.01–1.03 at κbr=0.33 and κmbg=1 to 1.22–1.66 at κbr=0.25 and κmbgr=0.0625. The range gets its maximum value with fine and superfine grinding

scholarly journals The unraveling of balanced complexes in metabolic networks

2021 ◽  
Author(s):  
Damoun Langary ◽  
Anika Kueken ◽  
Zoran Nikoloski
Keyword(s):  
Steady State ◽  
Large Scale ◽  
Metabolic Networks ◽  
Network Models ◽  
Steady States ◽  
Biochemical Networks ◽  
Computational Approaches ◽  
Metabolic Models ◽  
Large Scale Networks ◽  
General Conditions

Balanced complexes in biochemical networks are at core of several theoretical and computational approaches that make statements about the properties of the steady states supported by the network. Recent computational approaches have employed balanced complexes to reduce metabolic networks, while ensuring preservation of particular steady-state properties; however, the underlying factors leading to the formation of balanced complexes have not been studied, yet. Here, we present a number of factorizations providing insights in mechanisms that lead to the origins of the corresponding balanced complexes. The proposed factorizations enable us to categorize balanced complexes into four distinct classes, each with specific origins and characteristics. They also provide the means to efficiently determine if a balanced complex in large-scale networks belongs to a particular class from the categorization. The results are obtained under very general conditions and irrespective of the network kinetics, rendering them broadly applicable across variety of network models. Application of the categorization shows that all classes of balanced complexes are present in large-scale metabolic models across all kingdoms of life, therefore paving the way to study their relevance with respect to different properties of steady states supported by these networks.

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