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In multi-label classification, machine learning encounters the challenge of domain generalization when handling tasks with distributions differing from the training data. Existing approaches primarily focus on vision object recognition and neglect the integration of natural language. Recent advancements in vision-language pre-training leverage supervision from extensive visual-language pairs, enabling learning across diverse domains and enhancing recognition in multi-modal scenarios. However, these approaches face limitations in loss function utilization, generality across backbones, and class-aware visual fusion. This paper proposes solutions to these limitations by inferring the actual loss, broadening evaluations to larger vision-language backbones, and introducing Mixup-CLIPood, which incorporates a novel mix-up loss for enhanced class-aware visual fusion. Our method demonstrates superior performance in domain generalization across multiple datasets., Comment: 6 pages, 2 figures. This is a preprint version of the article. The final version will be published in the proceedings of the IEEE conference

This systematic literature review comprehensively examines the application of Large Language Models (LLMs) in forecasting and anomaly detection, highlighting the current state of research, inherent challenges, and prospective future directions. LLMs have demonstrated significant potential in parsing and analyzing extensive datasets to identify patterns, predict future events, and detect anomalous behavior across various domains. However, this review identifies several critical challenges that impede their broader adoption and effectiveness, including the reliance on vast historical datasets, issues with generalizability across different contexts, the phenomenon of model hallucinations, limitations within the models' knowledge boundaries, and the substantial computational resources required. Through detailed analysis, this review discusses potential solutions and strategies to overcome these obstacles, such as integrating multimodal data, advancements in learning methodologies, and emphasizing model explainability and computational efficiency. Moreover, this review outlines critical trends that are likely to shape the evolution of LLMs in these fields, including the push toward real-time processing, the importance of sustainable modeling practices, and the value of interdisciplinary collaboration. Conclusively, this review underscores the transformative impact LLMs could have on forecasting and anomaly detection while emphasizing the need for continuous innovation, ethical considerations, and practical solutions to realize their full potential.

It is necessary to study the kinematics of landslide prior to its failure for accurately estimating the time of landslide instability. Based on a spring block model, considering the Dieterich Ruina's friction, the kinematic displacement and velocity of landslide along the slip surface are analyzed under quasistatic approximation. A algebraic relationship including three parameters between the displacement (or velocity) and time is obtained, and then applied to two typical landslides: Vaiont in Italy, and Maoxian in China. The results show that the proposed spring block friction model can well describe the kinematic data of landslides before their failure. If the effective data of displacement can be obtained to determine the three parameters above, this simple physical model could be used to estimate the time of landslide instability. This spring block friction model also provides clear physical basis for the usual inverse velocity method of the landslide warning, the stick slip of some landslides, and the scaling relationship between the numbers of the landslides and their volume., Comment: 16 pages; 7 figures; 1 Table

We demonstrate a distributed atomic clocks network between Shanghai Institute of Optics and fine Mechanics (SIOM) and Shanghai Institute of Measurement and Test (SIMT). The frequency signals from three different clocks transfer in one fiber link and four clocks can have comparison in two different labs.By comparing the results of the comparison between the two labs, it was found that the consistency of the frequency signal is on the order of lower than 1E-15. And we also achieve consistency between two locations at the E-15 level of frequency reporting. This scheme can achieve distributed time counting and frequency dissemination of remote atomic clocks, which is a new exploration of the future time keeping laboratory mode., Comment: 11 pages, 7 figures

In this paper, we prove a large deviation principle for the empirical measures of a system of weakly interacting diffusion with reflection. We adopt the weak convergence approach. To make this approach work, we show that the sequence of empirical measures of the controlled reflected system will converge to the weak solution of an associated reflected McKean--Vlasov equation.

In this paper, we consider a class of Mckean-Vlasov stochastic differential equation with oblique reflection over an non-smooth time dependent domain. We establish the existence and uniqueness results of this class, address the propagation of chaos and prove a Fredlin-Wentzell type large deviations principle (LDP). One of the main difficulties is raised by the setting of non-smooth time dependent domain. To prove the LDP, a sufficient condition for the weak convergence method, which is suitable for Mckean-Vlasov stochastic differential equation, plays an important role.

