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Nowadays developing fluorescent probes that are cheaper, nontoxic, robust and easy to use for determination of heavy metal ions with high selectivity and sensitivity is still an ongoing challenge. In this paper, inherently fluorescent aminated polystyrene microspheres (PS-NH2) were fabricated from cross-linked polystyrene (PS) microspheres through acetylation, oximation and reduction, which can serve as a selective and sensitive fluorescence (FL) probe for the determination of chromium (VI) (Cr(VI)) and mercury (II) (Hg2+) ions. The photostability, selectivity and sensitivity of the fluorescent PS-NH2 microspheres were studied in detail. The feasibility of PS-NH2 microspheres as a fluorescent probe was conducted by determining Cr(VI) or Hg2+ in real water samples. Results revealed that no photoleaching or leaking issues were observed on PS-NH2 microspheres. The fluorescent probe could analyze Cr(VI) and Hg2+ separately in water samples with high sensitivity and good accuracy in the range of 0.01–1 μM. The detection limits for Cr(VI) and Hg2+ were 9.1 nM and 9.9 nM, respectively. Additionally, two possible FL quenching mechanisms were proposed for Cr(VI) and Hg2+. This work provides a new platform for accurate determination of Cr(VI) and Hg2+ in environmental fields.

The spin-1/2 antiferromagnetic Heisenberg systems are studied on three typical diamond-type hierarchical lattices (systems A, B and C) with fractal dimensions 1.63, 2 and 2.58, respectively, and the phase diagrams, critical phenomena and quantum correlations are calculated by a combination of the equivalent transformation and real-space renormalization group methods. We find that there exist a reentrant behavior for system A and a finite temperature transition in the isotropic Heisenberg limit for system C (not for system B). Unlike the ferromagnetic case, the Neel temperatures of antiferromagnetic systems A and B are inversely proportional to ln(Delta_c-Delta) (when Delta->Delta_c) and ln Delta (when Delta->0), respectively. And we also find that there is a turning point of quantum correlation in the isotropic Heisenberg limit Delta=0 where there is a peak of the contour and no matter how large the size of system is, quantum correlation will change to zero in the Ising limit for the three systems. The quantum correlation decreases with the increase of lattice size L and it is almost zero when L>=30 for system A, and for systems B and C, they still exist when L is larger than that of system A. Moreover, as an example, we discuss the error of result in system A, which is induced by the noncommutativity., 28 pages, 13 figures

The diffusion of passing over the saddle point of a three-dimensional quadric potential energy surface was studied by analytically solving a set of coupled generalized Langevin equations. An accurate expression of the passing probability was obtained. The effect of the coupling between different degrees of freedom which is represented by the off-diagonal elements of the inertia, friction and potential-curvature tensors was analysed in detail. It is found that some of the coupling have great influence on the diffusion process, while others not. The combination of them results in an optimal injecting direction of the diffusing particles, revealing an optimal three-dimensional diffusion path.

Quantum entanglement and correlations in the spin-1 Heisenberg chain with single-ion anisotropy are investigated using the quantum renormalization group method. Negativity and quantum discord (QD) are calculated with various anisotropy parameters $\bigtriangleup$ and single-ion anisotropy parameters $D$. We focus on the relations between two abovementioned physical quantities and on transitions between the N\'eel, Haldane, and Large-D phases. It is found that both negativity and QD exhibit step-like patterns in different phases as the size of the system increases. Interestingly, the single-ion anisotropy parameter $D$, which can be modulated using nuclear electric resonance (2020 \textit{Nature} \textbf{579} 205), plays an important role in tuning the quantum phase transition (QPT) of the system. Both the first partial derivative of the negativity and quantum discord with respect to $D$ or $\bigtriangleup$ exhibit nonanalytic behavior at the phase transition points, which corresponds directly to the divergence of the correlation length. The quantum correlation critical exponents derived from negativity and QD are equal, and are the reciprocal of the correlation length exponent at each critical point. This work extends the application of quantum entanglement and correlations as tools for depicting QPTs in spin-1 systems., Comment: 28 pages, 17 figures

Employing the correlation matrix technique, the spatial distribution of thermal energy in two-dimensional triangular lattices in equilibrium, interacting with linear springs, is studied. It is found that the spatial distribution of thermal energy varies with the included angle of the springs. In addition, the average thermal energy of the longer springs is lower. Springs with different included angle and length will lead to an inhomogeneous spatial distribution of thermal energy. This suggests that the spatial distribution of thermal energy is affected by the geometrical structure of the system: the more asymmetric the geometrical structure of the system is, the more inhomogeneous is the spatial distribution of thermal energy.

