Phase Space Of Parameters Research Articles

Robustness, Death of Spiral Wave in the Network of Neurons under Partial Ion Channel Block

The development of spiral wave in a two-dimensional square array due to partial ion channel block (Potassium, Sodium) is investigated, the dynamics of the node is described by Hodgkin—Huxley neuron and these neurons are coupled with nearest neighbor connection. The parameter ratio xNa (and xK), which defines the ratio of working ion channel number of sodium (potassium) to the total ion channel number of sodium (and potassium), is used to measure the shift conductance induced by channel block. The distribution of statistical variable R in the two-parameter phase space (parameter ratio vs. poisoning area) is extensively calculated to mark the parameter region for transition of spiral wave induced by partial ion channel block, the area with smaller factors of synchronization R is associated the parameter region that spiral wave keeps alive and robust to the channel poisoning. Spiral wave keeps alive when the poisoned area (potassium or sodium) and degree of intoxication are small, distinct transition (death, several spiral waves coexist or multi-arm spiral wave emergence) occurs under moderate ratio xNa (and xK) when the size of blocked area exceeds certain thresholds. Breakup of spiral wave occurs and multi-arm of spiral waves are observed when the channel noise is considered.

Application of the pencil-beam redefinition algorithm in heterogeneous media for proton beam therapy

In proton beam therapy, changes in the proton range due to lateral heterogeneity may cause serious errors in the dose distribution. In the present study, the pencil-beam redefinition algorithm (PBRA) was applied to proton beam therapy to address the problem of lateral density heterogeneity. In the calculation, the phase-space parameters were characterized for multiple range (i.e. proton energy) bins for given pencil beams. The particles that were included in each pencil beam were transported and redefined periodically until they had stopped. The redefined beams formed a detouring path that was different from that of the non-redefined pencil beams, and the path of each redefined beam was straight. The results calculated by the PBRA were compared with measured proton dose distributions in a heterogeneous slab phantom and an anthropomorphic phantom. Through the beam redefinition process, the PBRA was able to predict the measured proton-detouring effects. Therefore, the PBRA may allow improved calculation accuracy when dealing with lateral heterogeneities in proton therapy applications.

Searching, Stepping, and Stomping: What Polymer Theory can teach us about the Molecular Motor Myosin V

Though myosin V is among the most extensively studied of motor proteins, improvements in experimental techniques continue to provide new insights into the details of its dynamics. High-speed atomic force microscopy has visualized not only the expected hand-over-hand stepping of the two-headed motor along actin filaments, but additional, less well understood behaviors like “foot stomping”, where one head detaches and rebinds to the same site. A comprehensive picture of myosin motility needs to account for all the kinetic pathways, including backstepping and foot stomping, how they vary under load, and their relationship to the structural and chemical parameters of the motor. Starting from a simple polymer model, we develop an analytical theory to understand the minimal physical properties that govern motor dynamics. In particular, we solve the first-passage problem of the head reaching the target binding site, investigating the competing effects of load pulling back at the motor, strain in the leading head that biases the diffusion in the direction of the target, and the possibility of preferential binding to the forward site due to the recovery stroke. The theory reproduces a variety of experimental data, including the power stroke and slow diffusive search regimes in the mean trajectory of the detached head, and the force dependence of the forward-to-backward step ratio, run length, and velocity. The analytical approach yields a formula for the stall force, identifying the relative contributions of the chemical cycle rates versus mechanical features like the bending rigidities of the lever arms. Moreover we can fully explore the parameter phase space, to determine the robustness of the dynamical behavior to perturbations, and the natural constraints that dictate the structure of the motor.

Bifurcation Approach to Analysis of Travelling Waves in Some Taxis–Cross-Diffusion Models