There have been a lot of methods aimed at studying the limiting free energy per particle (LFEPP) for 3D Ising model in absence of an external magnetic field. These methods are elegant, but most of them are complicated and often require specialized knowledge and special skills. Here we approximate the LFEPP for Ising model from its corresponding functional integral. The resulting Ising LFEPP, which includes an integral of a special function, is exact asymptotically. For 1D and 2D Ising model, this LFEPPs in two limiting cases are consistent or formally consistent with those well-known, respectively. Based on these consistences, we infer the LFEPPs for 3D model in these special cases. Additionally, with this LFEPP, we derive a further approximate one for 3D Ising model, from which we infer the critical temperature $z_c\approx 0.21\sim 0.22$. Furthermore, we suggest similar LFEPPs for 1D-3D Ising models with an external magnetic field, although they are too complicated., Comment: 38 pages; 1 figure

We suggest a closed solution for the roots of polynomial trinomial algebraic equation $$z^n+xz^{n-1}-1=0$$ with an appropriate $x$. This solution is a minor modification to the work of Mikhalkin (Mikhalkin E N, 2006. On solving general algebraic equations by integrals of elementary functions, Siberian Mathematical Jounral, 47(2), 301-306). This modification, together with Mikhalkin's integral formula, provides a relatively simple analytical expression for the solution to a general algebraic equation when the polynomial coefficients are over the corresponding convergent domain. Numerical examples show that this expression can be another alternative to finding numerically the roots of a general polynomial algebraic equation when the integral involved exists and is calculated correctly., Comment: 14 pages, 7 figures, 1 table

The hypocentral depth is a key requirement in seismology and earthquake engineering, but it is very difficult to be determined. The current accepted improvement is taking advantage of the depth phases, such as the pP, to constrain this parameter. However, it is not easy to pick such a phase in a seismogram from the other phases and the backgound noises. Here we propose the use of the minimum entropy deconvolution (MED) to detect it. Synthetic tests show that impulse(s) hidden in the seimic noises, eg. discrete unit impulses or the Gaussian mono impulses, can be detected completely. Further, we assume that the pP phase is an impulse-like signal buried in the Z component of the seismogram and applied this technique to 12 earthquakes in the International Association of Seismology and Physics (IASPEI) Ground Truth (GT) reference events list. Results show that 9 out of 12 earthquakes have absolute errors of less than 2.00 s for the travel-time differences of pP-P, and the maximum absolute error is 3.06 s . This demonstrate that the assumption above is reasonable, and this technique works well and effectively even for a single seismogram. Due to its little cost and effectiveness, this technique may be also useful in the starting points for other methods to detect pP phase., Comment: 16 pages, 11 figures, 1 table

We present a method for locating the seismic event epicenters without assuming an Earth model of the seismic velocity structure, based on the linear relationship between $\log R$ and $\log t$ (where $R$ is the radius of spherical P wave propagated outwards from the hypocenter, $t$ is the travle-time of the P wave). This relationship is derived from the dimensional analysis and a lot of theoretical or real seismic data, in which the earthquake can be considered to be a point source. Application to 1209 events occurred from 2014 to 2017 in the IASPEI Ground Truth (GT) reference events list shows that our method can locate the correct seismic event epicenters in a simple way. $\sim 97.2$ % of seismic epicenters are located with both longitude and latitude errors $\in[-0.1^\circ, +0.1^\circ]$. This ratio can increase if with a finer search grid. As a direct and global-search location, this method may be useful in obtaining the earthquake epicenters occurred in the areas where the seismic velocity structure is poorly known, the starting points or the constraints for other location methods., Comment: 14 pages, 9 figures

The specific heat-phonon spectrum inversion has played a significant role in solid physics. But for this inherently ill-posed problem, most of the known solutions are complex both in form and content, although they are rigorous and perfect. Here we suggest another simpler series solution to this problem, which can be easily calculated if the ratio of specific heat to temperature can be expanded into a power series, or specific heat can be expanded asymptotically and conditionally. Furthermore, we suggest similar solutions to the black-body radiation inversion., Comment: 9 pages, 1 figures

Through an inversion approach, we suggest a possible estimation for the absolute value of Mertens function $\vert M(x) \vert$ that $ \left\vert M(x) \right\vert \sim \left[\frac{1}{\pi \sqrt{\varepsilon}(x+\varepsilon)}\right]\sqrt{x}$ (where $x$ is an appropriately large real number, and $\varepsilon$ ($0<\varepsilon<1$) is a small real number which makes $2x+\varepsilon$ to be an integer). For any large $x$, we can always find an $\varepsilon$, so that $\vert M(x) \vert < \left[\frac{1}{\pi \sqrt{\varepsilon}(x+\varepsilon)}\right]\sqrt{x}$., Comment: 11 pages, no figures

Precise measurement of frequency sensitivity coefficients (FSCs) of some physical effects contributing to uncertainty is an important work in type-B uncertainty (u_B) evaluation of atomic frequency standards. We proposed a method based on statistical correlation of noise to measure FSCs and evaluate u_B for atomic frequency standards, and giving a full statistical expression of FSC as K_I=COV_A(y,x_I)/(sigma(x_I))^2 , where y and x_I are fractional frequency of atomic frequency standards and noise independent variable of Ith physical effects, respectively. The confidence value and the effect of time interval have also been discussed. Except for theoretical derivation, the method also has been validated by numerical simulation and demonstration experiments. Comparing with standard method, the statistical correlation of noise method combines u_B evaluation with type-A uncertainty (u_A), measures FSCs not by special experiments, but from the monitoring data when the device is running. It not only gives a criterion to test the standard method, but also can evaluate many effects at the same time when the device is operating. The method can be extended to other precision measurement fields and is available to comprehend the physical effectiveness of the least square method., Comment: 6 figures

