Geometry, thermodynamics, and finite-size corrections in the critical Potts model

We establish an intriguing connection between geometry and thermodynamics in the critical q-state Potts model on two-dimensional lattices, using the q-state bond-correlated percolation model (QBCPM) representation. We find that the number of clusters of the QBCPM has an energy-like singularity for q different from 1, which is reached and supported by exact results, numerical simulation, and scaling arguments. We also establish that the finite-size correction to the number of bonds, has no constant term and explains the divergence of related quantities as q --> 4, the multicritical point. Similar analyses are applicable to a variety of other systems.Comment: 12 pages, 6 figure

Universality of the Crossing Probability for the Potts Model for q=1,2,3,4

The universality of the crossing probability $\pi_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for percolation $q=1$. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction $\pi_{hs}$ has universal form $\pi_{hs}=A(q) Q(z)$ for $q=1,2,3,4$ as a function of the scaling variable $z= [ b(q)L^{\frac{1}{\nu(q)}}(p-p_{c}(q,L)) ]^{\zeta(q)}$. Here, $p=1-\exp(-\beta)$ is the probability of a bond to be closed, $A(q)$ is the nonuniversal crossing amplitude, $b(q)$ is the nonuniversal metric factor, $\zeta(q)$ is the nonuniversal scaling index, $\nu(q)$ is the correlation length index. The universal function $Q(x) \simeq \exp(-z)$. Nonuniversal scaling factors were found numerically.Comment: 15 pages, 3 figures, revtex4b, (minor errors in text fixed, journal-ref added

Study of the influence of temperature on the measurement accuracy of transit-time ultrasonic flowmeters

Purpose: The purpose of this study is to deal largely with the influence of temperature variation on the measurement accuracy of transit-time ultrasonic flowmeter. Design/methodology/approach: The causes of measurement error due to temperature are qualitatively and quantitatively analyzed, and a mathematical model is established. The experimental data are processed and analyzed, and the temperature compensation coefficient of flow measurement is obtained. Findings: The experimental results show that the flow measurement results by temperature compensation are helpful in improving the measurement accuracy of the ultrasonic flowmeter. Practical implications: This study has certain application value, which can provide theoretical support for the design of high-precision ultrasonic flowmeters and design guidance. Originality/value: It is worth emphasizing that there are few research studies on the influence factors of temperature. This paper focuses on the influence of the temperature change on the flowmeter that is modeled, and the high precision flow parameter test system is designed based on the established model

Novel annular flow electromagnetic measurement system for drilling engineering

Downhole micro-flux control drilling technology can effectively solve drilling accidents, such as kick and loss in narrow density window drilling scenarios. Using a downhole annular flow measurement system to obtain real-time information of downhole annular flow is the core and foundation of downhole micro-flux control drilling technology. The research work of electromagnetic flowmeters in recent years creates a challenge for downhole annular flow measurement. This paper proposes a new method for an annular flow measurement system based on the electromagnetic induction principle. First, the annular flow measuring principle, the weight function, the density of virtual current, and the magnetic field of the annular flow electromagnetic measurement system are described. Second, the basic design of the annular flow electromagnetic measurement system is described. Third, model simulation and dynamic experiments on an annular flow electromagnetic measurement system are carried out. The simulation and experimental results show a linear relationship between the system output and the annular flow rate, and also verify the correctness of annular flow electromagnetic measurement theory

Relation between Tunneling and Particle Production in Vacuum Decay

The field-theoretical description of quantum fluctuations on the background of a tunneling field $\sigma$ is revisited in the case of a functional Schrodinger approach. We apply this method in the case when quantum fluctuations are coupled to the $\sigma$ field through a mass-squared term, which is 'time-dependent' since we include the dynamics of $\sigma$ . The resulting mode functions of the fluctuation field, which determine the quantum state after tunneling, display a previously unseen resonance effect when their mode number is comparable to the curvature scale of the bubble. A detailed analysis of the relation between the excitations of the field about the true vacuum (interpreted as particle creation) and the phase shift coming from tunneling is presented.Comment: 20 pages, 4 figures, submitted to PR

Non-ideality of quantum operations with the electron spin of a 31P donor in a Si crystal due to interaction with a nuclear spin system

We examine a 31P donor electron spin in a Si crystal to be used for the purposes of quantum computation. The interaction with an uncontrolled system of 29Si nuclear spins influences the electron spin dynamics appreciably. The hyperfine field at the 29Si nuclei positions is non-collinear with the external magnetic field. Quantum operations with the electron wave function, i.e. using magnetic field pulses or electrical gates, change the orientation of hyperfine field and disturb the nuclear spin system. This disturbance produces a deviation of the electron spin qubit from an ideal state, at a short time scale in comparison with the nuclear spin diffusion time. For H_ext=9 T, the estimated error rate is comparable to the threshold value required by the quantum error correction algorithms. The rate is lower at higher external magnetic fields.Comment: 11 pages, 2 figure

