Enhanced sampling in generalized ensemble with large gap of sampling parameter: case study in temperature space random walk

We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes a canonical ensemble such as the reciprocal temperature $\beta$ or any variable that the Hamiltonian explicitly depends on. The partition function is determined by minimizing the difference of the thermal conjugates of $\lambda$ (the energy in the case of $\lambda=\beta$), defined as the difference between the value from the dynamically updated derivatives of the partition function and the value directly measured from simulation. Higher-order derivatives of the partition function are included to enhance the Brownian motion in the $\lambda$ space. The method is much less sensitive to the system size, and the size of $\lambda$ window than other methods. On the two dimensional Ising model, it is shown that the method asymptotically converges the partition function, and the error of the logarithm of the partition function is much smaller than the algorithm using the Wang-Landau recursive scheme. The method is also applied to off-lattice model proteins, the $AB$ models, in which cases many low energy states are found in different models.Comment: 7 pages, 3 figure

Estimating statistical distributions using an integral identity

We present an identity for an unbiased estimate of a general statistical distribution. The identity computes the distribution density from dividing a histogram sum over a local window by a correction factor from a mean-force integral, and the mean force can be evaluated as a configuration average. We show that the optimal window size is roughly the inverse of the local mean-force fluctuation. The new identity offers a more robust and precise estimate than a previous one by Adib and Jarzynski [J. Chem. Phys. 122, 014114, (2005)]. It also allows a straightforward generalization to an arbitrary ensemble and a joint distribution of multiple variables. Particularly we derive a mean-force enhanced version of the weighted histogram analysis method (WHAM). The method can be used to improve distributions computed from molecular simulations. We illustrate the use in computing a potential energy distribution, a volume distribution in a constant-pressure ensemble, a radial distribution function and a joint distribution of amino acid backbone dihedral angles.Comment: 45 pages, 7 figures, simplified derivation, a more general mean-force formula, add discussions to the window size, add extensions to WHAM, and 2d distribution

Spin polarized nematic order, quantum valley Hall states, and field tunable topological transitions in twisted multilayer graphene systems

We theoretically study the correlated insulator states, quantum anomalous Hall (QAH) states, and field-induced topological transitions between different correlated states in twisted multilayer graphene systems. Taking twisted bilayer-monolayer graphene and twisted double-bilayer graphene as examples, we show that both systems stay in spin polarized, $C_{3z}$-broken insulator states with zero Chern number at 1/2 filling of the flat bands under finite displacement fields. In some cases these spin polarized, nematic insulator states are in the quantum valley Hall phase by virtue of the nontrivial band topology of the systems. The spin polarized insulator state is quasi-degenerate with the valley polarized state when only the dominant intra-valley Coulomb interactions are included. Such quasi-degeneracy can be split by atomic on-site interactions such that the spin polarized, nematic state become the unique ground state. Such a scenario applies to various twisted multilayer graphene systems at 1/2 filling, thus can be considered as a universal mechanism. Moreover, under vertical magnetic fields, the giant orbital Zeeman splittings in twisited multilayer graphene systems compete with the atomic Hubbard interactions, which can drive transitions from spin polarized zero-Chern-number states to valley-polarized QAH states with small onset magnetic fields.Comment: 5+17 page

INTERVENTION EFFECT OF RESEARCH-BASED PSYCHOLOGICAL COUNSELING ON ADOLESCENTS’ MENTAL HEALTH DURING THE COVID-19 EPIDEMIC

Background: This study aims to explore the intervention effect of research-based psychological counseling on adolescents’ mental health during the COVID-19 epidemic. Subjects and methods: From May to July 2020, 160 young students were selected from 5 middle schools in Shandong Province of China as the participants of this study and were randomly divided into the experiment and control groups with 80 members in each group. The routine in-campus education of health knowledge related to the epidemic was conducted in the control group, while the experiment group received both the routine education and the intervention of psychological counseling in combination with outdoor exercise. Results: No significant difference exists between the experiment and control groups (P>0.05) before the intervention, but the scores of the experiment group in anxiety and depression are lower than those of the control group (P<0.05) after the intervention; the PSQI score of the experiment group is significantly lower after the intervention, suggesting that the effect on the experiment group is better than the control group (P<0.05); the scores of the experiment group in psychological resilience and its 5 dimensions are higher than those of the control group (P<0.05). Conclusions: This intervention model has a good intervention effect on adolescents’ mental health and psychological resilience. At the same time, this study enlightens the introduction of the research-based psychological counseling model when helping adolescents solve mental health problems and highlights the important role of exercise in improving adolescents’ mental health and psychological resilience