There is no an accepted exact partition function (PF) for the two-dimensional (2D) Ising model with a non-zero external magnetic field to our knowledge. Here we infer an empirical PF for such an Ising model. We compare the PFs for two finite-size Ising lattices ($4\times 4$ and $4\times 6$) from this empirical PF with those from Wei (2018) (Wei, R.Q., 2018. An exact solution to the partition function of the finite-size Ising Model, arXiv: General Physics: 1805.01366.), and find that they are consistent very well. Based on this empirical PF, we further analyze and calculate the thermodynamic functions (heat capacity, magnetization, susceptibility) of this 2D Ising model and discuss the model's singularity semiquantitatively. Analysis and calculations from this PF show that they are coincident with those from other related studies; Especially the 2D Ising model in an external magnetic field has spontaneous magnetization (SM) calling the phenomenon at the critical temperature a phase transition, and the SM decreases with the increasing temperature. However, the decreasing variation of the SM here is different from that obtained by Yang (1952) from the 2D Ising model in a weak magnetic field., Comment: 13 pages, 6 figures

There is no an accepted exact partition function (PF) for the three dimensional (3D) Ising model to our knowledge. Mainly based on the connection between the lattice Green function (LGF) for the simple cubic lattice and that for the honeycomb lattice, we infer an empirical partition function (EPF) for the simple cubic Ising model in the absence of an external magnetic field. This ${\rm EPF}_{_{\rm 3D}}=\frac{1}{{2{\pi ^3}}}\int_0^\pi \int_0^\pi \int_0^\pi \log [2(2{{\cosh }^3}2z + 3{{\sinh }^2}2z + 2)^{\frac{1}{2}} -2\alpha\sinh 2z \ (\cos\omega_1 + \cos \omega_2 + \cos\omega_3)] {\rm{d}}\omega_1{\rm{d}}\omega_2{\rm{d}}\omega_3, \alpha\in[\sqrt{2},\sqrt{3}]$ (where $z=\frac{\epsilon}{kT}$, $\epsilon$ the interaction energy, $T$ the temperature, and $k$ Boltzmann constant). When $\alpha=\sqrt{2}$, this EPF is consistent well numerically with the result from high temperature expansions by Guttmann and Enting (1993). The specific heat from this EPF approaches infinity non-logarithmically at the critical temperature $T_c$. $\frac{\epsilon}{kT_c}=\cosh^{-1}[\frac{1}{4} (17-3\sqrt{17})]/2\approx 0.277212$, which is greater than 0.221654 from the recent Monte Carlo study., Comment: 12 pages, 2 figures

Correlation between the variations of quasar absorption lines and the ionizing continuum have been recently confirmed in systematic studies. However, no convincing individual case is reported. We present a statistical analysis of the variable C iv broad absorption line (BAL) in the quasar SDSS J141007.74+541203.3, which have been observed with 44 epochs by the Sloan Digital Sky Survey Data Release 14. Grier et al. (2015) has recently concluded that the most likely cause of the variability of the BAL in SDSS J141007.74+541203.3 is a rapid response to changes in the incident ionizing continuum. In this paper, we confirm the anticorrelation between the equivalent width of BALs and the flux of the continuum based on the spectra of this quasar that show significant variations, which serve as another independent evidence for the view of Grier et al. (2015).

Transport of an inertial particle advected by a two-dimensional steady laminar flow is numerically investigated in the presences of a constant force and a periodic potential. Within particular parameter regimes this system exhibits absolute negative mobility, which means that the particle can travel in a direction opposite to the constant force. It is found that the profile of the periodic potential plays an important role in the nonlinear response regime. Absolute negative mobility can be drastically enhanced by applying appropriate periodic potential, the parameter regime for this phenomenon becomes larger and the amplitude of negative mobility grows exceedingly large (giant negative mobility). In addition, giant positive mobility is also observed in the presence of appropriate periodic potential., Comment: 7 pages, 7 figures

We provide some upper bounds for the Mertens function ($M(n)$: the cumulative sum of the M$\ddot{\mathrm{o}}$bius function) by an approach of statistical mechanics, in which the M$\ddot{\mathrm{o}}$bius function is taken as a particular state of a modified one-dimensional (1D) Ising model without the exchange interaction between the spins. Further, based on the assumptions and conclusions of the statistical mechanics, we discuss the problem that $M(n)$ can be equivalent to the sum of an independent random sequence. It holds in the sense of equivalent probability, from which another two upper bounds for the $M(n)$ can be inferred. Besides, if $M(n)$ is a measured quantity, its upper bound is $\sqrt{\frac{B}{\alpha} n}$ ($B$ is constant) with a probability $>1-\alpha$ ($0<\alpha<1$) from the view point of the energy fluctuations in the canonical ensemble., Comment: 6 pages