A novel layer-structured PtN₂: first-principles calculations

Platinum nitride as the first successfully synthesized noble metal nitride shows superior mechanical properties and exotic electronic structure that rival those of conventional transition metal nitrides. In the past diverse crystal structures have been proposed to understand its unusual properties. However, very few works pay attention to the dynamic stability of these phases. Here, we examine the potential structures of platinum nitride with a chemical composition of PtN₂ by utilizing a widely adopted evolutionary methodology for crystal structure prediction. Except reproducing the previously proposed phases, we also identify a Pmmm symmetric novel layer structure with a low formation enthalpy that is slightly lower than those of marcasite and CoSb₂ structures but slightly higher than that of pyrite structure. The elastic constants and the lattice dynamical calculations show that this layer-structured PtN₂ is mechanically and dynamically stable. The calculated band structures suggest this new phase together with the simple tetragonal phase are metallic, while other phases are insulators. In addition, it is found that the fluorite structure is dynamically unstable by the phonon spectrum calculations, although it is mechanically stable as suggested by calculated elastic constants.Розглянуто потенційні структури нітриду платини з хімічним складом PtN₂, використовуючи широко прийняту еволюційну методологію прогнозування кристалічних структур. Крім відтворення раніше запропонованих фаз, ідентифіковано нову симетричну шарувату структуру, просторова група Pmmm, з низькою ентальпією формування, яка трохи менша, ніж ентальпії структур марказиту і CoSb₂, але дещо більша, ніж ентальпія структури піриту. Постійні пружності і динамічні розрахунки решітки показують, що цей нітрид платини (PtN₂) з шаруватою структурою механічно і динамічно стабільний. Розраховані зонні структури дозволяють припустити, що ця нова фаза разом з простою тетрагональною фазою є металічною, тоді як інші фази є діелектричні. Розрахунками фононного спектру встановлено, що структура флюориту динамічно нестабільна, хоча механічно стабільна, як передбачається розрахованими константами пружності.Рассмотрены потенциальные структуры нитрида платины с химическим составом PtN₂, используя широко принятую эволюционную методологию прогнозирования кристаллических структур. Кроме воспроизведения ранее предложенных фаз, идентифировано новую симметричную слоистую структуру, пространственная группа Pmmm, с низкой энтальпией формирования, которая немного меньше, чем энтальпии структур марказита и CoSb₂, но немного больше, чем энтальпия структуры пирита. Постоянные упругости и динамические расчеты решетки показывают, что этот нитрид платины (PtN₂) со слоистой структурой механически и динамически стабилен. Рассчитанные зонные структуры позволяют предположить, что эта новая фаза вместе с простой тетрагональной фазой является металлической, тогда как другие фазы являются диэлектрическими. Расчетами фононного спектра установлено, что структура флюорита динамически нестабильна, хотя механически стабильна, как предполагается рассчитанными константами упругости

Global Solution to the Three-Dimensional Incompressible Flow of Liquid Crystals

The equations for the three-dimensional incompressible flow of liquid crystals are considered in a smooth bounded domain. The existence and uniqueness of the global strong solution with small initial data are established. It is also proved that when the strong solution exists, all the global weak solutions constructed in [16] must be equal to the unique strong solution

Open-closed field algebras

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a \C-extension of the Swiss-cheese partial operad. We also give a tensor categorical formulation and categorical constructions of open-closed field algebras over V.Comment: 55 pages, largely revised, an old subsection is deleted, a few references are adde

Free field realization of SL(2) correlators for admissible representations, and hamiltonian reduction for correlators

Talk presented by J.L. Petersen at the 29th Symposium Ahrenshop, Buckow August 29-September 2, 1995. A presentation is given of the free field realization relevant to SL(2) WZW theories with a Hilbert space based on admissible representations. It is known that this implies the presence of two screening charges, one involving a fractional power of a free field. We develop the use of fractional calculus for treating in general such cases. We derive explicit integral representations of $N$-point conformal blocks. We show that they satisfy the Knizhnik-Zamolodchikov equations and we prove how they are related to minimal conformal blocks via a formulation of hamiltonian reduction advocated by Furlan, Ganchev, Paunov and Petkova.Comment: 8 pages, LaTeX, article.sty, espcrc2.st