Symmetric Cycle Research Articles

Bumpy black holes

We study six-dimensional rotating black holes with bumpy horizons: these are topologically spherical, but the sizes of symmetric cycles on the horizon vary non-monotonically with the polar angle. We construct them numerically for the first three bumpy families, and follow them in solution space until they approach critical solutions with localized singularities on the horizon. We find strong evidence of the conical structures that have been conjectured to mediate the transitions to black rings, to black Saturns, and to a novel class of bumpy black rings. For a different, recently identified class of bumpy black holes, we find evidence that this family ends in solutions with a localized singularity that exhibits apparently universal properties, and which does not seem to allow for transitions to any known class of black holes.

Biaxial Ratcheting of Ultra High Molecular Weight Polyethylene: Experiments and Constitutive Modeling

Abstract Responses of ultra-high molecular weight polyethylene (UHMWPE) under biaxial cyclic loading were investigated through systematically conducting experiments. Biaxial experiments on UHMWPE tubular specimens were conducted first by prescribing a steady internal pressure followed by a symmetric axial-strain controlled cycle. The steady internal pressure induced a steady nominal circumferential stress, which under the application of the axial strain-controlled cycle, induced circumferential strain ratcheting in the UHMWPE tubular specimens. Experimentally observed ratcheting responses of UHMWPE under biaxial cyclic loading was simulated using one of the unified state variable theories, the viscoplasticity theory based on overstress for polymers (VBOP). To improve the circumferential strain ratcheting simulation of the VBOP model, the Chaboche kinematic hardening rule was implemented in the model. The simulation of the VBOP model with the classical kinematic hardening model was also carried out to demonstrate the current state of the modeling for UHMWPE. Improvement of the circumferential strain ratcheting simulation by the modified VBOP model is demonstrated; however, simulations also indicate that further model modification will be needed.

Early Mississippian Orbital-Scale Glacio-Eustasy Detected From High-Resolution Oxygen Isotopes of Marine Apatite (Conodonts)

Abstract Stratigraphic and geochemical studies from tropical through polar latitude records now recognize that the late Paleozoic ice age (LPIA) began earlier and ended later than traditionally thought and was characterized by discrete, My-scale intervals of increased glacial ice volumes that were separated by My-scale intervals of diminished ice volumes. Whereas the onset of LPIA glaciation now is recognized to have started as early as the Late Devonian, the continuity and patterns of glaciation in the > 15 My interval between this onset date and the well-documented mid-Carboniferous portion of the LPIA are less well understood. This study utilizes detailed cyclostratigraphic and δ18O records from Lower Mississippian (mid Tournaisian) tropical marine deposits and conodont apatite to argue that in addition to evidence for a discrete, My-scale early LPIA glaciation, there is compelling evidence for superimposed high-frequency (orbital-scale) glacial–interglacial climate oscillations driving glacio-eustasy and changes in sea-surface temperature (SST). Cyclostratigraphic evidence includes the development of asymmetric (progressive shallowing) and symmetric (deepening followed by shallowing) subtidal cycles in the Tournaisian Woodhurst Member of Lodgepole Formation which record repeated high-frequency water-depth changes from below storm wave base to above fairweather wave base. δ18O values from samples originating from six cycles range from 17.8‰ to 21.6‰, and intracycle trends record progressive increases in isotopic values from the deepest-water facies (at cycle base for asymmetric cycles or mid cycle for symmetric cycles) into the shallower-water cycle caps. Four of the cycles record average intracycle isotopic shifts of 1.4‰, and two cycles record shifts of ≥ 2.5‰. These co-varying trends between interpreted water-depth and δ18O changes are consistent with the hypothesis that the water-depth changes were controlled by orbital-scale glacio-eustasy. Assuming that the observed intracycle δ18O shifts represent the combined effects of ice-volume and SST changes, calculated glacio-eustatic magnitudes were < 50 m with tropical SST changes of < 4°C. Cycles recording ≥ 2.5‰ shifts may reflect additional SST cooling related to intensification of coastal upwelling during the onset of glacial stages. Orbital-scale glacio-eustatic interpretations imply that in addition to overall long-term Early Mississippian cooling and glaciation, the mid Tournaisian was characterized by superimposed high-frequency orbital-scale climate changes which controlled marked changes in glacial ice volumes, eustatic sea levels, coastal-upwelling intensities, and tropical SSTs. These long-term and superimposed short-term climate changes highlight the dynamic nature of the early LPIA and are reminiscent of climate patterns observed for Cenozoic and Late Ordovician greenhouse-to-icehouse climatic transitions.

