Volume Form Factors Research Articles

Finite volume form factors in integrable theories

We develop a new method to calculate finite size corrections for form factors in two-dimensional integrable quantum field theories. We extract these corrections from the excited state expectation value of bilocal operators in the limit when the operators are far apart. We elaborate the finite size effects explicitly up to the 3rd Lüscher order and conjecture the structure of the general form. We also fully recover the explicitly known massive fermion finite volume form factors.

Study of the Performance of a Photovoltaic Solar Panel by Using a Nanofluid as a Cooler

Abstract In this paper, we study by numerical simulation, the cooling of a solar photovoltaic panel using a nanofluid as a cooler. The solar panel is subjected to a hot temperature that character-ises the climate of the city of Bechar located in southwestern Algeria. The nanofluid (Al2O3-water) is introduced in the cavity with a constant horizontal speed and subjected to the ambient (cold) temperature. The equations governing the hydrodynamics of the flow and the heat transfer are described by the Navier-Stockes and energy equations. The finite element method is used to solve the system of partial differential equations (PDEs) based on the Galerkin method. We consider the effect of solid volume fraction and form factor for different values of Reynolds number on the results in the form of isotherms, streamlines, temperature, velocity, average Nusselt numbers and solar panel efficiency.

Age Contributes to Volume Estimation and Form Factor of Pinus Pseudostrobus Lindley in Commercial Forest Plantations from Western Mexico

ABSTRACT Sectional equations and mathematical volume models are a reliable way to estimate carbon sequestration and storage, which is a key foundation for forest management and conservation. The objective of this study was to assess stem volume and form factor through the classical sectional method to then, using five regression models commonly used for forest management, identify the most suitable mathematical model to estimate the stem volume in a commercial forest plantation (CFP) of Pinus pseudostrobus Lindley in the Comunidad Indígena de Nuevo San Juan Parangaricutiro, Michoacán, in Western Mexico. By using 10, 15 and 20 yr.-old sampling points and two sampling methods (destructive and nondestructive), we found a form factor 0.42, 0.48 and 0.51 and stem volume of 0.098 m3, 0.400 m3 and 0.804 m3 for the three ages assessed, which presented diameter classes (DC), from 10 to 45 cm. The mathematical models identified that age of plantation determines stem volume and form factor, and the models that best fit volume estimation were the Schumacher-Hall model and the Australian model with an R2 adj range between 0.89 and 0.99. Estimation of stem volume is of vital importance to assess the income generated by the timber industry, and relevant for forest conservation, management, and carbon sequestration studies.

Individual Tree Volume Models and Form Factors for Woody Species in Dry Afromontane Forest, Central Ethiopia

Individual Tree Volume Models and Form Factors for Woody Species in Dry Afromontane Forest, Central Ethiopia

Height, volume and form factor equations for Tectona grandis L.f. in Alta Floresta (MT)

Studies on allometric models are essential for quantifying the potential of a stand, especially when the objective is to know the wood stock through estimates. This study aimed to select height, volume and artificial form factor equations for a teak stand with data from a sample with 81 trees at 96 months in different diameter classes. The correlation analysis was performed between the variables total height, diameter with and without bark at 1.30 m soil height (dbhcc and dbhsc), total volume with and without bark (VTcc and VTsc) and artificial form factor with and without bark (ffcc and ffsc), using the Pearson coefficient. Six models were evaluated for each category: height, volume and artificial form factor, which were selected by the following criteria: analysis of variance, adjusted coefficient of determination, standard error of estimate, Akaike information criterion and graphical analysis of residues. The selected equations were validated by applying the L & O test. The variables dbhcc, dbhsc, HT, VTcc and VTsc presented significant correlations, ranging from moderate to very strong, the others presented weak correlation. The model that presented the best relation of total height to diameter was the model of Azevedo and contributors. For the total volume with and without bark, Schumacher and Hall model in its logarithmic form was the one that presented the best results. The adjusted models for artificial form factor did not present satisfactory results and, therefore, the use of average form factor is recommended. The mean form factor values by diameter class ranged from 0.4498 to 0.7139 and 0.4480 to 0.7075 for diameter with and without bark, respectively.

A Review on the Potential of Forest Biomass for Bioenergy in Australia

The use of forest biomass for bioenergy in Australia represents only 1% of total energy production but is being recognized for having the potential to deliver low-cost and low-emission, renewable energy solutions. This review addresses the potential of forest biomass for bioenergy production in Australia relative to the amount of biomass energy measures available for production, harvest and transport, conversion, distribution and emission. Thirty-Five Australian studies on forest biomass for bioenergy are reviewed and categorized under five hierarchical terms delimiting the level of assessment on the biomass potential. Most of these studies assess the amount of biomass at a production level using measures such as the allometric volume equation and form factor assumptions linked to forest inventory data or applied in-field weighing of samples to predict the theoretical potential of forest biomass across an area or region. However, when estimating the potential of forest biomass for bioenergy production, it is essential to consider the entire supply chain that includes many limitations and reductions on the recovery of the forest biomass from production in the field to distribution to the network. This review reiterated definitions for theoretical, available, technological, economic and environmental biomass potential and identified missing links between them in the Australian literature. There is a need for further research on the forest biomass potential to explore lower cost and lowest net emission solutions as a replacement to fossil resources for energy production in Australia but methods the could provide promising solutions are available and can be applied to address this gap.

