Statistical physics of hard combinatorial optimization:Vertex cover problem

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomi＇al （NP）-complete combinatorial opti- mization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

Theoretical study on fusion dynamics and evaporation residue cross sections for superheavy elements

The nuclear dynamical deformation,the fusion probability and the evaporation residue(ER) cross sections for the synthesis of superheavy nuclei are studied with the di-nuclear system model and the related dynamical potential energy surface.The intrinsic energy and the maximum dynamical deformations for48Ca+248Cm are calculated.The effect of dynamical deformation on the potential energy surface and fusion is investigated.It is found that the dynamical deformation influences the potential energy surface and fusion probability significantly.The dependence of the fusion probability on the angular momentum is investigated.The ER cross sections for some superheavy nuclei in48Ca induced reactions are calculated and it is found that the theoretical results are in good agreement with the experimental results.

Theoretical studies on s RNA-mediated regulation in bacteria

Small RNA（sRNA）-mediated post-transcriptional regulation differs from protein-mediated regulation. Through basepairing, sRNA can regulate the target m RNA in a catalytic or stoichiometric manner. Some theoretical models were built for comparison of the protein-mediated and sRNA-mediated modes in the steady-state behaviors and noise properties. Many experiments demonstrated that a single sRNA can regulate several m RNAs, which causes crosstalk between the targets.Here, we focus on some models in which two target mRNAs are silenced by the same sRNA to discuss their crosstalk features. Additionally, the sequence-function relationship of sRNA and its role in the kinetic process of base-pairing have been highlighted in model building.

Constraining Equation of State of Dark Matter:Including Weak Gravitational Lensing

Usually the equation of state （EoS） of dark matter is zero when it is cold, however there exists the possibility of a （effective） nonzero EoS of dark matter due to its decay and interaction with dark energy. In this work, we try to constrain the EoS of dark matter/JAdm using the currently available cosmic observations which include the geometrical and dynamical measurements. For the geometrical measurements, the luminosity distance of type Ia supernovae, the angular diameter distance and comoving sound horizon from baryon acoustic oscillations and the cosmic microwave background radiation will be employed. The data points from the redshift-space distortion and weak gravitational lensing will be taken as dynamical measurements. Using the Markov chain Monte Carlomethod, we obtain a very tight constraint on the-EoS of dark matter：wdm=0.0000532 ＋0.000692＋0.00136＋0.00183 -0.000686-0.00136-0.00177.

Odd Systems in Deformed Relativistic Hartree Bogoliubov Theory in Continuum

In order to describe the exotic nuclear structure in unstable odd-A or odd-odd nuclei,the deformed relativistic Hartree Bogoliubov theory in continuum is extended to incorporate the blocking effect due to the odd nucleon.For a microscopic and self-consistent description of pairing correlations,continuum,deformation,blocking effects,and the extended spatial density distribution in exotic nuclei,the deformed relativistic Hartree Bogoliubov equations are solved in a Woods Saxon basis in which the radial wave functions have a proper asymptotic behavior at large r.The formalism and numerical details are provided.The code is checked by comparing the results with those of spherical relativistic continuum Hartree Bogoliubov theory in the nucleus 19O.The prolate deformed nucleus 15 C is studied by examining the neutron levels and density distributions.

Observation of the Superheavy Nuclide ^(271)Ds

With the recent commissioning of a gas-filled recoil separator at Institute of Modern Physics (IMP) in Lanzhou,the decay properties of 271Ds (Z =110) were studied via the 20sPb(64Ni,n) reaction at a beam energy of 313.3 MeV.Based on the separator coupled with a position sensitive silicon strip detector,we carried out the energy-position-time correlation measurements for the implanted nucleus and its subsequent decay α's.One α-decay chain for 271Ds was established.The α energy and decay time of the 27iDs nucleus were measured to be 10.644 MeV and 96.8ms,which are consistent with the values reported in the literature.

Systematics of a-preformation factors in closed-shell regions

The a-preformation factors of medium and heavy-mass nuclei are calculated by using the cluster-formation model.The obtained preformation factors of even–even,odd-A,and odd–odd nuclei consist in both magnitude and trend with the general features predicted by standard calculations.The variation of a clustering affected by the evolution of nuclear structure is observed from different behaviors of preformation factors.We typically analyze the variation of preformation factors in the closed-shell N =126 and Z =82 regions,and discuss in detail the structural effects on a-cluster formation.This work shows the strong correlation between a-preformation factors and the shell structure,which would be a useful reference for microscopic cluster-model calculations of a-decay half-lives.