Synthesis and extreme rate capability of Si-Al-C-N functionalized carbon nanotube spray-on coatings as Li-ion battery electrode.

Silicon-based precursor derived glass-ceramics or PDCs have proven to be an attractive alternative anode material for Li ion batteries. Main challenges associated with PDC anodes are their low electrical conductivity, first cycle loss, and meager C-rate performance. Here, we show that thermal conversion of single source aluminum-modified polysilazane on the surfaces of carbon nanotubes (CNTs) results in a robust Si-Al-C-N/CNT shell/core composite that offers extreme C-rate capability as battery electrode. Addition of Al to the molecular network of Si-C-N improved electrical conductivity of Si-C-N by 4 orders of magnitude, while interfacing with CNTs showed 7-fold enhancement. Further, we present a convenient spray-coating technique for PDC composite electrode preparation that eliminates polymeric binder and conductive agent there-by reducing processing steps and eradicating foreign material in the electrode. The Si-Al-C-N/CNT electrode showed stable charge capacity of 577 mAh g(-1) at 100 mA g(-1) and a remarkable 400 mAh g(-1) at 10,000 mA g(-1), which is the highest reported value for a silazane derived glass-ceramic or nanocomposite electrode. Under symmetric cycling conditions, a high charge capacity of ∼350 mA g(-1) at 1600 mA g(-1) was continuously observed for over 1000 cycles.

Cyclic Plastic Response and Damage in Materials for High Temperature Applications*

The characteristic changes of the cyclic plastic stress-strain response of stainless steel and superalloys derived from the analysis of hysteresis loop at different temperatures are reported. The evolution of the surface relief in strain controlled cycling is documented using high resolution SEM and TEM. The mechanisms leading to cyclic strain localization, formation of surface relief, fatigue crack initiation and early crack growth are discussed. The study of the low cycle fatigue behavior of these materials was concentrated mostly to the analysis of the stress-strain response, internal structures, fatigue life and crack growth (1-3). In recent years, considerable attention has been attracted to the study of the early damage mechanisms in crystalline materials, starting with the cyclic slip localization and resulting finally in the initiation of fatigue cracks and their early growth (4, 5). In this contribution, the methods allowing to study the sources of cyclic stress and early fatigue damage at room and elevated temperatures are presented and used to reveal details of the mechanisms of cyclic plastic straining and fatigue damage evolution in austenitic steels and nickel superalloys. 1. Cyclic Plastic Stress-Strain Response. Cyclic plasticity of materials is usually studied in strain- controlled cycling with constant strain rate, since stress response of the material depends not only on temperature but also on the strain rate. In a standard low cycle fatigue experiment, several specimens are cycled in a symmetrical cycle with constant total or plastic strain amplitudes, and their stress response is recorded and evaluated. Hysteresis loops can be stored in computer memory, and stress, strain and plastic strain amplitudes are evaluated during the fatigue life. The plot of the stress amplitudes vs. number of loading cycles represents the fatigue hardening/softening curves. The plot of the saturated stress amplitude (or stress amplitude at half-life) vs. strain or plastic strain amplitude represents the cyclic stress-strain curve. In order to find the sources of the cyclic stress, more detailed analysis is necessary. Hysteresis loop and the analysis of its shape using the generalized statistical theory (6) can yield information on the sources of the cyclic

Relationship Between the Threshold Stress Intensity Factor Ranges of the Material and the Transition From Short to Long Fatigue Crack

A relationship between the threshold stress intensity factor ranges of the material is established for microstructurally short, physically small and long fatigue cracks depending on the microstructure at a symmetrical loading cycle. The threshold stress intensity factor ranges calculated by the proposed concept for titanium alloy VT3-1 in different structural states agree well with those determined experimentally. The criteria are proposed for the transition from a small to a long fatigue crack depending on the level of the applied load amplitude. In the whole range of the load amplitudes, the condition when a reversible plastic zone at the crack tip reaches the grain size is taken as a criterion for the transition from a physically small to a long fatigue crack. In the high cycle fatigue region, the physically small crack growth range is to be divided into two areas because of a change in the mechanisms of the physically small crack growth upon the attainment by the stress intensity factor range of the threshold value for the long crack.