An overview of recently obtained authors’ results on traveling wave solutions of some classes of PDEs is presented. The main aim is to describe all possible travelling wave solutions of the equations. The analysis was conducted using the methods of qualitative and bifurcation analysis in order to study the phase-parameter space of the corresponding wave systems of ODEs. In the first part we analyze the wave dynamic modes of populations described by the “growth - taxis - diffusion polynomial models. It is shown that “suitable nonlinear taxis can affect the wave front sets and generate non-monotone waves, such as trains and pulses, which represent the exact solutions of the model system. Parametric critical points whose neighborhood displays the full spectrum of possible model wave regimes are identified; the wave mode systematization is given in the form of bifurcation diagrams. In the second part we study a modified version of the FitzHugh-Nagumo equations, which model the spatial propagation of neuron firing. We assume that this propagation is (at least, partially) caused by the cross-diffusion connection between the potential and recovery variables. We show that the cross-diffusion version of the model, besides giving rise to the typical fast travelling wave solution exhibited in the original “diffusion FitzHugh-Nagumo equations, additionally gives rise to a slow traveling wave solution. We analyze all possible traveling wave solutions of the model and show that there exists a threshold of the cross-diffusion coefficient (for a given speed of propagation), which bounds the area where “normal impulse propagation is possible. In the third part we describe all possible wave solutions for a class of PDEs with cross-diffusion, which fall in a general class of the classical Keller-Segel models describing chemotaxis. Conditions for existence of front-impulse, impulse-front, and front-front traveling wave solutions are formulated. In particular, we show that a non-isolated singular point in the ODE wave system implies existence of free-boundary fronts.

Constraints of the variation of fundamental couplings and sensitivity of the equation of state of dense matter

We discuss the coupled variations of the gravitational, strong and electroweak coupling constants and the current knowledge of the nuclear equation of state based on heavy ion collision experiments and neutron star mass–radius relationship. In particular we focus in our description on phenomenological parameters, R, relating variations in the quantum chromodynamics scale ΛQCD and the fine structure constant α, and S, relating variations of v, the Higgs vacuum expectation value and the Yukawa couplings, h, in the quark sector. This parametrization is valid for any model where gauge coupling unification occurs at some (unspecified) high energy scale. From a physically motivated set of equations of state for dense matter we obtain the constrained parameter phase space (R,S) in high density nuclear environments. This procedure is complementary to (although currently less powerful than) those used in low-density conditions. For variations of Δα/α=0.005 we find that the obtained constrained parameter lies on a strip region in the (R,S) plane that partially overlaps some of the allowed values of parameters derived from primordial abundances. This may be of interest in the context of unification scenarios where a dense phase of the universe may have existed at early times.

THE M31 VELOCITY VECTOR. III. FUTURE MILKY WAY M31–M33 ORBITAL EVOLUTION, MERGING, AND FATE OF THE SUN

We study the future orbital evolution and merging of the MW-M31-M33 system, using a combination of collisionless N-body simulations and semi-analytic orbit integrations. Monte-Carlo simulations are used to explore the consequences of varying the initial phase-space and mass parameters within their observational uncertainties. The observed M31 transverse velocity implies that the MW and M31 will merge t = 5.86 (+1.61-0.72) Gyr from now, after a first pericenter at t = 3.87 (+0.42-0.32) Gyr. M31 may (probability p=41%) make a direct hit with the MW (defined here as a first-pericenter distance less than 25 kpc). Most likely, the MW and M31 will merge first, with M33 settling onto an orbit around them. Alternatively, M33 may make a direct hit with the MW first (p=9%), or M33 may get ejected from the Local Group (p=7%). The MW-M31 merger remnant will resemble an elliptical galaxy. The Sun will most likely (p=85%) end up at larger radius from the center of the MW-M31 merger remnant than its current distance from the MW center, possibly further than 50 kpc (p=10%). The Sun may (p=20%) at some time in the next 10 Gyr find itself moving through M33 (within 10 kpc), but while dynamically still bound to the MW-M31 merger remnant. The arrival and possible collision of M31 (and possibly M33) with the MW is the next major cosmic event affecting the environment of our Sun and solar system that can be predicted with some certainty. (Abridged)

CONDITIONS OF PASSAGE AND ENTRAPMENT OF TERRESTRIAL PLANETS IN SPIN-ORBIT RESONANCES

The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into account the frequency-dependent quality factors and Love numbers. The torque equations are integrated numerically with a small step in time, includng the oscillating triaxial torque components but neglecting the layered structure of the planet and assuming a zero obliquity. We find that a Mercury-like planet with its current value of orbital eccentricity (0.2056) is always captured in the 3:2 resonance. The probability of capture in the higher 2:1 resonance is approximately 0.23. These results are confirmed by a semi-analytical estimation of capture probabilities as functions of eccentricity for both prograde and retrograde evolution of spin rate. As follows from analysis of equilibrium torques, entrapment in the 3:2 resonance is inevitable at eccentricities between 0.2 and 0.41. Considering the phase space parameters at the times of periastron, the range of spin rates and phase angles, for which an immediate resonance passage is triggered, is very narrow, and yet, a planet like Mercury rarely fails to align itself into this state of unstable equilibrium before it traverses the 2:1 resonance.

