arXiv subjects

M. A. Nikitina

Publications and source records attributed to M. A. Nikitina.

8 recordsLinked to original sources

arXiv2017

Modeling of local seismic events in the area of Valaam's island

A lot of seismic phenomena with small magnitude has been taking place in the Ladoga lake region. One of them is the earthquake which was recorded on the 31$^\text{th}$ of July, 2010 followed by an earthquake swarm near Nikonovsky cape. There is only one station in the region that is why it is difficult to process the data. In this work we propose a new method for obtaining main event focal mechanism and constructing the synthetic seismograms for this event. The data of swarm events is used to test the method of constructing synthetic seismograms and the data of close events to determine the parameters of the media. Since the amplitude of the wave P is close to zero, the location of the nodal plane can be submitted. That is the reason why we can find the focal mechanism for the earthquake using data of the single seismostation. Resulting fault plane has the same inclination as known tectonics line which the earthquake source is placed on. Our proposed method is based on Green function method with using several kinds of sources and temporal $δ$-shaped sequences.

physics.geo-ph↗

arXiv2017

Effective potential of the three-dimensional Ising model: the pseudo-$ε$ expansion study

The ratios $R_{2k}$ of renormalized coupling constants $g_{2k}$ that enter the effective potential and small-field equation of state acquire the universal values at criticality. They are calculated for the three-dimensional scalar $λϕ^4$ field theory (3D Ising model) within the pseudo-$ε$ expansion approach. Pseudo-$ε$ expansions for the critical values of $g_6$, $g_8$, $g_{10}$, $R_6 = g_6/g_4^2$, $R_8 = g_8/g_4^3$ and $R_{10} = g_{10}/g_4^4$ originating from the five-loop renormalization group (RG) series are derived. Pseudo-$ε$ expansions for the sextic coupling have rapidly diminishing coefficients, so addressing Padé approximants yields proper numerical results. Use of Padé--Borel--Leroy and conformal mapping resummation techniques further improves the accuracy leading to the values $R_6^* = 1.6488$ and $R_6^* = 1.6490$ which are in a brilliant agreement with the result of advanced lattice calculations. For the octic coupling the numerical structure of the pseudo-$ε$ expansions is less favorable. Nevertheless, the conform-Borel resummation gives $R_8^* = 0.868$, the number being close to the lattice estimate $R_8^* = 0.871$ and compatible with the result of 3D RG analysis $R_8^* = 0.857$. Pseudo-$ε$ expansions for $R_{10}^*$ and $g_{10}^*$ are also found to have much smaller coefficients than those of the original RG series. They remain, however, fast growing and big enough to prevent obtaining fair numerical estimates.

cond-mat.stat-mech↗

arXiv2016

Critical exponents and the pseudo-$ε$ expansion

We present the pseudo-$ε$ expansions ($τ$-series) for the critical exponents of a $λϕ^4$ three-dimensional $O(n)$-symmetric model obtained on the basis of six-loop renormalization-group expansions. Concrete numerical results are presented for physically interesting cases $n = 1$, $n = 2$, $n = 3$ and $n = 0$, as well as for $4 \le n \le 32$ in order to clarify the general properties of the obtained series. The pseudo-$ε$-expansions for the exponents $γ$ and $α$ have small and rapidly decreasing coefficients. So, even the direct summation of the $τ$-series leads to fair estimates for critical exponents, while addressing Pade approximants enables one to get high-precision numerical results. In contrast, the coefficients of the pseudo-$ε$ expansion of the scaling correction exponent $ω$ do not exhibit any tendency to decrease at physical values of $n$. But the corresponding series are sign-alternating, and to obtain reliable numerical estimates, it also suffices to use simple Padé approximants in this case. The pseudo-$ε$ expansion technique can therefore be regarded as a specific resummation method converting divergent renormalization-group series into expansions that are computationally convenient.

cond-mat.stat-mech↗

arXiv2016

Renormalized coupling constants for 3D scalar λϕ^4 field theory and pseudo-ε-expansion

Renormalized coupling constants g_{2k} that enter the critical equation of state and determine nonlinear susceptibilities of the system possess universal values g*_{2k} at the Curie point. They are calculated, along with the ratios R_{2k} = g_{2k}/g_4^{k-1}, for the three-dimensional scalar λϕ^4 field theory within the pseudo-ε-expansion approach. Pseudo-ε-expansions for g*_6, g*_8, R*_6, and R*_8 are derived in the five-loop approximation, numerical estimates are presented for R*_6 and R*_8. The higher-order coefficients of the pseudo-ε-expansions for the sextic coupling are so small that simple Pade approximants turn out to be sufficient to yield very good numerical results. Their use gives R*_6 = 1.650 while the most recent lattice estimate is R*_6 = 1.649(2). For the octic coupling pseudo-ε-expansions are less favorable from the numerical point of view. Nevertheless, Pade-Borel resummation leads in this case to R*_8 = 0.890, the number differing only slightly from the values R*_8 = 0.871, R*_8 = 0.857 extracted from the lattice and field-theoretical calculations.

