arXiv subjects

Rong Qiang Wei

Publications and source records attributed to Rong Qiang Wei.

17 recordsLinked to original sources

arXiv2025

Limiting free energy per particle for Ising Model by approximating its functional integral

There have been a lot of methods aimed at studying the limiting free energy per particle (LFEPP) for 3-dimensional (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 functional integral using classic mathematical-physical methods. The resulting LFEPPs for 1-dimensional (1D) to 3D Ising model have similar structures and forms. We then verify that these LFEPPs are correct for two limiting cases of the 1D and 2-dimensional (2D) models, as well as for the critical inverse temperature $z_c$ of the 2D model. Based on these verifications, we derive naturally the LFEPP and the $z_c$ ($\approx 0.21\sim 0.22$) for the 3D model. Furthermore, we suggest similar LFEPPs for 1D-3D Ising models with an external magnetic field, although they are too complicated.

cond-mat.stat-mech↗

arXiv2024

Spring-block friction model for landslides: Application to Vaiont and Maoxian landslides

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.

physics.geo-ph↗

arXiv2022

A closed solution to a special polynomial trinomial equation and semi-analytical roots for a general algebraic equation

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.

math.GM↗

arXiv2021

Application of minimum entropy deconvolution to detect $pP$ phase in a seismogram

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.

physics.geo-ph↗

arXiv2021

Locating earthquake epicenter without a seismic velocity model

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.

physics.geo-ph↗

arXiv2021

Simple series solutions to specific heat-phonon spectrum inversion

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.

cond-mat.stat-mech↗

arXiv2020

Inferring the paleo-longitude directly from the paleo-geomagnetic data

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 $θ_p$ and $λ_p$ 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.

physics.geo-ph↗

arXiv2020

An empirical partition function for the simple cubic Ising Model with a zero external magnetic field

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 ${\rm EPF}_{_{\rm 3D}}=\frac{1}{2{π^3}}\int_0^π\int_0^π\int_0^π\log [2(2{{\cosh }^3}2z + 3{{\sinh }^2}2z + 2)^{\frac{1}{2}} -2α\sinh 2z \ (\cosω_1 + \cos ω_2 + \cosω_3)] {\rm{d}}ω_1{\rm{d}}ω_2{\rm{d}}ω_3, α\in[\sqrt{2},\sqrt{3}]$ (where $z=\fracε{kT}$, $ε$ the interaction energy, $T$ the temperature, and $k$ Boltzmann constant). When $α=\sqrt{2}$, 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 $T_c$. $\fracε{kT_c}=\cosh^{-1}[\frac{1}{4} (17-3\sqrt{17})]/2\approx 0.277212$, which is greater than 0.221654 from the recent Monte Carlo study.

cond-mat.stat-mech↗

arXiv2020

Another estimating the absolute value of Mertens function

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}{π\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 $\vert M(x) \vert < \left[\frac{1}{π\sqrt{\varepsilon}(x+\varepsilon)}\right]\sqrt{x}$.

math.GM↗

arXiv2019

The upper bound of the Mertens function from the viewpoint of statistical mechanics

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 $\sqrt{\frac{B}α n}$ ($B$ is constant) with a probability $>1-α$ ($0<α<1$) from the view point of the energy fluctuations in the canonical ensemble.

math.GM↗

arXiv2019

An empirical partition function for two-dimensional Ising Model in an external magnetic field

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.

cond-mat.stat-mech↗

arXiv2018

An exact solution to the partition function of the finite-size Ising Model

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.

physics.gen-ph↗

arXiv2017

Heat flows inferred from a Parker's-like formula for stable or quasi-stable continents

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.

physics.geo-ph↗

arXiv2017

A heat production model for stable continental lithosphere by the inversion of the surface heat flows

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.

physics.geo-ph↗

arXiv2016

A definite recursive relation and some statistical properties for Möbius function

An elementary recursive relation for M$\ddot{\mathrm{o}}$bius function $μ(n)$ is introduced by two simple ways. With this recursive relation, $μ(n)$ can be calculated without directly knowing the factorization of the $n$. $μ(1) \sim μ(2 \times 10^7) $ are calculated recursively one by one. Based on these $2\times 10^7$ samples, the empirical probabilities of $μ(n)$ 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 $μ(n)$ could be seen as an independent random sequence when $n$ is large. The expectation and variance of the $μ(n)$ are $0$ and $6 n/ π^2$, 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 $μ(n)$ with a certain probability.

math.NT↗

arXiv2016

Two elementary formulae and some complicated properties for Mertens function

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.

math.NT↗

arXiv2016

Magnetic fields induced by a mechanical singularity in a magnetoelastic half plane and their applications to the seismicities in the crust of the Chinese continent

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.

physics.geo-ph↗