Non-intercepting diagnostic for high brightness electron beams using Optical Diffraction Radiation Interference (ODRI)

High-gain Free Electron Lasers and future Linear Colliders require development of modern electron linacs with high brightness beams. Conventional intercepting transverse electron beam diagnostics, e.g. based on Optical Transition Radiation (OTR), cannot tolerate such high power beams without remarkable mechanical damages on the diagnostics device. Optical Diffraction Radiation (ODR) is an excellent candidate for measurements of the transverse phase space parameters in a non-intercepting way. One of the main problems of this method is the low signal to noise ratio, mainly due to the unavoidable synchrotron radiation background. This problem can be overcome by using two slits on metallic foils, placed at a distance shorter than the radiation formation zone. In this case a nearly background-free ODR interference pattern is produced allowing the determination of the beam size and angular divergence. The accuracy on these parameters can be increased by exploiting both ODR polarization states, as well as different wavelengths. Here we report measurements of the ODR interference between two slits with different aperture sizes in a non-collinear geometry, carried out at FLASH (DESY, Germany). Our results demonstrate the unique potential of this technique to determine the beam parameters.

On the accuracy of conservation of adiabatic invariants in slow-fast Hamiltonian systems

Let the adiabatic invariant of action variable in slow-fast Hamiltonian system with two degrees of freedom have two limiting values along the trajectories as time tends to infinity. The difference of two limits is exponentially small in analytic systems. An iso-energetic reduction and canonical transformations are applied to transform the slow-fast systems to form of systems depending on slowly varying parameters in a complexified phase space. On the basis of this method an estimate for the accuracy of conservation of adiabatic invariant is given for such systems.

Modeling morphology evolution during solvent-based fabrication of organic solar cells

Solvent-based thin-film deposition constitutes a popular class of fabrication strategies for manufacturing organic electronic devices like organic solar cells. All such solvent-based techniques usually involve preparing dilute blends of electron-donor and electron-acceptor materials dissolved in a volatile solvent. After some form of coating onto a substrate to form a thin film, the solvent evaporates. An initially homogeneous mixture separates into electron-acceptor rich and electron-donor rich regions as the solvent evaporates. Depending on the specifics of the blend, processing conditions, and substrate characteristics different morphologies are typically formed. Experimental evidence consistently confirms that the resultant morphology critically affects device performance. A computational framework that can predict morphology evolution can significantly augment experimental analysis. Such a framework will also allow high throughput analysis of the large phase space of processing parameters, thus yielding considerable insight into the process–structure–property relationships governing organic solar cell behavior.In this paper, we formulate a computational framework to predict evolution of morphology during solvent-based fabrication of organic thin films. This is accomplished by developing a phase field-based model of evaporation-induced and substrate-induced phase-separation in ternary systems. This formulation allows most of the important physical phenomena affecting morphology evolution during fabrication to be naturally incorporated. We discuss the various numerical and computational challenges associated with a three dimensional, finite-element based, massively parallel implementation of this framework. This formulation allows, for the first time, to model three-dimensional nanomorphology evolution over large time spans on device scale domains. We illustrate this framework by investigating and quantifying the effect of various process and system variables on morphology evolution. We explore ways to control the morphology evolution by investigating different evaporation rates, blend ratios and interaction parameters between components.

Parameter determination based on composite evolutionary algorithm for reconstructing phase-space in chaos time series

To improve the prediction accuracy of the chaotic time series prediction model, a composite optimization method of the differential evolution (DE) algorithm that is based on the phase space reconstruction and least square supported vector machine (LSSVM), is proposed. The phase space parameters and LSSVM model parameters are taken as differential evolution algorithm individuals while the prediction accuracy of the chaotic time series is used as the evaluation function of DE algorithm. The optimal parameters are obtained by mutation, crossover, and selection operators of DE algorithm. Several numerical simulation results show that not only four parameters are determined at the same time, but also the performance of chaotic time series prediction is improved.

Simulation of Spread and Control of Lesions in Brain

A simulation model for the spread and control of lesions in the brain is constructed using a planar network (graph) representation for the central nervous system (CNS). The model is inspired by the lesion structures observed in the case of multiple sclerosis (MS), a chronic disease of the CNS. The initial lesion site is at the center of a unit square and spreads outwards based on the success rate in damaging edges (axons) of the network. The damaged edges send out alarm signals which, at appropriate intensity levels, generate programmed cell death. Depending on the extent and timing of the programmed cell death, the lesion may get controlled or aggravated akin to the control of wild fires by burning of peripheral vegetation. The parameter phase space of the model shows smooth transition from uncontrolled situation to controlled situation. The simulations show that the model is capable of generating a wide variety of lesion growth and arrest scenarios.

