Nonlinear viscoelastic dynamics of nano-confined water

The viscoelastic dynamics of nano-confined water is studied by means of atomic force microscopy (AFM). We observe a nonlinear viscoelastic behavior remarkably similar to that widely observed in metastable complex fluids. We show that the origin of the measured nonlinear viscoelasticity in nano-confined water is a strain rate dependent relaxation time and slow dynamics. By measuring the viscoelastic modulus at different frequencies and strains, we find that the intrinsic relaxation time of nano-confined water is in the range 0.1-0.0001 s, orders of magnitude longer than that of bulk water, and comparable to the dielectric relaxation time measured in supercooled water at 170-210 K.Comment: 4 Figure

Strongly first order phase transition in the singlet fermionic dark matter model after LUX

We investigate an extension of the standard model (SM) with a singlet fermionic dark matter (DM) particle which interacts with the SM sector through a real singlet scalar. The presence of a new scalar provides the possibility of generating a strongly first order phase transition needed for electroweak baryogenesis. Taking into account the latest Higgs search results at the LHC and the upper limits from the DM direct detection experiments especially that from the LUX experiment, and combining the constraints from the LEP experiment and the electroweak precision test, we explore the parameter space of this model which can lead to the strongly first order phase transition. Both the tree- and loop-level barriers are included in the calculations. We find that the allowed mass of the second Higgs particle is in the range $\sim 30-350\hbox{ GeV}$. The allowed mixing angle $\alpha$ between the SM-like Higgs particle and the second Higgs particle is constrained to $\alpha \lesssim 28^{\circ}$. The DM particle mass is predicted to be in the range $\sim 15-350\hbox{ GeV}$. The future XENON1T experiment can rule out a significant proportion of the parameter space of this model. The constraint can be relaxed only when the mass of the SM-like Higgs particle is degenerate with that of the second Higgs particle, or the mixing angle is small enough.Comment: 37 pages, 9 figures; v4: the version accepted by JHE

Applications of degree estimate for subalgebras

Let $K$ be a field of positive characteristic and $K$ be the free algebra of rank two over $K$. Based on the degree estimate done by Y.-C. Li and J.-T. Yu, we extend the results of S.J. Gong and J.T. Yu's results: (1) An element $p(x,y)\in K$ is a test element if and only if $p(x,y)$ does not belong to any proper retract of $K$; (2) Every endomorphism preserving the automorphic orbit of a nonconstant element of $K$ is an automorphism; (3) If there exists some injective endomorphism $\phi$ of $K$ such that $\phi(p(x,y))=x$ where $p(x,y)\in K$, then $p(x,y)$ is a coordinate. And we reprove that all the automorphisms of $K$ are tame. Moreover, we also give counterexamples for two conjectures established by Leonid Makar-Limanov, V. Drensky and J.-T. Yu in the positive characteristic case.Comment: 12 page

Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.National Science Foundation (IIS 0308213, IIS 0329009, CNS 0202067

An improved chaos method for monitoring the depth of anaesthesia

This paper proposed a new method to monitor the depth of anaesthesia (DoA) by modifying the Hurst parameters in Chaos method. Two new indices (CDoA and CsDoA) are proposed to estimate the anaesthesia states of patients. In order to reduce the fluctuation of CDoA and CsDoA trends, the Chaos and Modified Detrended Average methods (C-MDMA) are combined together. Compared with Bispectrum (BIS) index, CDoA, the CsDoA and C-MDMA trends are close to the BIS trend in the whole scale from 100 to 0 with a full recording time