TOPOLOGICAL ENTROPY OF SWITCHED SYSTEMS
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- Journal of the Korean Mathematical Society
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- v.55 no.5
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- pp.1157-1175
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- 2018
For a switched system with constraint on switching sequences, which is also called a subshift action, on a metric space not necessarily compact, two kinds of topological entropies, average topological entropy and maximal topological entropy, are introduced. Then we give some properties of those topological entropies and estimate the bounds of them for some special systems, such as subshift actions generated by finite smooth maps on p-dimensional Riemannian manifold and by a family of surjective endomorphisms on a compact metrizable group. In particular, for linear switched systems on
The real moment-angle complex (or, more generally, real polyhedral product) and its real toric space have recently attracted much attention in toric topology. The aim of this paper is to give two interesting remarks regarding real polyhedral products and real toric spaces. That is, we first show that Moore's conjecture holds to be true for certain real polyhedral products. In general, real polyhedral products show some drastic difference between the rational and torsion homotopy groups. Our result shows that at least in terms of the homotopy exponent at a prime this is not the case for real polyhedral products associated to a simplicial complex whose minimal missing faces are all k-simplices with
A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.
To ensure that fire induced collapse of a building is prevented it is important to understand the sequence of events that can lead to this event. In this paper, the initiation of collapse mechanisms of generic a multi-storey steel frame subjected to vertical and horizontal travelling fires are analysed computationally by tracking the formation of plastic hinges in the frame and generation of fire induced loads. Both uniform and travelling fires are considered. In total 58 different cases are analysed using finite element software LS-DYNA. For the frame examined with a simple and generic structural arrangement and higher applied fire protection to the columns, the results indicate that collapse mechanisms for singe floor and multiple floor fires can be each split into two main groups. For single floor fires (taking place in the upper floors of the frame (Group S1)), collapse is initiated by the pull-in of external columns when heated beams in end bays go into catenary action. For single floor fires occurring on the lower floors(Group S2), failure is initiated (i.e. ultimate strain of the material is exceeded) after the local beam collapse. Failure in both groups for single floor fires is governed by the generation of high loads due to restrained thermal expansion and the loss of material strength. For multiple floor fires with a low number of fire floors (1 to 3) - Group M1, failure is dominated by the loss of material strength and collapse is mainly initiated by the pull-in of external columns. For the cases with a larger number of fire floors (5 to 10) - Group M2, failure is dominated by thermal expansion and collapse is mainly initiated by swaying of the frame to the side of fire origin. The results show that for the investigated frame initiation of collapse mechanisms are affected by the fire type, the number of fire floors, and the location of the fire floor. The findings of this study could be of use to designers of buildings when developing fire protection strategies for steel framed buildings where the potential for a multifloor fire exists.
In recent years, the stability, safety and comfort of trains has received increased attention. The mechanical characteristics and differential settlement of the foundation are the main problems studied in high-speed railway research. The mechanical characteristics and differential settlement of the foundation are greatly affected by the ground treatment. Additionally, the effects of train load and earthquakes have a great impact. The dynamic action of the train will increase the vibration acceleration of the foundation and increase the cumulative deformation, and the earthquake action will affect the stability of the substructure. Earthquakes have an important practical significance for the dynamic analysis of the railway operation stage; therefore, considering the impact of earthquakes on the railway substructure stability has engineering significance. In this paper, finite element model of the CFG (Cement Fly-ash Gravel) pile + cement-soil compacted pile about composite foundation is established, and manual numerical incentive method is selected as the simulation principle. The mechanical characteristics and differential settlement of CFG pile + cement-soil compacted pile about composite foundation under train load are studied. The results show: under the train load, the neutral point of the side friction about CFG pile is located at nearly 7/8 of the pile length; the vertical dynamic stress-time history curves of the cement-soil compacted pile, CFG pile and soil between piles are all regular serrated shape, the vertical dynamic stress of CFG pile changes greatly, but the vertical dynamic stress of cement-soil compacted pile and soil between piles does not change much; the vertical displacement of CFG pile, cement-soil compacted pile and soil between piles change very little.
For long underground box utility tunnels, post-tensioned precast concrete is often used. Between precast tunnel segments, sealed waterproof flexible joints are often specified. Fault displacement can lead to excessive deformation of the joints, which can lead to reduction in waterproofing due to diminished contact pressure between the sealant strip and the tunnel segment. This paper authenticates utilization of a finite element model for a prefabricated tunnel fault-crossing founded on ABAQUS software. In addition, material parameter selection, contact setting and boundary condition are reviewed. Analyzed under normal fault action are: the influence of fault displacement; buried depth; soil friction coefficient, and angle of crossing at the fault plane. In addition, distribution characteristics of the utility tunnel structure for vertical and longitudinal/horizontal relative displacement at segmented interface for the top and bottom slab are analyzed. It is found that the effect of increase in fault displacement on the splice joint deformation is significant, whereas the effects of changes in burial depth, pipe-soil friction coefficient and fault-crossing angle on the overall tunnel and joint deformations were not so significant.