Mechano-chemical selections of two competitive unfolding pathways of a single DNA i-motif

The DNA i-motif is a quadruplex structure formed in tandem cytosine-rich sequences in slightly acidic conditions. Besides being considered as a building block of DNA nano-devices, it may also play potential roles in regulating chromo- some stability and gene transcriptions. The stability of i-motif is crucial for these functions. In this work, we investigated the mechanical stability of a single i-motif formed in the human telomeric sequence 51-（CCCTAA）3CCC, which revealed a novel pH and loading rate-dependent bimodal unfolding force distribution. Although the cause of the bimodal unfolding force species is not clear, we proposed a phenomenological model involving a direct unfolding favored at lower loading rate or higher pH value, which is subject to competition with another unfolding pathway through a mechanically stable inter- mediate state whose nature is yet to be determined. Overall, the unique mechano-chemical responses of i-motif-provide a new perspective to its stability, which may be useful to guide designing new i-motif-based DNA mechanical nano-devices.

Protection-against-water-attack determined difference between strengths of backbone hydrogen bonds in kinesin＇s neck zipper region

Docking of the kinesin＇s neck linker （NL） to the motor domain is the key force-generation process of the kinesin. In this process, NL＇sβ10 portion forms four backbone hydrogen bonds （HBs） with the motor domain. These backbone hydrogen bonds show big differences in their effective strength. The origins of these strength differences are still unclear. Using molecular dynamics method, we investigate the stability of the backbone HBs in explicit water environment. We find that the strength differences of these backbone HBs mainly arise from their relationships with water molecules which are controlled by arranging the surrounding residue sidechains. The arrangement of the residues in the C-terminal part of /310 results in the existence of the water-attack channels around the backbone HBs in this region. Along these channels the water molecules can directly attack the backbone HBs and make these HBs relatively weak. In contrast, the backbone HB at the N-terminus ofβ 10 is protected by the surrounding hydrophobic and hydrophilic residues which cooperate positively with the central backbone HB and make this HB highly strong. The intimate relationship between the effective strength of protein backbone HB and water revealed here should be considered when performing mechanical analysis for protein conformational changes.

Tilted Axis Rotation of ^(57)Mn in Covariant Density Functional Theory

The self-consistent tilted axis cranking covariant density functional theory based on the point-coupling interaction is applied to investigate the tilted axis rotation in ^57 Mn. The observed data for band C are reproduced well with the assigned configuration eonfig 1. The shears mechanism for magnetic rotation is examined by investigating microscopically the orientation of angular momentum and the corresponding contributions. It is found that config 1 and config 3 correspond to a rotation of high-K character. Config 2 corresponds to a rotation of magnetic character. However, due to the presence of electromagnetic transition B（M1） and B（E2）, collective rotation plays an essential role in the competition with magnetic rotation.

Cosmic Constraints to the wCDM Model from Strong Gravitational Lensing

We study the cosmic constraint to the wCDM （cold dark matter with a constant equation of state w） model via 118 strong gravitational lensing systems which are compiled from SLA CS, BELLS, LSD and SL2S surveys, where the ratio between two angular diameter distances Dobs =DA（Zl, Zs ） / D A （ O, Zs ） is taken as a cosmic observable. To obtain this ratio, we adopt two strong tensing models： one is the singular isothermal sphere model （SIS） and the other one is the power-law density profile （PLP） model. Via the Markov chain Monte Carlo method, the posterior distribution of the cosmological model parameters space is obtained. The results show that the cosmological model parameters are not sensitive to the parameterized forms of the power-law index γ. Furthermore, the PLP model gives a relatively tighter constraint to the cosmological parameters than that of the SIS model. The predicted value of Ωm = 0.31＋0.44 -0.24 by the SIS model is compatible with that obtained by P1anck2015： Ωm = 0.313 ± 0.013. However, the value of Ωm =0.15＋0.13 -0.11 based on the PLP model is smaller and has 1.25σ tension with that obtained by Planck2015.

Nuclear dynamics induced by antiprotons

Reaction dynamics in collisions of antiprotons on nuclei is investigated within the Lanzhou quantum molecular dynamics model. The reaction channels of elastic scattering, annihilation, charge exchange and inelastic collisions of antiprotons on nucleons have been included in the model. Dynamics on particle production, in particular pions, kaons, antikaons and hyperons, is investigated in collisions of p on12 C,20Ne,40 Ca and181Ta from low to high incident momenta. It is found that the annihilations of p on nucleons are of importance to the dynamics of particle production in phase space. Hyperons are mainly produced via meson induced reactions on nucleons and strangeness exchange collisions, which lead to delayed emission in antiproton-nucleus collisions.

Saturated sodium chloride solution under an external static electric field: A molecular dynamics study

The behavior of saturated aqueous Na Cl solutions under a constant external electric field（E） was studied by molecular dynamics（MD） simulation. Our dynamic MD simulations indicated that the irreversible nucleation process towards crystallization is accelerated by a moderate E but retarded or even prohibited under a stronger E, which can be understood by the competition between self-diffusion and drift motion. The former increases with E, thereby accelerating the nucleation process, whereas the latter pulls oppositely charged ions apart under a stronger E, thereby decelerating nucleation.Additionally, our steady-state MD simulations indicated that a first-order phase transition occurs in saturated solutions at a certain threshold Ec. The magnitude of Ec increases with concentration because larger clusters form more easily when the solution is more concentrated and require a stronger E to dissociate.