We study a binary mixture of polar chiral (counterclockwise or clockwise) active particles in a two-dimensional box with periodic boundary conditions. Beside the excluded volume interactions between particles, particles are also subject to the polar velocity alignment. From the extensive Brownian dynamics simulations, it is found that the particle configuration (mixing or demixing) is determined by the competition between the chirality difference and the polar velocity alignment. When the chirality difference competes with the polar velocity alignment, the clockwise particles aggregate in one cluster and the counterclockwise particles aggregate in the other cluster, thus particles are demixed and can be separated. However, when the chirality difference or the polar velocity alignment is dominated, particles are mixed. Our findings could be used for the experimental pursuit of the separation of binary mixtures of chiral active particles., Comment: 11 pages, 9 figures

There is no an exact solution to three-dimensional (3D) finite-size Ising model (referred to as the Ising model hereafter for simplicity) and even two-dimensional (2D) Ising model with non-zero external field to our knowledge. Here by using an elementary but rigorous method, we obtain an exact solution to the partition function of the Ising model with $N$ lattice sites. It is a sum of $2^N$ exponential functions and holds for $D$-dimensional ($D=1,2,3,...$) Ising model with or without the external field. This solution provides a new insight into the problem of the Ising model and the related difficulties, and new understanding of the classic exact solutions for one-dimensional (1D) (Kramers and Wannier, 1941) or 2D Ising model (Onsager, 1944). With this solution, the specific heat and magnetisation of a simple 3D Ising model are calculated, which are consistent with the results from experiments and/or numerical simulations. Furthermore, the solution here and the related approaches, can also be available to other models like the percolation and/or the Potts model., Comment: 14 pages, 8 figures

Using the SDSS spectra of quasars included in the DR7Q or DR12Q catalogs, we search for Mg II narrow absorption doublets in the spectra data around Mg II emission lines. We obtain 17,316 Mg II doublets, within the redshift range of 0.3299<= z_abs <= 2.5663. We find that a velocity offset of v_r < 6000 km/s is a safe boundary to constrain the vast majority of associated Mg II systems, although we find some doublets at v_r > 6000 km/s. If associated Mg II absorbers are defined by v_r < 6000 km/s, ~33.3% of the absorbers supposed to be contaminants of intervening systems. Removing the 33.3% contaminants, ~4.5% of the quasars present at least one associated Mg II system with W_r\lambda2796>=0.2 \AA. The fraction of associated Mg II systems with high velocity outflows correlates with the average luminosities of their central quasars, indicating a relationship between outflows and the quasar feedback power. The v_r distribution of the outflow Mg II absorbers is peaked at 1023 km/s, which is smaller than the corresponding value of the outflow C IV absorbers. The redshift number density evolution of absorbers (dn/dz) limited by v_r > -3000 km/s differs from that of absorbers constrained by v_r > 2000 km/s. While, absorbers limited by v_r > 2000 km/s and higher values exhibit similar profile of dn/dz. In addition, the dn/dz is smaller when absorbers are constrained with larger v_r. The distributions of equivalent widths, and the ratio of W_r\lambda2796/W_r\lambda2803 is the same for associated and intervening systems, and independent on quasar luminosity., Comment: 8 pages, 8 figures. Accepted by ApJS

Surface heat flow is a key parameter for the geothermal structure, rheology, and hence the dynamics of continents. However, the coverage of heat flow measurements is still poor in many continental areas. By transforming the stable nonlinear heat conduction equation into a Poisson's one, we develop a method to infer surface heat flow for a stable or quasi-stable continent from a Parker's-like formula. This formula provides the relationship between the Fourier transform of surface heat flow and the sum of the Fourier transform of the powers of geometry for the heat production (HP) interface in the continental lithosphere. Once the interface geometry is known, one to three dimensional distribution of the surface heat flow can be calculated accurately by this formula. As a case study, we estimate the three-dimensional surface heat flows for the Ordos geological block and its adjacent areas in China on a $1^\circ \times 1^\circ$ grid based on a simple layered constant HP model. Comparing to the measurements, most relative errors of the heat flows inferred are less than 20\%, showing this method is a favorable way to estimate surface heat flow for stable or quasi-stable continental regions where measurements are rare or absent., Comment: 11 pages, 6 figures