In this manuscript we investigate the one-dimensional anisotropic XY model with ferromagnetic and antiferromagnetic interactions, which gives more interesting phase diagrams and dynamic critical behaviors. By using quantum renormalization-group method, we find that there are three phases in the system: antiferromagnetic Ising phase ordered in "x direction", spin-fluid phase and ferromagnetic Ising phase ordered in "y direction". In order to study the dynamical critical behaviors of the system, two quantum quenching methods are used. In both cases, the concurrence, a measure of entanglement, oscillates periodically over time. We show that the periods are the same and can be used as a new order parameter for quantum phase transitions. For further discussion, we derive the scaling exponent, {\theta}, and correlation length exponent, {\nu}, from the scaling behavior of the evolution period., Comment: 15 pages,6 figures

The dynamics of the random Ising spin chain in coexisting transverse and longitudinal magnetic fields is studied by the recursion method. Both the spin autocorrelation function and its spectral density are investigated by numerical calculations. It is found that system’s dynamical behaviors depend on the deviation σ J of the random exchange coupling between nearest-neighbor spins and the ratio r l t of the longitudinal and the transverse fields: (i) For r l t = 0 , the system undergoes two crossovers from N independent spins precessing about the transverse magnetic field to a collective-mode behavior, and then to a central-peak behavior as σ J increases. (ii) For r l t ≠ 0 , the system may exhibit a coexistence behavior of a collective-mode one and a central-peak one. When σ J is small (or large enough), system undergoes a crossover from a coexistence behavior (or a disordered behavior) to a central-peak behavior as r l t increases. (iii) Increasing σ J depresses effects of both the transverse and the longitudinal magnetic fields. (iv) Quantum random Ising chain in coexisting magnetic fields may exhibit under-damping and critical-damping characteristics simultaneously. These results indicate that changing the external magnetic fields may control and manipulate the dynamics of the random Ising chain.

Commercially available polystyrene (PS) fluorescent microspheres are widely used in biological field for tracing, in vivo imaging and calibration of flow cytometry, among other applications. However, these particles do suffer from some drawbacks such as the leakage and photobleaching of organic dyes within them. In the present study, inherently fluorescent properties of PS based microspheres have been explored for the first time. Here we find that a simple chloromethylation reaction endows the polystyrene particles with inherent fluorescence without any subsequent conjugation of an external fluorophore. A possible mechanism for fluorescence is elucidated by synthesizing and investigating p-ethylbenzyl chloride, a compound with similar structure. Significantly, no photobleaching or leaking issues were observed owing to the stable structure of the microspheres. Chloromethylated PS (CMPS) microspheres can keep their perpetual blue fluorescence even in dry powder state making them attractive as a potential coating material. Furthermore, the chloromethyl groups on CMPS microspheres make them very convenient for further functionalization. Poly(ethylene glycol) (PEG) grafted microspheres showed good biocompatibility and negligible cytotoxicity, and could be used to image intracellular Fe3+ due to the selective fluorescence quenching effect of aqueous Fe3+ in cytoplasm.

A theory of coherent resonant energy transfer with initial system-bath correlations [Qin et al., Phys. Rev. A 99, 032111 (2019)] is extended for a coherent initial system condition, which is a linear superposition of donor and acceptor excitations, and is more general and actual in many respects. The nonequilibrium bath state, containing initial system-bath correlations, is expanded in powers of coupling strength within the polaron formalism of second-order time-convolutionless quantum master equation. Detailed expressions for both homogeneous and inhomogeneous terms are derived and calculations are performed under the assumption of super-Ohmic spectral densities where the case of common bath modes is also included. Numerical results indicate that, for certain initial system conditions, the nonequilibrium due to the initial system-bath correlations brings about larger amplitude of population oscillation. And the initial system condition is of crucial importance in determining whether the initial system-bath correlations would play a significant role in the transfer dynamics. We identify a sensitive window in which the transfer dynamics is especially vulnerable to the bath such that there exists a greatly obvious difference between the dynamics with and without initial correlations. Besides, the system-bath coupling strength, the evolution time, and the nature of common bath modes are also shown to contribute to these effects. Rate equations based on F\"orster-Dexter energy transfer theory are derived for comparison.

In order to study the entanglement properties of mixed-spin systems, taking Negativity as a measure of quantum entanglement, it is studied in (1/2, 1) mixed-spin XY systems. It is found that both ferromagnetic or antiferromagnetic cases, the Negativity of systems decreases with increasing temperature and finally changes to zero smoothly. An interesting phenomenon is that the temperature T 0 (defined as the characteristic temperature) at which the Negativity becomes zero is low when the value of the crystal field parameter D is large. The relation between the thermal entanglement( T → 0 ) and ground-state entanglement with two and three sites is studied, respectively. It is also found that the mixed-state entanglement and the thermal entanglement at T → 0 can be well corresponding in both systems studied; but the Negativity in pure state and that in mixed state are quite different in the system with two sites.