hep-th↗

arXiv2014

Critical Exponents in Two Dimensions and Pseudo-ε Expansion

The critical behavior of two-dimensional $n$-vector $λϕ^4$ field model is studied within the framework of pseudo-$ε$ expansion approach. Pseudo-$ε$ expansions for Wilson fixed point location $g^*$ and critical exponents originating from five-loop 2D renormalization group series are derived. Numerical estimates obtained within Padé and Padé-Borel resummation procedures as well as by direct summation are presented for $n = 1$, $n = 0$ and $n = -1$, i. e. for the models which are exactly solvable. The pseudo-$ε$ expansions for $g^*$, critical exponents $γ$ and $ν$ have small lower-order coefficients and slow increasing higher-order ones. As a result, direct summation of these series with optimal cut off provides numerical estimates that are no worse than those given by the resummation approaches mentioned. This enables one to consider the pseudo-$ε$ expansion technique itself as some specific resummation method.

cond-mat.stat-mech↗

arXiv2014

Critical Exponents of Superfluid Helium and Pseudo-$ε$ Expansion

Pseudo-$ε$ expansions ($τ$-series) for critical exponents of 3D XY model describing $λ$-transition in liquid helium are derived up to $τ^6$ terms. Numerical estimates extracted from the $τ$-series obtained using Padé-Borel resummation technique, scaling relations and seven-loop ($τ^7$) estimate for the Fisher exponent $η$ are presented including those for exponents $α$ and $ν$ measured in experiments with record accuracy. For the exponent $α$ the procedure argued to be most reliable gives $α= -0.0117$. This number is very close to the most accurate experimental values differing appreciably from the results of numerous lattice and field-theoretical calculations. It signals that the pseudo-$ε$ expansion is a powerful tool robust enough to evaluate critical exponents with very small absolute error. The arguments in favour of such a robustness are presented.

cond-mat.stat-mech↗

arXiv2014

Fisher Exponent from Pseudo-$ε$ Expansion

Critical exponent $η$ for three-dimensional systems with $n$-vector order parameter is evaluated in the frame of pseudo-$ε$ expansion approach. Pseudo-$ε$ expansion ($τ$-series) for $η$ found up to $τ^7$ term for $n$ = 0, 1, 2, 3 and within $τ^6$ order for general $n$ is shown to have a structure rather favorable for getting numerical estimates. Use of Padé approximants and direct summation of $τ$-series result in iteration procedures rapidly converging to the asymptotic values that are very close to most reliable numerical estimates of $η$ known today. The origin of this fortune is discussed and shown to lie in general properties of the pseudo-$ε$ expansion machinery interfering with some peculiarities of the renormalization group expansion of $η$.

cond-mat.stat-mech↗

arXiv2014

Pseudo-$ε$ Expansion and Renormalized Coupling Constants at Criticality

Universal values of dimensional effective coupling constants $g_{2k}$ that determine nonlinear susceptibilities $χ_{2k}$ and enter the scaling equation of state are calculated for $n$-vector field theory within the pseudo-$ε$ expansion approach. Pseudo-$ε$ expansions for $g_6$ and $g_8$ at criticality are derived for arbitrary $n$. Analogous series for ratios $R_6 = g_6/g_4^2$ and $R_8 = g_8/g_4^3$ figuring in the equation of state are also found and the pseudo-$ε$ expansion for Wilson fixed point location $g_{4}^*$ descending from the six-loop RG expansion for $β$-function is reported. Numerical results are presented for $0 \le n \le 64$ with main attention paid to physically important cases $n = 0, 1, 2, 3$. Pseudo-$ε$ expansions for quartic and sextic couplings have rapidly diminishing coefficients, so Padé resummation turns out to be sufficient to yield high-precision numerical estimates. Moreover, direct summation of these series with optimal truncation gives the values of $g_4^*$ and $R_6^*$ almost as accurate as those provided by Padé technique. Pseudo-$ε$ expansion estimates for $g_8^*$ and $R_8^*$ are found to be much worse than that for the lower-order couplings independently on the resummation method employed. Numerical effectiveness of the pseudo-$ε$ expansion approach in two dimensions is also studied. Pseudo-$ε$ expansion for $g_4^*$ originating from the five-loop RG series for $β$-function of 2D $λϕ^4$ field theory is used to get numerical estimates for $n$ ranging from 0 to 64. The approach discussed gives accurate enough values of $g_{4}^*$ down to $n = 2$ and leads to fair estimates for Ising and polymer ($n = 0$) models.

cond-mat.stat-mech↗