Three-dimensional solitons in two-component Bose–Einstein condensates

We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R2 × S1 space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional （3D） skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time.

Schrdinger Equation of a Particle on a Rotating Curved Surface

We derive the Schr6dinger equation of a particle constrained to move on a rotating curved surface S. Using the thin-layer quantization scheme to confine the particle on S, and with a proper choice of gauge transformation for the wave function, we obtain the well-known geometric potentiM Vg and an additive Coriolis-induced geometric potential in the co-rotationM curvilinear coordinates. This novel effective potential, which is included in the surface Schr6dinger equation and is coupled with the mean curvature of S, contains an imaginary part in the general case which gives rise to a non-Hermitian surface Hamiltonian. We find that the non-Hermitian term vanishes when S is a minimal surface or a revolution surface which is axially symmetric around the rolling axis.

Skyrmion crystals in pseudo-spin-1/2 Bose–Einstein condensates

Exact two-dimensional solutions are constructed for the pseudo-spin-1/2 Bose-Einstein condensates, which are de- scribed by the coupled nonlinear Gross-Pitaevskii equations where the intra-and inter-species coupling constants are as- sumed to be equal. The equations are decoupled by means of re-combinations of the nonlinear terms of the hyperfine states according to the spatial dimensions. The stationary solutions form various spin textures which are identified as skyrmion crystals. In a special case, a crystal of skyrmion-anti-skyrmion pairs is formed in the soliton limit.

Specific Heat of a Unitary Fermi Gas Including Particle-Hole Fluctuation

We investigate the particle-hole fluctuation correction to the specific heat of an ultracold Fermi gas at unitarity within the framework of the non-self-consistent T-matrix approximation in the normal phase. We find good agreement between our theoretical predictions and the experimental data measured by the MIT group, apart from discrepancies near the transition temperature. At high temperature, our calculated specific heat has the tendency to approach the specific heat of the Boltzmann gas.

Formation and dissociation of protonated cytosine–cytosine base pairs in i-motifs by ab initio quantum chemical calculations

Formation and dissociation mechanisms of C-C＋ base pairs in acidic and alkaline environments are investigated, employing ab initio quantum chemical calculations. Our calculations suggest that, in an acidic environment, a cytosine monomer is first protonated and then dimerized with an unprotonated cytosine monomer to form a C-C＋ base pair; in an alkaline environment, a protonated cytosine dimer is first unprotonated and then dissociated into two cytosine monomers. In addition, the force for detaching a C-C＋ base pair was found to be inversely proportional to the distance between the two cytosine monomers. These results provide a microscopic mechanism to qualitatively explain the experimentally observed reversible formation and dissociation of i-motifs.

Quantum and semiclassical studies on photodetachment cross sections of H^- in a harmonic potential

The photodetachment cross section of H- in a linear harmonic oscillator potential is investigated. This system pro- vides a rare example that can be studied analytically by both quantum and semiclassical methods with some approxi- mations. The formulas of the cross section for different laser polarization directions are explicitly derived by both the traditional quantum approach and closed-orbit theory. In the traditional quantum approach, we calculate the cross sections in coordinate representation and momentum representation, and get the same formulas. We compare the quantum formulas with closed-orbit theory formulas, and find that when the detachment electron energy is larger than hco, where co is the frequency of the oscillator potential, the quantum results are shown to be in good agreement with the semiclassical results.

Covalent intermolecular interaction of the nitric oxide dimer (NO)_2

Covalent bonds arise from the overlap of the electronic clouds in the internucleus region, which is a pure quantum effect and cannot be obtained in any classical way. If the intermolecular interaction is of covalent character, the result from direct applications of classical simulation methods to the molecular system would be questionable. Here, we analyze the special intermolecular interaction between two NO molecules based on quantum chemical calculation. This weak intermolecular interaction, which is of covalent character, is responsible for the formation of the NO dimer,（NO）2, in its most stable conformation, a cis conformation. The natural bond orbital（NBO） analysis gives an intuitive illustration of the formation of the dimer bonding and antibonding orbitals concomitant with the breaking of the πbonds with bond order 0.5of the monomers. The dimer bonding is counteracted by partially filling the antibonding dimer orbital and the repulsion between those fully or nearly fully occupied nonbonding dimer orbitals that make the dimer binding rather weak. The direct molecular mechanics（MM） calculation with the UFF force fields predicts a trans conformation as the most stable state, which contradicts the result of quantum mechanics（QM）. The lesson from the investigation of this special system is that for the case where intermolecular interaction is of covalent character, a specific modification of the force fields of the molecular simulation method is necessary.