Abstract:
The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such situation, we provide a method of reducing stiffness of the stochastic protein kinetic equation by means of a kind of variable transformation. Theoretical and numerical analysis show effectiveness of this method. Its generalization to a more general class of stochastic differential equation models is also discussed.

Abstract:
We find that the density dependence of the glass transition temperature of Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) systems can be predicted from properties of the zero-temperature ($T=0$) glasses. Below a crossover density $\rho_s$, LJ and WCA glasses show different structures, leading to different vibrational properties and consequently making LJ glasses more stable with higher glass transition temperatures than WCA ones. Above $\rho_s$, structural and vibrational quantities of the $T=0$ glasses show scaling collapse. From scaling relations and dimensional analysis, we predict a density scaling of the glass transition temperature, in excellent agreement with simulation results. We also propose an empirical expression of the glass transition temperature using structural and vibrational properties of the $T=0$ glasses, which works well over a wide range of densities.

Abstract:
During the jamming of thermal colloids, the first peak of the pair distribution function shows a maximum height $g_1^{\rm max}$. We find that $g_1^{\rm max}$ is accompanied by significant change of material properties and thus signifies the transition from unjammed to jammed glasses. The scaling laws at $g_1^{\rm max}$ lead to scaling collapse of structural and thermodynamic quantities, indicating the criticality of the T=0 jamming transition. The physical significance of $g_1^{\rm max}$ is highlighted by its coincidence with the equality of the kinetic and potential energy and the maximum fluctuation of the coordination number. In jammed glasses, we find the strong coupling between the isostaticity and flattening of the density of vibrational states at the isostatic temperature scaled well with the compression.

Abstract:
In this paper, a systematic approach of constructing modified equations for weak stochastic symplectic methods of stochastic Hamiltonian systems is given via using the generating functions of the stochastic symplectic methods. This approach is valid for stochastic Hamiltonian systems with either additive noises or half-multiplicative noises, and we prove that the modified equation of the weak stochastic symplectic methods are perturbed stochastic Hamiltonian systems of the original systems, which reveals in certain sense the reason for the good long time numerical behavior of stochastic symplectic methods.

Abstract:
In this article, we introduce a kind of numerical schemes, based on Pad$\acute{e}$ approximation, for two stochastic Hamiltonian systems which are treated separately. For the linear stochastic Hamiltonian systems, it is shown that the applied Pad$\acute e$ approximations $P_{(k,k)}$ give numerical solutions that inherit the symplecticity and the proposed numerical schemes based on $P_{(r,s)}$ are of mean-square order $\frac{r+s}{2}$ under appropriate conditions. In case of the special stochastic Hamiltonian systems with additive noises, the numerical method using two kinds of Pad$\acute e$ approximation $P_{(\hat r,\hat s)}$ and $P_{(\check r,\check s)}$ has mean-square order $\check r+\check s+1$ when $\hat r+\hat s=\check r+\check s+2$. Moreover, the numerical solution is symplectic if $\hat r=\hat s$.

Abstract:
A complex of phycobiliproteins, containing phycoerythrocyanin (PEC), C-phycovyanin (C-PC) and allo-phycocyanin (APC) as well as some linker polypeptides, was reconstructed. The absorption and fluoreacence spectra of the complex were compared with those of native phycobilisomes (PBS) and the phycobiliproteins. Based on the measured data, it can be concluded that the complex can be taken as a model of PBS and is an entirely functional group for excitation energy transfer step by step from peripheral PEC to APC. The single terminal emitter feature of the complex makes it favorable for clarifying energy transfer pathways and the kinetics in comparison with native PBS. Further research is carried on in the lab.

Abstract:
A complex of phycobiliproteins, containing phycoerythrocyanin (PEC), C-phycovyanin (C-PC) and allo-phycocyanin (APC) as well as some linker polypeptides, was reconstructed. The absorption and fluoreacence spectra of the complex were compared with those of native phycobilisomes (PBS) and the phycobiliproteins. Based on the measured data, it can be concluded that the complex can be taken as a model of PBS and is an entirely functional group for excitation energy transfer step by step from peripheral PEC to APC. The single terminal emitter feature of the complex makes it favorable for clarifying energy transfer pathways and the kinetics in comparison with native PBS. Further research is carried on in the lab.

Abstract:
In molecular dynamics simulations of soft glass-formers interacting via repulsions, we find that the glass transition temperature, dynamical heterogeneity, and glass fragility reach their maxima at the same crossover pressure $P_d$. Our analysis of the zero-temperature jammed states indicates that states at $P_d$ have the highest bond orientational order with the largest spatial fluctuation. Correspondingly, the low-frequency normal modes of vibration are the least localized and the average potential energy barrier along these modes are the highest for jammed states in the vicinity of $P_d$. The reentrant glass transition and dynamics of supercooled liquids are thus predictable by these structural and vibrational precursors in the zero-temperature jammed states.