Obtaining the heat production (HP) in the lithosphere has always been a challenge for the geotherms and evolution of continents. By transforming the nonlinear stable heat conduction equation into a linear Poisson's potential one, we propose a method to infer the HP in the stable continental lithosphere. This method estimates the HP through the inversion of the corresponding heat flow (HF) observations. Either the distribution of HP within the lithosphere or geometry of HP interfaces (even the both) can be inverted. Herein we focus on the inversion of the geometry of the HP interface. An analogical Parker-Oldenburg formula, which is often used in the inversion of potential field, is deduced for this purpose. This analogical formula is based on a relationship between the Fourier transform of the corresponding HF observations and the sum of the Fourier transform for the powers of the interface geometry. When the mean depth of the HP interface and the HP contrast between the two media are given, one to three-dimensional geometry of the HP interface can be iteratively calculated. As a case study, we construct a HP model for the lithosphere of the Ordos geological block and its adjacent area in China, in which three-dimensional geometry of the upper crustal HP interface is estimated. It is found that the geometry of this HP interface distribute uneven in a magnitude of dozens of km. With this HP model, the geotherms for the Ordos geological block and its adjacent area is calculated further, which fit the constraints from the studies on the xenolith and tectonics well., Comment: 20 pages, 11 figures, 1 table

It is thought that paleo-magnetism has the incapability in providing paleo-longitude. To obtain this important location parameter many other indirect methods have been developed based on different assumptions. Here we present a scanning method to derive the paleo-longitude from the usual paleo-magnetic measurements. This method takes into account the contributions to the Earth's magnetic potential from additional dipoles with their axes in the equatorial plane, which were omitted by the traditional paleo-magnetism. In this method, firstly we assume that $\theta_p$ and $\lambda_p$ are accurate (or determined well enough), and define a cost function; And secondly we minimize this function by systematically searching through all longitudes and latitudes in their domain; Finally when a local minima of this cost function reaches, the corresponding longitude is the paleo-longitude that we look for. Simultaneously the paleo-latitude is obtained. Synthetic experiments show that this method works very well when there are no errors in the geomagntic measurements (Components of magnetic field: $B_x, B_y, B_z$, or declination $D$ and inclination $I$). If there exist errors in geomagntic measurements, we recommend adding a Tikhonov regularization factor to the cost function for deriving reasonable paleo-longitude, and provide two examples. Error analysis shows that the main error sources for paleo-longitude are $B_y$ and/or $I$ in our method. In addition, such a cost function and its like could be used as a theoretical framework that can directly invert the paleo-longitude, paleo-latitude, and even the location of the paleo-geomagnetic poles simultaneously from the paleo-geomagnetic measurements through any appropriate inversion method., Comment: 16 pages, 10 figures, 2 tables

In this Letter, we report the discovery of a strong correlation between the variability of narrow absorption lines (NALs) and the ionizing continuum from a two-epoch spectra sample of 40 quasars containing 52 variable C iv {\lambda}{\lambda}1548; 1551 absorption doublets. According to the concordance index, this sample is classified into two subsamples. Subsample I shows an anti-correlation between the variations of absorption lines and the continuum, while Subsample II exhibits a positive correlation. These results imply that these variable C iv {\lambda}{\lambda}1548; 1551 absorption doublets are intrinsic to the corresponding quasars and that their variations are caused primarily by the fluctuations of the ionizing continuum. Based on our analysis, we propose that there might be two kinds of absorption gas: one that is very sensitive to the continuum variations, the another that is not. In addition, we suggest that in many cases the emergence or disappearance of NALs is caused by fluctuations of the ionizing continuum., Comment: 6 pages, 2 figures

We demonstrate the measurement of mass of the absorbing micro-particle trapped in air by optical forced oscillation. When the trapping light intensity is modulated sinusoidally, the particle in the trap undergoes forced oscillation and the amplitude of the oscillation depends directly on the modulated frequency. Based on a simple spring model, we fit the amplitudes versus the modulated frequencies and obtain the stiffness of the optical trap and the mass of the trapped particle. The fitting results show that, for a certain particle, the stiffness varies linearly with the trapping light intensity while the mass is consistent. The density of the micro-particle is then estimated and could be used to classify different kinds of absorbing particles, like C and CuO.

Transport surrounding is full of all kinds of fields, like particle potential, external potential. Under these conditions, how elements work and how position and momentum redistribute in the diffusion? For enriching the Fick law in ordinary, nonequilibrium statistics physics need to be used to disintegrate the complex process. This study attempts to discuss the particle transport in the one-dimensional channel under external potential fields. Two type of potentials, potential well and barrier do not change the potential in total, are built during the diffusion process. There are quite distinct phenomena because of different one-dimensional periodic potentials. We meticulously explore reasons about why external potential field impacts transport by the subsection and statistics method. Besides, one of the evidences of Maxwell velocity distribution is confirmed in assumption of local equilibrium. In addition, we have also investigated the influence of temperature and concentration to the collective diffusion coefficient, by a variety of external force, attaching thermodynamics analyze to these opposite phenomena. So simply is this model that the most valuable point may be an idea, which relating flux to sectional statistics of position and momentum could be referenced in similar transport problems.