Chaotic Characteristic of Time Series of Partial Discharge in Oil-Paper Insulation

The chaotic characteristics of time series of five partial discharge (PD) patterns in oil-paper insulation are studied. The results verify obvious chaotic characteristic of the time series of discharge signals and the fact that PD is a chaotic process. These time series have distinctive features, and the chaotic attractors obtained from time series differed greatly from each other by shapes in the phase space, so they could be used to qualitatively identify the PD patterns. The phase space parameters are selected, then the chaotic characteristic quantities can be extracted. These quantities could quantificationally characterize the PD patterns. The effects on pattern recognition of PRPD and CAPD are compared by using the neural network of radial basis function. The results show that both of the two recognition methods work well and have their respective advantages. Then, both the statistical operators under PRPD mode and the chaotic characteristic quantities under CAPD mode are selected comprehensively as the input vectors of neural network, and the PD pattern recognition accuracy is thereby greatly improved.

Modeling the TrueBeam linac using a CAD to Geant4 geometry implementation: Dose and IAEA‐compliant phase space calculations

To create an accurate 6 MV Monte Carlo simulation phase space for the Varian TrueBeam treatment head geometry imported from CAD (computer aided design) without adjusting the input electron phase space parameters. GEANT4 v4.9.2.p01 was employed to simulate the 6 MV beam treatment head geometry of the Varian TrueBeam linac. The electron tracks in the linear accelerator were simulated with Parmela, and the obtained electron phase space was used as an input to the Monte Carlo beam transport and dose calculations. The geometry components are tessellated solids included in GEANT4 as GDML (generalized dynamic markup language) files obtained via STEP (standard for the exchange of product) export from Pro/Engineering, followed by STEP import in Fastrad, a STEP-GDML converter. The linac has a compact treatment head and the small space between the shielding collimator and the divergent are of the upper jaws forbids the implementation of a plane for storing the phase space. Instead, an IAEA (International Atomic Energy Agency) compliant phase space writer was implemented on a cylindrical surface. The simulation was run in parallel on a 1200 node Linux cluster. The 6 MV dose calculations were performed for field sizes varying from 4 x 4 to 40 x 40 cm2. The voxel size for the 60 x 60 x 40 cm3 water phantom was 4 x 4 x 4 mm3. For the 10 x 10 cm2 field, surface buildup calculations were performed using 4 x 4 x 2 mm3 voxels within 20 mm of the surface. For the depth dose curves, 98% of the calculated data points agree within 2% with the experimental measurements for depths between 2 and 40 cm. For depths between 5 and 30 cm, agreement within 1% is obtained for 99% (4 x 4), 95% (10 x 10), 94% (20 x 20 and 30 x 30), and 89% (40 x 40) of the data points, respectively. In the buildup region, the agreement is within 2%, except at 1 mm depth where the deviation is 5% for the 10 x 10 cm2 open field. For the lateral dose profiles, within the field size for fields up to 30 x 30 cm2, the agreement is within 2% for depths up to 10 cm. At 20 cm depth, the in-field maximum dose difference for the 30 x 30 cm2 open field is within 4%, while the smaller field sizes agree within 2%. Outside the field size, agreement within 1% of the maximum dose difference is obtained for all fields. The calculated output factors varied from 0.938 +/- 0.015 for the 4 x 4 cm2 field to 1.088 +/- 0.024 for the 40 x 40 cm2 field. Their agreement with the experimental output factors is within 1%. The authors have validated a GEANT4 simulated IAEA-compliant phase space of the TrueBeam linac for the 6 MV beam obtained using a high accuracy geometry implementation from CAD. These files are publicly available and can be used for further research.