Permanent polysaccharide coating on gigaporous polystyrene (PS) microspheres was achieved through direct chemical grafting of dextran via a facile method, minimizing nonspecific adsorption of proteins and providing easily derivatizable groups on microspheres. Chloroacetylated PS microspheres (PS-Cl) were first developed through acetylation, and hydrophilic dextran was directly grafted to hydrophobic PS-Cl via a Williamson reaction (PS-Dex). The homogeneous side-bound dextran coating has the advantage of masking the hydrophobic surface of the PS microspheres, while maintains their original gigaporous structure. After grafting, the hydrophobic surface of the PS microspheres was effectively masked, and nonspecific protein adsorption was greatly reduced. Moreover, the hydroxyl-rich coating can be easily derivatized through classical chemical methods. A column packed with PS-Dex presented both good permeability and mechanical strength at high flow velocities of up to 3612 cm/h. These results implied that PS-Dex should be an ideal matrix for high-speed protein chromatography. POLYM. ENG. SCI., 2016. © 2016 Society of Plastics Engineers

The quantum entanglement and quantum phase transition of the transverse-field Ising model on a two-dimensional square lattice were investigated by applying the quantum renormalization group method. The quantum critical point (QCP) and the correlation length exponent, ν , were obtained. By taking the concurrence as a measure of entanglement, the entanglement between spin blocks near the QCP is calculated as the size of the system becomes large. The entanglement reaches a maximum close to QCP, and can exist in a small range around QCP just at the limit of thermodynamics. The nonanalytic behavior of the derivative of the entanglement with the external field shows that the system undergoes a second order quantum phase transition from a ferromagnetic phase to a paramagnetic phase. The finite-size scaling behavior of the entanglement is described, and the relationship between the entanglement exponent, θ , the correlation length exponent, ν , and the dimension of the system d is also found, i.e., θ = 1 / ( ν d ) .

Quantum phase transitions (QPT) in the infinite-long Ising-XXZ diamond chain, characterized by the quantum correlations measured by the quantum discord (QD) and the entanglement of formation (EoF), are investigated exactly by the transfer-matrix method. QD and EoF are calculated numerically for different values of anisotropy parameter, external magnetic field, and temperature. It is found that the singularity of QD and EoF around quantum critical points (QCPs), especially that of their first derivatives may not only spotlight the QCPs but also depict the QPT from unentangled state in ferrimagnetic phase to an entangled state in frustrated phase or to an entangled state in the ferrimagnetic phase.

Adopting concurrence as entanglement measure, we study entanglement and quantum phase transition of the Ising spin systems on the triangular lattice and Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski fractal lattices by using the quantum renormalization-group method. It is found that the ground-state entanglement between two spins (or spin blocks) depends on the following factors: the size of system, the magnetic field, the exchange coupling, and the structure of lattice. As the size of the system becomes large, (a) the range of the magnetic field, in which the entanglement exists, contracts gradually and focuses on the critical point; and (b) the first derivative of entanglement shows singular behavior, and its maximum or minimum is approaching to the critical point gradually. The scaling behaviors of entanglement on the different lattices are similar but the scaling relations are diverse. For the triangular lattice, the space dimensionality determines the scaling relationship between the critical exponent of the entanglement and the critical exponent correlation length. However, for fractal lattices, it is the fractal dimensionality but not the space one to determine this relationship.

In this article we report the preparation of a graphene/room temperature vulcanized (RTV) silicone rubber composite. Both the morphology and the properties of the composite were investigated in detail. SEM study shows that the composite has a microphase-separated structure. PDMS is the continuous phase, and the randomly distributed graphene nanosheets and a few aggregates are the dispersed phase. However, DSC curves of the composites have only one glass transition temperature (Tg). With the increases of the graphene content, Tg increases and Tm decreases. Mechanical properties tests show that the addition of graphene has a significant reinforcement effect on silicone rubber. The tensile strength is 0.37MPa with graphene mass fraction at 1.0%, which increases 76% compared with that of pure silicone rubber parallel sample.

To deal with the health performance degradation of electronic equipment, a new health evaluation method based on improved manifold learning algorithm and HMM is proposed in this paper. Firstly, according to SNPP algorithm KSUNPP is proposed by introducing an uncorrelated constraint and kernel method, and the improved algorithm is used for feature extraction. Secondly, the health evaluation model of electronic equipment is constructed. Then, by calculating KL distance which can measure the fault degradation, the model can evaluate the health performance degradation. Finally, the proposed method is applied to health evaluation of electronic equipment which belongs to one type of missile, experiment results demonstrate that the method is effective.