Effect of Thermal Barrier Coating on Low Cycle Fatigue Behavior of Cast Inconel 713LC at 900 °C

The effect of thermal barrier coating (TBC) on low cycle fatigue behavior of cast superalloy Inconel 713 LC has been studied at 900 °C. The TBC consisting of a CoNiCrAlY bond coat and a zirconia (ZrO2) top coat stabilized by 8% yttria (Y2O3) was deposited on the gauge section of cylindrical specimens using the atmospheric plasma spray technique. Cylindrical specimens of Inconel 713LC in as-received condition and with surface treatment were cyclically strained under strain control with constant total strain amplitude in symmetrical cycle at 900 °C in air. Hardening/softening curves, cyclic stress-strain curve and fatigue life data of coated and uncoated material were obtained. The stress response of the TBC coated specimens is lower in comparison with the uncoated specimens. Detrimental effect of surface treatment on the Basquin curve is documented. Specimen sectioning and fracture surface observations revealed fatigue damage mechanisms and help to discuss differences in fatigue behavior of the coated and uncoated superalloy.

The influence mechanism of ferrite grain size on strength stress at the fatigue of low-carbon steel

Purpose. Explanation of the influence mechanism of ferrite grain size on the fatigue strength of low-carbon steel. Methodology. Material for research is the low-carbon steel with 0.1% of carbon contnent. The different size of ferrite grain was obtained due to varying the degree of cold plastic deformation and temperature of annealing. The estimation of grain size was conducted using methodologies of quantitative metallography. The microstructure of metal was investigated under a light microscope with increase up to 1500 times. As a fatigue response the fatigue strength of metal – a maximal value of load amplitude with endless endurance limit of specimen was used. Fatigue tests were carried out using the test machine «Saturn-10», at the symmetric cycle of alternating bend loading. Findings. On the basis of research the dependence for fatigue strength of low-carbon steel, which is based on an additive contribution from hardening of solid solution by the atoms of carbon, boundary of the ferrite grain and amount of mobile dislocations was obtained. It was established that as the grainy structure of low-carbon steel enlarges, the influence of grain size on the fatigue strength level is reduced. For the sizes of grains more than 100 mcm, basic influence on fatigue strength begins to pass to the solid solution hardening, which is determined by the state of solid solution of introduction. Originality. From the analysis of the obtained dependences it ensues that with the increase of ferrite grain size the required amount of mobile dislocations for maintenance of conditions for spreading plastic deformation becomes less dependent from the scheme of metal loading. Practical value. The obtained results present certain practical interest when developing of recommendations, directed on the increase of resource of products work from low-carbon steels in the conditions of cyclic loading. Estimation of separate contribution of the studied processes of structural changes with fatigue load allows one to choose a rational solution – to use the hardening effect from the ferrite alloying or to change the grain size of ferrite.

A new test to study the cyclic hardening behaviour of a range of high strength rail materials

Plastic ratcheting plays a key role in wear and rolling contact fatigue crack formation at the wheel–rail interface. Tests to examine the wear and rolling contact fatigue behaviour of rail materials over a wide range of service conditions are expensive and can be impractical. A physical simulation of the deformation behaviour associated with ratcheting is an attractive replacement for such tests. In this work, the Plane Stress Local Torsion (PSLT) test is proposed as a novel mechanical testing method to physically simulate near-surface deformation in rails and to characterize the cyclic deformation behaviour of rail materials. Contrary to the orthodox mechanical tests, the proposed method is capable of producing a nonlinear strain gradient in test samples which resembles the real gradient in the rail–wheel system. The PSLT testing was performed on specimens of the nominated rail steels in a strain-controlled fashion to simulate the unidirectional as well as the fully reversing strain cycles. The test was used to examine the cyclic hardening behaviour and ratcheting characteristics of a range of high strength rail materials under cyclic loading at room temperature. The effect of the cyclic strain amplitude under symmetrical strain cycling on the cyclic hardening behaviour was investigated. Experimental torque–twist data were used to compare the plastic flow behaviour of commonly used rail materials in heavy haul applications under cyclic loading. The cyclic and ratcheting strain accumulation behaviour in the test samples was characterized based on the torque–twist data to allow a comparative study of the mechanical properties. Optical microscopy of the tested samples was also performed to compare the microstructures at the flow localization zone for different materials subjected to cyclic strain accumulation.