This study introduces soil resistance multipliers at locations encompassed by the zone of influence of the helix plate to consider the added lateral resistance provided to the helical pile. The zone of influence of a helix plate is a function of its diameter and serves as a boundary condition for the modified soil resistance springs. The concept is based on implementing p-multipliers as a reduction factor for piles in group action. The application of modified p-y springs in the analysis of helical piles allows for better characterization and understanding of the lateral behavior of helical piles, which will help further the development of design methods. To execute the proposed method, a finite difference program, HPCap (Helical Pile Capacity), was developed by the authors using Matlab. The program computes the deflection, shear force, bending moment, and soil resistance of the helical pile and allows the user to freely input the value of the zone of influence and Ω (a coefficient that affects the value of the p-multiplier). Results from ten full-scale lateral load tests on helical piles embedded at depths of 3.0 m with varying shaft diameters, shaft thicknesses, and helix configurations were analyzed to determine the zone of influence and the magnitude of the p-multipliers. The analysis determined that the value of the p-multipliers is influenced by the ratio between the pile embedment length and the shaft diameter (Dp), the effective helix diameter (Dh-Dp), and the zone of influence. Furthermore, the zone of influence is recommended to be 1.75 times the helix diameter (Dh). Using the numerical analysis method presented in this study, the predicted deflections of the various helical pile cases showed good agreement with the observed field test results.
This paper is concerned with the dynamics of hyperelastic solids and structures. We seek for a smart control actuation that produces a desired (prescribed) displacement field in the presence of transient imposed forces. In the literature, this problem is denoted as displacement tracking, or also as shape morphing problem. One talks about shape control, when the displacements to be tracked do vanish. In the present paper, it is assumed that the control actuation is provided by imposed eigenstrains, e.g., by the electric field in piezoelectric actuators, or by thermal actuators, or via analogous physical effects, such as magneto-striction or pre-stress. Structures with a controlled eigenstrain-type actuation belong to the class of smart structures. The action of the eigenstrains can be conveniently characterized by actuation stresses. Our theoretical derivations are performed in the framework of the theory of small incremental dynamic deformations superimposed upon a statically pre-deformed configuration of a hyperelastic solid or structure. We particularly ask for a distribution of incremental actuation stresses, such that the incremental displacements follow exactly a prescribed trajectory field, despite the imposed incremental forces are present. An exact solution of this problem is presented under the assumption that the actuation stresses can be tailored freely and applied everywhere within the body. Extending a Neumann-type solution strategy, it is shown that the actuation stresses due to the distributed control eigenstrains must satisfy certain quasi-static equilibrium conditions, where auxiliary body-forces and auxiliary surface tractions are to be taken into account. The latter auxiliary loading can be directly computed from the imposed forces and from the desired displacement field to be tracked. Hence, despite the problem is a dynamic one, a straightforward computation of proper actuator distributions can be obtained in the framework of quasi-static equilibrium conditions. Necessary conditions for the functioning of this concept are presented. Particularly, it must be required that the intermediate configuration is infinitesimally superstable. Previous results of our group for the case of shape control and displacement tracking in linear elastic structures are included as special cases. The high potential of the solution is demonstrated via Finite Element computations for an irregularly shaped four-corner plate in a state of plain strain.
The wall shear stress in the vicinity of end-to end anastomoses under steady flow conditions was measured using a flush-mounted hot-film anemometer(FMHFA) probe. The experimental measurements were in good agreement with numerical results except in flow with low Reynolds numbers. The wall shear stress increased proximal to the anastomosis in flow from the Penrose tubing (simulating an artery) to the PTFE: graft. In flow from the PTFE graft to the Penrose tubing, low wall shear stress was observed distal to the anastomosis. Abnormal distributions of wall shear stress in the vicinity of the anastomosis, resulting from the compliance mismatch between the graft and the host artery, might be an important factor of ANFH formation and the graft failure. The present study suggests a correlation between regions of the low wall shear stress and the development of anastomotic neointimal fibrous hyperplasia(ANPH) in end-to-end anastomoses. 30523 T00401030523 ^x Air pressure decay(APD) rate and ultrafiltration rate(UFR) tests were performed on new and saline rinsed dialyzers as well as those roused in patients several times. C-DAK 4000 (Cordis Dow) and CF IS-11 (Baxter Travenol) reused dialyzers obtained from the dialysis clinic were used in the present study. The new dialyzers exhibited a relatively flat APD, whereas saline rinsed and reused dialyzers showed considerable amount of decay. C-DAH dialyzers had a larger APD(11.70
The wall shear stress in the vicinity of end-to end anastomoses under steady flow conditions was measured using a flush-mounted hot-film anemometer(FMHFA) probe. The experimental measurements were in good agreement with numerical results except in flow with low Reynolds numbers. The wall shear stress increased proximal to the anastomosis in flow from the Penrose tubing (simulating an artery) to the PTFE: graft. In flow from the PTFE graft to the Penrose tubing, low wall shear stress was observed distal to the anastomosis. Abnormal distributions of wall shear stress in the vicinity of the anastomosis, resulting from the compliance mismatch between the graft and the host artery, might be an important factor of ANFH formation and the graft failure. The present study suggests a correlation between regions of the low wall shear stress and the development of anastomotic neointimal fibrous hyperplasia(ANPH) in end-to-end anastomoses. 30523 T00401030523 ^x Air pressure decay(APD) rate and ultrafiltration rate(UFR) tests were performed on new and saline rinsed dialyzers as well as those roused in patients several times. C-DAK 4000 (Cordis Dow) and CF IS-11 (Baxter Travenol) reused dialyzers obtained from the dialysis clinic were used in the present study. The new dialyzers exhibited a relatively flat APD, whereas saline rinsed and reused dialyzers showed considerable amount of decay. C-DAH dialyzers had a larger APD(11.70