Directed transport of self-propelled particles is numerically investigated in a three-dimensional asymmetric potential. Beside the steric repulsive forces, hydrodynamic interactions between particles have been taken into account in an approximate way. From numerical simulations, we find that hydrodynamic interactions can strongly affect the rectified transport of self-propelled particles. Hydrodynamic interactions enhance the performance of the rectified transport when particles can easily pass across the barrier of the potential, and reduce the rectified transport when particles are mainly trapped in the potential well., Comment: 12 pages, 3 figures, Physical Review E 2017

We present a trajectory dynamically tracing compensation method to smooth the spatial fluctuation of the static magnetic field (C-field) that provides a quantization axis in the fountain clock. The C-field coil current is point-to-point adjusted in accordance to the atoms experienced magnetic field along the flight trajectory. A homogeneous field with a 0.2 nT uncertainty is realized compared to 5 nT under the static magnetic field with constant current during the Ramsey interrogation. The corresponding uncertainty associated with the second-order Zeeman shift that we calculate is improved by one order of magnitude. The technique provides an alternative method to improve the magnetic field uniformity particularly for large-scale equipment that is difficult to machine with magnetic shielding. Our method is simple, robust, and essentially important in frequency evaluations concerning the dominant uncertainty contribution due to the quadratic Zeeman shift.

Two elementary formulae for Mertens function $M(n)$ are obtained. With these formulae, $M(n)$ can be calculated directly and simply, which can be easily implemented by computer. $M (1) \sim M (2 \times 10^7) $ are calculated one by one. Based on these $2\times 10^7$ samples, some of the complicated properties for Mertens function $M(n)$, its 16479 zeros, the 10043 local maximum/minimum between two neighbor zeros, and the relation with the cumulative sum of the squarefree integers, are understood numerically and empirically., Comment: 12 pages, 8 figures, 1 table

The interaction between the magnetic field and the elastic deformation field in the crust is studied in a simplified way. The magnetic fields generated by the line singularities in a magnetized elastic half-plane are investigated. Using the general solution and Fourier transform technique, the exact solutions for the generated magnetic inductions due to various cases are obtained in a closed form. The results show that the line concentrated force will induced a perturbed magnetic field; The induced magnetic field will indicate the line concentrated force in reverse. The distribution of the vertical component of the magnetic induction caused by the line mechanical singularities is simpler than that of the horizontal component, and it is zero at the origin when the applied magnetic field and the line concentrated force satisfies some conditions. This result is applied to locate the epicenters of the earthquakes and historical earthquakes occurred in the Chinese continental crust. Results show that more than 80\% epicenters are at or near the zero-contours of the vertical component of the magnetic induction observed from satellite. These regions of zero-contours, especially those in active tectonic zones, could be the possible seismogenic zones in the future. The zero-contours of the vertical component of the magnetic induction from satellite could be as geophysical constraints to the risk information on the shallow seismicities, or they can be used as an early monitor for the shallow seismicities in the continental crust, or an auxiliary sign in the determination of the great historical earthquake., Comment: 16 pages, 6 figures

An elementary recursive relation for M$\ddot{\mathrm{o}}$bius function $\mu (n)$ is introduced by two simple ways. With this recursive relation, $\mu (n)$ can be calculated without directly knowing the factorization of the $n$. $\mu (1) \sim \mu (2 \times 10^7) $ are calculated recursively one by one. Based on these $2\times 10^7$ samples, the empirical probabilities of $\mu (n)$ of taking $-1$, 0, and 1 in classic statistics are calculated and compared with the theoretical probabilities in number theory. The numerical consistency between these two kinds of probability show that $\mu (n)$ could be seen as an independent random sequence when $n$ is large. The expectation and variance of the $\mu (n)$ are $0$ and $6 n/ \pi^2$, respectively. Furthermore, we show that any conjecture of the Mertens type is false in probability sense, and present an upper bound for cumulative sums of $\mu (n)$ with a certain probability., Comment: 28 pages, 6 figues, 4 tables

The environmental perturbation on atoms is the key factor restricting the performance of atomic frequency standards, especially in long term scale. In this letter, we demonstrate a real-time noise distinguish operation of atomic clocks. The operation improves the statistical uncertainty by about an order of magnitude of our fountain clock which is deteriorated previously by extra noises. The frequency offset bring by the extra noise is also corrected. The experiment proves the real-time noise distinguish operation can reduce the contribution of ambient noises and improve the uncertainty limit of atomic clocks., Comment: 5 pages, 4 figures, 1 table