Liquefaction susceptibility study of sandy soils: effect of low plastic fines

The objective of this paper is to present a study on the mechanical behavior of three Algerian sands through cyclic triaxial tests with focus on the effect of the fines content. The particularity of this study is to keep the amount of the sand material matrix as a constant parameter for the entire range of fines content. This choice was considered due to the difficulty to determine experimentally the maximum and minimum void ratios of soil mixtures for fines content exceeding 15 %. The materials used in this investigation are originated from two different regions (Chlef and Boumerdes) in northern Algeria and are known for their higher seismicity levels. By varying the cyclic stress ratios and the proportion of fines contained naturally in the sand, a series of cyclic triaxial tests were carried out on reconstituted samples with a density index of 0.5 and an initial confining pressure of 100 kPa, on a servo-controlled dynamic machine with a sinusoidal frequency signal of 0.05 Hz and alternated symmetrical cycles. Comparing the clean and natural sands, the test results indicate that the presence of fines influences significantly the liquefaction resistance. Indeed, the fines content increases the liquefaction resistance for Zemmouri sand, decreases or stabilizes it for the Rass and Chlef sands, respectively. The effect of fines on the Chlef and Rass sands is in good agreement with the published literature, where the liquefaction resistance decreases to a threshold value and then increases with the increase of the fines content. This study can be used in soil classification and determination of liquefaction potential of seismic areas with smaller amounts of fines.

The Ratcheting Behaviour of Stainless Steel Pressurized Piping Elbows Subjected to Dynamic Out-of-Plane Moments

In this paper the ratcheting behavior of four pairs of stainless steel elbows is studied under conditions of steady internal pressure and dynamic conditions that induced out-of-plane external moments at frequencies typical of seismic excitations. The finite element analysis with the nonlinear kinematic hardening model has been used to evaluate ratcheting behavior of the piping elbows under mentioned loading condition. Material parameters have been obtained from several stabilized cycles of specimens that are subjected to symmetric strain cycles. The direction of maximum strain is at about 45° between the hoop and axial directions. The results show that the direction of highest ratcheting is along the hoop direction rather than the direction of maximum principal strain. Also, the initial rate of ratcheting is large and then it decreases with the increasing cycles. Also, the FE method gives over estimated values compared with the experimental data.

The Effect of Dynamic Bending Moments on the Ratchetting Behavior of Stainless Steel Pressurized Piping Elbows

In this paper the ratchetting behavior of four pairs of stainless steel, long and short radius welding elbows is studied under conditions of steady internal pressure and in-plane, resonant dynamic moments that simulated seismic excitations. The finite element analysis with the nonlinear kinematic hardening model has been used to evaluate ratchetting behavior of the elbow under mentioned loading condition. Stress–strain data and material parameters have been obtained from several stabilized cycles of specimens that are subjected to symmetric strain cycles. The results show that the maximum ratcheting strain occurred mainly in the hoop direction at flanks. Ratcheting strain rate increases with increase of the bending loading level at the constant internal pressure. The results show that the FE method gives over estimated values comparing with the experimental data.

The Ratcheting Behaviour of Plain Carbon Steel Pressurized Piping Elbows Subjected to Simulated Seismic In-Plane Bending

In this paper, cyclic loading behavior of carbon steel pressurized piping elbows are described. Effects of internal pressure and bending moment amplitude on the ratcheting rate are investigated. The AF kinematic hardening model is used to predict the plastic behavior of the elbows. Material parameters and stress-strain data have been obtained from several stabilized cycles of specimens that are subjected to symmetric strain cycles. The results show that the maximum ratcheting strain occurred mainly in the hoop direction at flanks. Hoop strain ratcheting was found at intrados for individual specimen. Ratcheting strain rate increases with increase of the bending loading level at the constant internal pressure. The results show that the initial rate of ratcheting is large and then it decreases with the increasing cycles. The FE model predicts the hoop strain ratcheting rate to be near that found experimentally in all cases that M/Ml≤1..