Bulk density of small meteoroids

Aims. Here we report on precise metric and photometric observations of 107 optical meteors, which were simultaneously recorded at multiple stations using three different intensified video camera systems. The purpose is to estimate bulk meteoroid density, link small meteoroids to their parent bodies based on dynamical and physical density values expected for different small body populations, to better understand and explain the dynamical evolution of meteoroids after release from their parent bodies. Methods. The video systems used had image sizes ranging from 640 × 480 to 1360 × 1036 pixels, with pixel scales from 0.01 ◦ per pixel to 0.05 ◦ per pixel, and limiting meteor magnitudes ranging from Mv =+ 2.5 to +6.0. We find that 78% of our sample show noticeable deceleration, allowing more robust constraints to be placed on density estimates. The density of each meteoroid is estimated by simultaneously fitting the observed deceleration and lightcurve using a model based on thermal fragmentation, conservation of energy and momentum. The entire phase space of the model free parameters is explored for each event to find ranges of parameters which fit the observations within the measurement uncertainty. Results. (a) We have analysed our data by first associating each of our events with one of the five meteoroid classes. The average density of meteoroids whose orbits are asteroidal and chondritic (AC) is 4200 kg m −3 suggesting an asteroidal parentage, possibly related to the high-iron content population. Meteoroids with orbits belonging to Jupiter family comets (JFCs) have an average density of 3100 ± 300 kg m −3 . This high density is found for all meteoroids with JFC-like orbits and supports the notion that the refractory material reported from the Stardust measurements of 81P/Wild 2 dust is common among the broader JFC population. This high density is also the average bulk density for the 4 meteoroids with orbits belonging to the Ecliptic shower-type class (ES) also related to JFCs. Both categories we suggest are chondritic based on their high bulk density. Meteoroids of HT (Halley type) orbits have a minimum bulk density value of 360 +400 −900 kg m −3 . This is consistent with many previous works which suggest bulk cometary meteoroid density is low. SA (Sun-approaching)-type meteoroids show a density spread from 1000 kg m −3 to 4000 kg m −3 , reflecting multiple origins. (b) We found two different meteor showers in our sample: Perseids (10 meteoroids, ∼11% of our sample) with an average bulk density of 620 kg m −3 and Northern Iota Aquariids (4 meteoroids) with an average bulk density of 3200 kg m −3 , consistent with the notion that the NIA derive from 2P/Encke.

Spin Coherent State Representation of the Crow-Kimura and Eigen Models of Quasispecies Theory

We present a spin coherent state representation of the Crow-Kimura and Eigen models of biological evolution. We deal with quasispecies models where the fitness is a function of Hamming distances from one or more reference sequences. In the limit of large sequence length N, we find exact expressions for the mean fitness and magnetization of the asymptotic quasispecies distribution in symmetric fitness landscapes. The results are obtained by constructing a path integral for the propagator on the coset SU(2)/U(1) and taking the classical limit. The classical limit gives a Hamiltonian function on a circle for one reference sequence, and on the product of 2m−1 circles for m reference sequences. We apply our representation to study the Schuster-Swetina phenomena, where a wide lower peak is selected over a narrow higher peak. The quadratic landscape with two reference sequences is also analyzed specifically and we present the phase diagram on the mutation-fitness parameter phase space. Furthermore, we use our method to investigate more biologically relevant system, a model of escape from adaptive conflict through gene duplication, and find three different phases for the asymptotic population distribution.

Trans-Theta Logistics: A New Family of Population Growth Sigmoid Functions

Sigmoid functions have been applied in many areas to model self limited population growth. The most popular functions; General Logistic (GL), General von Bertalanffy (GV), and Gompertz (G), comprise a family of functions called Theta Logistic ([Formula: see text] L). Previously, we introduced a simple model of tumor cell population dynamics which provided a unifying foundation for these functions. In the model the total population (N) is divided into reproducing (P) and non-reproducing/quiescent (Q) sub-populations. The modes of the rate of change of ratio P/N was shown to produce GL, GV or G growth. We now generalize the population dynamics model and extend the possible modes of the P/N rate of change. We produce a new family of sigmoid growth functions, Trans-General Logistic (TGL), Trans-General von Bertalanffy (TGV) and Trans-Gompertz (TG)), which as a group we have named Trans-Theta Logistic (T [Formula: see text] L) since they exist when the [Formula: see text] L are translated from a two parameter into a three parameter phase space. Additionally, the model produces a new trigonometric based sigmoid (TS). The [Formula: see text] L sigmoids have an inflection point size fixed by a single parameter and an inflection age fixed by both of the defining parameters. T [Formula: see text] L and TS sigmoids have an inflection point size defined by two parameters in bounding relationships and inflection point age defined by three parameters (two bounded). While the Theta Logistic sigmoids provided flexibility in defining the inflection point size, the Trans-Theta Logistic sigmoids provide flexibility in defining the inflection point size and age. By matching the slopes at the inflection points we compare the range of values of inflection point age for T [Formula: see text] L versus [Formula: see text] L for model growth curves.