Dynamics and separation of mixed chiral microswimmers are numerically investigated in a channel with regular arrays of rigid half-circle obstacles. For zero shear flow, transport behaviors are the same for different chiral particles: the average velocity decreases with increase of the rotational diffusion coefficient, the direction of the transport can be reversed by tuning the angular velocity, and there exists an optimal value of the packing fraction at which the average velocity takes its maximal value. However, when the shear flow is considered, different chiral particles show different behaviors. By suitably tailoring parameters, particles with different chiralities can move in different directions and be separated. In addition, we also proposed a space separation method by introducing a constant load, where counterclockwise and clockwise particles stay in different regions of the channel., Comment: 8 pages, 11figures

Directed transport of interacting active (self-propelled)Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity firstly decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical interaction at which the average velocity is minimal, nearly tends to zero, however, for the strong interaction, the average velocity is independent of the interaction., Comment: 12 pages, 5figures

Rectification and diffusion of non-interacting self-propelled particles is numerically investigated in a two-dimensional corrugated channel. From numerical simulations, we obtain the average velocity and the effective diffusion coefficient. It is found that the self-propelled particles can be rectified by the self-propelled velocity. There exist optimal values of the parameters (the self-propelled velocity, the translational diffusion constant, and the height of the potential) at which the average velocity takes its maximal value. There exists an optimal translational diffusion at which the effective diffusion constant is maximal. The self-propelled velocity can strongly increase the effective diffusion, while the large rotational diffusion rate can strongly suppress the effective diffusion., Comment: 16pages, 11figures

Negative differential thermal resistance (NDTR) in approximate graphene nanoribbons (GNRs) is investigated from one dimension to three dimensions by using classical molecular dynamics method. For single-layer GNRs, NDTR can not be observed for very narrow GNRs (one dimension), NDTR appears when the width of GNRs increases (two dimensions). However, NDTR disappears gradually on further increasing the width. For multiple-layer GNRs, when the number of the layers increases, GNRs becomes from two-dimensional system to three-dimensional system, NDTR regime reduces and eventually disappears. In addition, when the length of GNRs increases, NDTR regime also reduces and vanishes in the thermodynamic limit. These effects may be useful for designing thermal devices where NDTR plays an important role., Comment: 14pages, 9figures

We have assembled absorption systems by visually identifying $C~IV\lambda\lambda1548,1551$ absorption doublets in the quasar spectra of the Baryon Oscillation Spectroscopic Survey (BOSS) one by one. This paper is the first of the series work. In this paper, we concern quasars with relatively low redshifts and high signal-to-noise ratios for their spectra, and hence we limit our analysis on quasars with $z_{em}\le2.4$ and on the doublets with $W_r\lambda1548\ge0.2$ \AA. Out of the more than 87,000 quasars in the Data Release 9, we limit our search to 10,121 quasars that have the appropriate redshifts and spectra with high enough signal-to-noise ratios to identify narrow C IV absorption lines. Among them, 5,442 quasars are detected to have at least one $C~IV\lambda\lambda1548,1551$ absorption doublet. We obtain a catalog containing 8,368 $C~IV\lambda\lambda1548,1551$ absorption systems, whose redshifts are within $z_{abs}=1.4544$ - $2.2805$. In this catalog, about $33.7\%$ absorbers have $0.2$ \AA$\le W_r\lambda1548<0.5$ \AA, about $45.9\%$ absorbers have $0.5$ \AA$\le W_r\lambda1548<1.0$ \AA, about $19.2\%$ absorbers have $1.0$ \AA$\le W_r\lambda1548<2.0$ \AA, and about $1.2\%$ absorbers have $W_r\lambda1548\ge2.0$ \AA.

In this paper, we report on two C IV narrow absorption systems emerging from the spectrum of the quasar SDSS J095254.10 +021932.8, which are located at $z_{\rm abs}=2.0053$ and $z_{\rm abs}=1.8011$, respectively. These features have velocity offsets of $\rm \sim 13,800$ and $\rm \sim 34,700~km~s^{-1}$ with respect to the quasar, and show obviously partial coverage to the background emission sources. The two C IV absorption systems are imprinted on the spectrum obtained by the Sloan Digital Sky Survey (SDSS) III on 2011 March 25, which cannot be observed from the spectrum obtained by SDSS-I/II on 2000 December 30. The time interval of the two SDSS observations is 1186.4 d at the quasar rest frame. Because the continuum radiation, broad emission lines and mass accretion rate are stable for the two observations, together with the time interval of observations, we believe that the observed spectral variations are less likely to be caused by the changes in the ionization states of the absorbing gas or by a new outflow, arising from the situation where there was previously no outflow at all. Instead, they probably arise from the motions of multiple streaming gas across the sightline of the quasar.