Three-Phase Three-Level DC/DC Converter for High Input Voltage and High Power Applications-Adopting Symmetrical Duty Cycle Control

Three-phase dc/dc converters have the superior characteristics including lower current rating of switches, the reduced output filter requirement, and effective utilization of transformers. To further reduce the voltage stress on switches, three-phase three-level (TPTL) dc/dc converters have been investigated recently; however, numerous active power switches result in a complicated configuration in the available topologies. Therefore, a novel TPTL dc/dc converter adopting a symmetrical duty cycle control is proposed in this paper. Compared with the available TPTL converters, the proposed converter has fewer switches and simpler configuration. The voltage stress on all switches can be reduced to the half of the input voltage. Meanwhile, the ripple frequency of output current can be increased significantly, resulting in a reduced filter requirement. Experimental results from a 540-660-V input and 48-V/20-A output are presented to verify the theoretical analysis and the performance of the proposed converter.

Complex dynamics of a nonlinear voter model with contrarian agents

We investigate mean-field dynamics of a nonlinear opinion formation model with congregator and contrarian agents. Each agent assumes one of the two possible states. Congregators imitate the state of other agents with a rate that increases with the number of other agents in the opposite state, as in the linear voter model and nonlinear majority voting models. Contrarians flip the state with a rate that increases with the number of other agents in the same state. The nonlinearity controls the strength of the majority voting and is used as a main bifurcation parameter. We show that the model undergoes a rich bifurcation scenario comprising the egalitarian equilibrium, two symmetric lopsided equilibria, limit cycle, and coexistence of different types of stable equilibria with intertwining attractive basins.

Degradation of TBC Coating during Low-Cycle Fatigue Tests at High Temperature

The work is focused on the study of degradation of ZrO2 stabilized by Y2O3 (YSZ) thermal barrier-coating system with CoNiCrAlY bond coat applied on cast polycrystalline nickel-based superalloy Inconel 713LC. Cylindrical specimens in as-coated conditions were cyclically strained under strain control with constant total strain amplitude in symmetrical cycle at high temperature (900 °C) in air. Coating system YSZ with CoNiCrAlY bond coat were prepared by APS method on blasted surface. The microstructure of TBC was characterized with scanning electron microscopy and energy dispersion X-ray analysis. The coating thickness and hardness profile was measured. Fracture surface, surface relief and polished sections parallel to the specimen axis were examined to study damage mechanisms in coatings under cyclic loading at high temperature. It was find that initiation of the fatigue crack usually occurs on interface YSZ-CoNiCrAlY and the trajectory of the further crack propagation was documented.

Substrate protein switches GroE chaperonins from asymmetric to symmetric cycling by catalyzing nucleotide exchange

The complex kinetics of Pi and ADP release by the chaperonin GroEL/GroES is influenced by the presence of unfolded substrate protein (SP). Without SP, the kinetics of Pi release are described by four phases: a "lag," a "burst" of ATP hydrolysis by the nascent cis ring, a "delay" caused by ADP release from the nascent trans ring, and steady-state ATP hydrolysis. The release of Pi precedes the release of ADP. The rate-determining step of the asymmetric cycle is the release of ADP from the trans ring of the GroEL-GroES1 "bullet" complex that is, consequently, the predominant species. In the asymmetric cycle, the two rings of GroEL function alternately, 180° out of phase. In the presence of SP, a change in the kinetic mechanism occurs. With SP present, the kinetics of ADP release are also described by four phases: a lag, a "surge" of ADP release attributable to SP-induced ADP/ATP exchange, and a "pause" during which symmetrical "football" particles are formed, followed by steady-state ATP hydrolysis. SP catalyzes ADP/ATP exchange on the trans ring. Now ADP release precedes the release of Pi, and the rate-determining step of the symmetric cycle becomes the hydrolysis of ATP by the symmetric GroEL-GroES2 football complex that is, consequently, the predominant species. A FRET-based analysis confirms that asymmetric GroEL-GroES1 bullets predominate in the absence of SP, whereas symmetric GroEL-GroES2 footballs predominate in the presence of SP. This evidence suggests that symmetrical football particles are the folding functional form of the chaperonin machine in vivo.