The geometrically frustrated spin-1 Blume-Capel model on an infinite sawtooth chain is exactly solved by the transfer matrix method. The magnetization, ground-state phase diagram, magnetocaloric properties, and specific heat of the system are investigated. The results indicate that: (i) Magnetization plateaus appear at zero temperature. Their number depends on the sign of the crystal field D. For D≥0 there are two magnetization plateaus; however, for D

Dual thermo- and pH-responsive chromatography has been proposed using poly(N-isopropylacrylamide-co-butyl methacrylate-co-N,N-dimethylaminopropyl acrylamide) (P(NIPAM-co-BMA-co-DMAPAAM)) brushes grafted gigaporous polystyrene microspheres (GPM) as matrix. Atom transfer radical polymerization (ATRP) initiator was first coupled onto GPM through Friedel-Crafts acylation with 2-bromoisobutyryl bromide. The dual-responsive polymer brushes were then grafted onto GPM via surface-initiated ATRP. The surface composition, gigaporous structure, protein adsorption and dual-responsive chromatographic properties of the matrix (GPM-P(NIPAM-co-BMA-co-DMAPAAM) were characterized in detail. Results showed that GPM were successfully grafted with thermoresponsive cationic polymer brushes and that the gigaporous structure was well maintained. A column packed with GPM-P(NIPAM-co-BMA-co-DMAPAAM presented low backpressure, good permeability and appreciable thermo-responsibility. By changing pH of the mobile phase and temperature of the column in turn, the column can separate three model proteins at the mobile phase velocity up to 2528cmh(-1). A separation mechanism of this matrix was also proposed. All results indicate that the dual thermo- and pH-responsive chromatography matrix has great potentials in 'green' high-speed protein chromatography.

We investigate the quantum correlation measured by quantum discord (QD) for thermalized ferromagnetic Heisenberg spin systems in one-dimensional chains and on fractal lattices using the decimation renormalization group approach. It is found that the QD between two non-nearest-neighbor end spins exhibits some interesting behaviors which depend on the anisotropic parameter Δ, the temperature T, and the size of system L. With increasing Δ continuously, the QD possesses a cuspate change at Δ = 0 which is a critical point of quantum phase transition (QPT). There presents the “regrowth” tendency of QD with increasing T at Δ 0. As the size of the system L becomes large, there still exists considerable thermal QD between long-distance end sites in spin chains and on the fractal lattices even at unentangled states, and the long-distance QD can spotlight the presence of QPT. The robustness of QD on the diamond-type hierarchical lattices is stronger than that in spin chains and Koch curves, which indicates that the fractal can affect the behaviors of quantum correlation.

We investigate thermal entanglement between two non-nearest-neighbor sites in ferromagnetic Heisenberg chain and on fractal lattices by means of the decimation renormalization-group (RG) method. It is found that the entanglement decreases with increasing temperature and it disappears beyond a critical value T_{c}. Thermal entanglement at a certain temperature first increases with the increase of the anisotropy parameter {\Delta} and then decreases sharply to zero when {\Delta} is close to the isotropic point. We also show how the entanglement evolves as the size of the system L becomes large via the RG method. As L increases, for the spin chain and Koch curve the entanglement between two terminal spins is fragile and vanishes when L\geq17, but for two kinds of diamond-type hierarchical (DH) lattices the entanglement is rather robust and can exist even when L becomes very large. Our result indicates that the special fractal structure can affect the change of entanglement with system size., Comment: 10 pages, 6 figures

The paper discusses the design and the implementation of a general-purpose robots simulation system, ZDRSSS, which can simulates various types of industrial robots in real time. ZDRSSS focuses on the simulation of robots' kinematics, mechanism and trajectory planning, on the test of forward and inverse kinematic algorithms, and on the, test of forward and inverse differential kinematic algorithms. The system works with man machine communication. In addition to common interactive methods,ZDRSSS is equipped with a graphic Interactive system. This is a 3D graphic processing system. It can produce the 3D continuously changed pictures of robots and of their work environment. The geometric model creator consists of 12 classes of solids in order to set up the geometric models of robots. The animated cartoon of the system vividly describes the kinematic features of robots. In ZDRSSS,many new ideas and methods are explored, such as design of robot mathematical model and robot geometric model, display of animated cartoon, back-screen management, fast picture generating algorithm based on the concept called fundamental graphic element transformation, and all optimal plotting algorithmg. Supported by IBM-PC basic system with 8087, ZDRSSS is programmed in C languake ( 13000 lines) and assembly language (3000 lines).