Transport of Brownian particles interacting with each other via the Morse potential is investigated in the presence of an ac driving force applied locally at one end of the chain. By using numerical simulations, we find that the system can behave as a particle diode for both overdamped and underdamped cases. For low frequencies, the transport from the free end to the ac acting end is prohibited, while the transport from the ac acting end to the free end is permitted. However, the polarity of the particle diode will reverse for medium frequencies. There exists an optimal value of the well depth of the interaction potential at which the average velocity takes its maximum. The average velocity $\upsilon$ decreases monotonically with the system size $N$ by a power law $\upsilon \propto N^{-1}$., Comment: 7 pages, 9 figures

We study heat conduction through one-dimensional homogeneous lattices in the presence of the nonlinear on-site potentials containing the bounded and unbounded parts, and the harmonic interaction potential. We observe the occurrence of double negative differential thermal resistance (NDTR), namely, there exist two regions of temperature difference, where the heat flux decreases as the applied temperature difference increases. The nonlinearity of the bounded part contributes to NDTR at low temperatures and NDTR at high temperatures is induced by the nonlinearity of the unbounded part. The nonlinearity of the on-site potentials is necessary to obtain NDTR for the harmonic interaction homogeneous lattices. However, for the anharmonic homogeneous lattices, NDTR even occurs in the absence of the on-site potentials, for example the rotator model., Comment: 5 pages, 4 figures

The thermal conductivity of graphene nanoribbons (layer from 1 to 8 atomic planes) is investigated by using the nonequilibrium molecular dynamics method. We present that the room-temperature thermal conductivity decays monotonically with the number of the layers in few-layer graphene. The superiority of zigzag graphene in thermal conductivity is only available in high temperature region and disappears in multi-layer case. It is explained that the phonon spectral shrink in high frequency induces the change of thermal conductivity. It is also reported that single-layer graphene has better ballistic transport property than the multi-layer graphene., Comment: 3 figures

A double-stranded system, modeled by a Frenkel-Kontorova lattice, is studied through nonequilibrium molecular dynamics simulations. We have investigated the thermal conductance influenced by the intra-chain interaction as well as by the inter-chain interaction. It is found that the intra-chain interaction always enhance the thermal conductance. The inter-chain interaction, however, has a positive effect on the thermal conductance in the case of strong nonlinear potential, and has a negative effect on the thermal conductance in the case of weak nonlinear potential. This phenomenon can be explained by the transition of thermal transport mode and the phonon band shift of the particles. It is suggested that the inter-and intra-chain interactions present different thermal properties in double-stranded lattices., Comment: 6 figures

We report on the first molecular device of heat pump modeled by a T-shape Frenkel-Kontorova lattice. The system is a three-terminal device with the important feature that the heat can be pumped from the low-temperature region to the high-temperature region through the third terminal. The pumping action is achieved by applying a stochastic external force that periodically modulates the atomic temperature. The temperature, the frequency and the system size dependence of heat pump are briefly discussed., Comment: 6 figures

We investigate the thermal conductivity of four types of deformed carbon nanotubes by using the nonequilibrium molecular dynamics method. It is reported that various deformations have different influence on the thermal properties of carbon nanotubes. For the bending carbon nanotubes, the thermal conductivity is independent on the bending angle. However, the thermal conductivity increases lightly with XY-distortion and decreases rapidly with Z-distortion. The thermal conductivity does not change with the screw ratio before the breaking of carbon nanotubes but decreases sharply after the critical screw ratio., Comment: 6figures

A two-segment Fermi-Pasta-Ulam lattices has been investigated by using nonequilibrium molecular dynamics. Here we present an anomalous negative differential thermal resistance (NDTR) that have not been reported in Frenkel-Kontorova and \phi_4 lattices up to the present. The NDTR disappears at low temperature region. The region of NDTR shifts from the large to the small temperature difference region as the system size increases. Anomalous dependence of NDTR on the temperature can be explained as the negative effect induced by the nonlinear coupling. The explanation can also cover the phenomenon of NDTR in momentum-nonconserved lattices., Comment: 5figures

Thermal rectification in thickness asymmetric graphene nanoribbons connecting single-layer with multi-layer graphene is investigated by using classical nonequilibrium molecular dynamics. It is reported that the graphene nanoribbons with thickness-asymmetry have a good thermal rectification. The thermal rectification factor depends on temperature as well as the thickness-ratio of the two-segment. Our results provide a direct evidence that the thermal rectifier can be achieved in a nanostructure crossing two- and three-dimension., Comment: 5figures, Accepted by Appl.Phys.Lett

Directed transport of overdamped Brownian particles driven by fractional Gaussian noises is investigated in asymmetrically periodic potentials. By using Langevin dynamics simulations, we find that rectified currents occur in the absence of any external driving forces. Unlike white Gaussian noises, fractional Gaussian noises can break thermodynamical equilibrium and induce directed transport. Remarkably, the average velocity for persistent fractional noise is opposite to that for anti-persistent fractional noise. The velocity increases monotonically with Hurst exponent for the persistent case, whereas there exists an optimal value of Hurst exponent at which the velocity takes its maximal value for the anti-persistent case., Comment: 13 pages, 6 figures