On the stability and chaos of a plate with motion constraints subjected to subsonic flow

The non-linear dynamical behavior of a cantilevered plate with motion constraints in subsonic flow is investigated in this paper. The governing partial differential equation is transformed to a series of ordinary differential equations by using the Galerkin method. The fixed points and their stabilities of the system are presented in a parameter space based on qualitative analysis and numerical studies. The complex non-linear behavior in the region of dynamical instability is investigated by using numerical simulations. The region of dynamical instability is divided into four sub-regions according to different types of plate motion. Results show that symmetric and asymmetric limit cycle motions would occur after dynamical instability; the route from periodic motions to chaos is via doubling-period bifurcation; symmetric and asymmetric period-3 and period-6 motions appear along with chaotic motions; chaotic divergence and divergent motions occur with the increases of dynamic pressure.

Effect of material inhomogeneity on the cyclic plastic deformation behavior at the microstructural level: micromechanics-based modeling of dual-phase steel

The microstructure of dual-phase (DP) steels typically consists of a soft ferrite matrix with dispersed islands of hard martensite phase. Due to the composite effect of ferrite and martensite, DP steels exhibit a unique combination of strain hardening, strength and ductility. A microstructure-based micromechanical modeling approach is adopted in this work to capture the tensile and cyclic plastic deformation behavior of DP steel. During tensile straining, strain incompatibility between the softer ferrite matrix and the harder martensite phase arises due to a difference in the flow characteristics of these two phases. Microstructural-level inhomogeneity serves as the initial imperfection, triggering strain incompatibility, strain partitioning and finally shear band localization during tensile straining. The local deformation in the ferrite phase is constrained by adjacent martensite islands, which locally results in stress triaxiality development in the ferrite phase. As the martensite distribution varies within the microstructure, the stress triaxiality also varies in a band within the microstructure. Inhomogeneous stress and strain distribution within the softer ferrite phase arises even during small tensile straining because of material inhomogeneity. The magnitude of cyclic plastic deformation within the softer ferrite phase also varies according to the stress distribution in the first-quarter cycle tensile loading. Accumulation of tensile/compressive plastic strain with number of cycles is noted in different locations within the ferrite phase during both symmetric stress and strain controlled cycling. The basic mode of cyclic plastic deformation in an inhomogeneous material is cyclic strain accumulation, i.e. ratcheting. Microstructural inhomogeneity results in cyclic strain accumulation in the aggregate DP material even in symmetric stress cycling.

Hamiltonian Cycle Systems Which Are Both Cyclic and Symmetric

AbstractThe notion of a symmetric Hamiltonian cycle system (HCS) of a graph Γ has been introduced and studied by J. Akiyama, M. Kobayashi, and G. Nakamura [J Combin Des 12 (2004), 39–45] for , by R. A. Brualdi and M. W. Schroeder [J Combin Des 19 (2011), 1–15] for , and then naturally extended by V. Chitra and A. Muthusamy [Discussiones Mathematicae Graph Theory, to appear] to the multigraphs and . In each case, there must be an involutory permutation ψ of the vertices fixing all the cycles of the HCS and at most one vertex. Furthermore, for , this ψ should be precisely the permutation switching all pairs of endpoints of the edges of I.An HCS is cyclic if it is invariant under some cyclic permutation of all the vertices. The existence question for a cyclic HCS of has been completely solved by Jordon and Morris [Discrete Math (2008), 2440–2449]—and we note that their cyclic construction is also symmetric for (mod 8). It is then natural to study the existence problem of an HCS of a graph or multigraph Γ as above which is both cyclic and symmetric. In this paper, we completely solve this problem: in the case of even order, the final answer is that cyclicity and symmetry can always cohabit when a cyclic solution exists. On the other hand, imposing that a cyclic HCS of odd order is also symmetric is very restrictive; we prove in fact that an HCS of with both properties exists if and only if is a prime.