Intercomparison of cloud model simulations of Arctic mixed-phase boundary layer clouds observed during SHEBA/FIRE-ACE

An intercomparison of six cloud-resolving and large-eddy simulation models is presented. This case study is based on observations of a persistent mixed-phase boundary layer cloud gathered on 7 May, 1998 from the Surface Heat Budget of Arctic Ocean (SHEBA) and First ISCCP Regional Experiment - Arctic Cloud Experiment (FIRE-ACE). Ice nucleation is constrained in the simulations in a way that holds the ice crystal concentration approximately fixed, with two sets of sensitivity runs in addition to the baseline simulations utilizing different specified ice nucleus (IN) concentrations. All of the baseline and sensitivity simulations group into two distinct quasi-steady states associated with either persistent mixed-phase clouds or all-ice clouds after the first few hours of integration, implying the existence of multiple states for this case. These two states are associated with distinctly different microphysical, thermodynamic, and radiative characteristics. Most but not all of the models produce a persistent mixed-phase cloud qualitatively similar to observations using the baseline IN/crystal concentration, while small increases in the IN/crystal concentration generally lead to rapid glaciation and conversion to the all-ice state. Budget analysis indicates that larger ice deposition rates associated with increased IN/crystal concentrations have a limited direct impact on dissipation of liquid in these simulations. However, the impact of increased ice deposition is greatly enhanced by several interaction pathways that lead to an increased surface precipitation flux, weaker cloud top radiative cooling and cloud dynamics, and reduced vertical mixing, promoting rapid glaciation of the mixed-phase cloud for deposition rates in the cloud layer greater than about 122610 –5 gk g –1 s –1 for this case. These results indicate the critical importance of precipitation-radiative-dynamical interactions in simulating cloud phase, which have been neglected in previous fixed-dynamical parcel studies of the cloud phase parameter space. Large sensitivity to the IN/crystal concentration also suggests the need for improved understanding of ice nucleation and its parameterization in models.

Modelling molecule–surface interactions—an automated quantum-classical approach using a genetic algorithm

We present an automated and efficient method to develop force fields for molecule-surface interactions. A genetic algorithm (GA) is used to parameterise a classical force field so that the classical adsorption energy landscape of a molecule on a surface matches the corresponding landscape from density functional theory (DFT) calculations. The procedure performs a sophisticated search in the parameter phase space and converges very quickly. The method is capable of fitting a significant number of structures and corresponding adsorption energies. Water on a ZnO(0001) surface was chosen as a benchmark system but the method is implemented in a flexible way and can be applied to any system of interest. In the present case, pairwise Lennard Jones (LJ) and Coulomb potentials are used to describe the molecule-surface interactions. In the course of the fitting procedure, the LJ parameters are refined in order to reproduce the adsorption energy landscape. The classical model is capable of describing a wide range of energies, which is essential for a realistic description of a fluid-solid interface.

Global symplectic structure-preserving integrators for spinning compact binaries

This paper deals mainly with the application of the second-order symplectic implicit midpoint rule and its symmetric compositions to a post-Newtonian Hamiltonian formulation with canonical spin variables in relativistic compact binaries. The midpoint rule, as a basic algorithm, is directly used to integrate the completely canonical Hamiltonian system. On the other hand, there are symmetric composite methods based on a splitting of the Hamiltonian into two parts: the Newtonian part associated with a Kepler motion, and a perturbation part involving the orbital post-Newtonian and spin contributions, where the Kepler flow has an analytic solution and the perturbation can be calculated by the midpoint rule. An example is the second-order mixed leapfrog symplectic integrator with one stage integration of the perturbation flow and two semistage computations of the Kepler flow at every integration step. Also, higher-order composite methods such as the Forest-Ruth fourth-order symplectic integrator and its optimized algorithm are applicable. Various numerical tests including simulations of chaotic orbits show that the mixed leapfrog integrator is always superior to the midpoint rule in energy accuracy, while both of them are almost equivalent in computational efficiency. Particularly, the optimized fourth-order algorithm compared with the mixed leapfrog scheme provides good precision and needs no expensive additional computational time. As a result, it is worth performing a more detailed and careful examination of the dynamical structure of chaos and order in the parameter windows and phase space of the binary system.