Leading exponential finite size corrections for non-diagonal form factors

We derive the leading exponential finite volume corrections in two dimensional integrable models for non-diagonal form factors in diagonally scattering theories. These formulas are expressed in terms of the infinite volume form factors and scattering matrices. If the particles are bound states then the leading exponential finite-size corrections (μ-terms) are related to virtual processes in which the particles disintegrate into their constituents. For non-bound state particles the leading exponential finite-size corrections (F-terms) come from virtual particles traveling around the finite world. In these F-terms a specifically regulated infinite volume form factor is integrated for the momenta of the virtual particles. The F-term is also present for bound states and the μ-term can be obtained by taking an appropriate residue of the F-term integral. We check our results numerically in the Lee-Yang and sinh-Gordon models based on newly developed Hamiltonian truncations.

On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin 1/2 chain

This work constructs a well-defined and operational form factor expansion in a model having a massless spectrum of excitations. More precisely, the dynamic two-point functions in the massless regime of the XXZ spin-1/2 chain are expressed in terms of a properly regularised series of multiple integrals. These series are obtained by taking, in an appropriate way, the thermodynamic limit of the finite volume form factor expansions. The series are structured in a way allowing one to identify directly the contributions to the correlator stemming from the conformal-type excitations on the Fermi surface and those issuing from the massive excitations (deep holes, particles, and bound states). The obtained form factor series opens up the possibility of a systematic and exact study of asymptotic regimes of dynamical correlation functions in the massless regime of the XXZ spin 1/2 chain. Furthermore, the assumptions on the microscopic structure of the model’s Hilbert space that are necessary so as to write down the series appear to be compatible with any model—not necessarily integrable—belonging to the Luttinger liquid universality class. Thus, the present analysis also provides the phenomenological structure of form factor expansions in massless models belonging to this universality class.

Field theoretical derivation of L\xfcscher\u2019s formula and calculation of finite volume form factors

We initiate a systematic method to calculate both the finite volume energy levels and form factors from the momentum space finite volume two-point function. By expanding the two point function in the volume we extracted the leading exponential volume correction both to the energy of a moving particle state and to the simplest non-diagonal form factor. The form factor corrections are given in terms of a regularized infinite volume 3-particle form factor and terms related to the Lüsher correction of the momentum quantization. We tested these results against second order Lagrangian and Hamiltonian perturbation theory in the sinh-Gordon theory and we obtained perfect agreement.

Lattice approach to finite volume form-factors of the Massive Thirring (Sine-Gordon) model

In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method, admits an appropriate framework for computing the finite volume form-factors of local operators of the model. In this work we compute the finite volume diagonal matrix elements of the U(1) conserved current in the pure soliton sector of the theory. Based on the systematic large volume expansion of our results, we conjecture an exact expression for the finite volume expectation values of local operators in pure soliton states. At large volume in leading order these expectation values have the same form as in purely elastic scattering theories, but exponentially small corrections differ from previous Thermodynamic Bethe Ansatz conjectures of purely elastic scattering theories.

Microscopic approach to a class of 1D quantum critical models

Starting from the finite volume form factors of local operators, we show how and under which hypothesis the c = 1 free boson conformal field theory in two-dimensions emerges as an effective theory governing the large-distance regime of multi-point correlation functions for a large class of one-dimensional massless quantum Hamiltonians. In our approach, in the large-distance critical regime, the local operators of the initial model are represented by well suited vertex operators associated to the free boson model. This provides an effective field theoretic description of the large distance behaviour of correlation functions in 1D quantum critical models. We develop this description starting from the first principles and directly at the microscopic level, namely in terms of the properties of the finite volume matrix elements of local operators.

Diagonal form factors and heavy-heavy-light three-point functions at weak coupling

In this paper we consider a special kind of three-point functions of HHL type at weak coupling in N=4 SYM theory and analyze its volume dependence. At strong coupling this kind of three-point functions were studied recently by Bajnok, Janik and Wereszczynski [1]. The authors considered some cases of HHL correlator in the su(2) sector and, relying on their explicit results, formulated a conjecture about the form of the volume dependence of the symmetric HHL structure constant to be valid at any coupling up to wrapping corrections. In order to test this hypothesis we considered the HHL correlator in su(2) sector at weak coupling and directly showed that, up to one loop, the finite volume dependence has exactly the form proposed in [1]. Another side of the conjecture suggests that computation of the symmetric structure constant is equivalent to computing the corresponding set of infinite volume form factors, which can be extracted as the coefficients of finite volume expansion. In this sense, extracting appropriate coefficients from our result gives a prediction for the corresponding infinite volume form factors.

Heat Capacity and Thermal Conductivity of Fabrics Based on Chemical Fibers

We present the results of an experimental study of the effective thermal conductivity and specific heat capacity of fabrics made from chemical fibers having different structures, in the bulk density range 383-606 kg/m3. We give equations for determining the effective thermal conductivity coefficient and the effective internal surface of the material, obtained on the basis of a macroquantum transfer mechanism. We give an example of a calculation using these equations. We describe and analyze the new parameters: the relaxation coefficients, the temperature and volume form factor for the macrocell. The results obtained for all the studied materials are generalized as a dependence of the thermal conductivity coefficient on a combination of physical constants.

Finite volume form factors in the presence of integrable defects

We developed the theory of finite volume form factors in the presence of integrable defects. These finite volume form factors are expressed in terms of the infinite volume form factors and the finite volume density of states and incorporate all polynomial corrections in the inverse of the volume. We tested our results, in the defect Lee–Yang model, against numerical data obtained by truncated conformal space approach (TCSA), which we improved by renormalization group methods adopted to the defect case. To perform these checks we determined the infinite volume defect form factors in the Lee–Yang model exactly, including their vacuum expectation values. We used these data to calculate the two point functions, which we compared, at short distance, to defect CFT. We also derived explicit expressions for the exact finite volume one point functions, which we checked numerically. In all of these comparisons excellent agreement was found.

On form factors in nested Bethe Ansatz systems

We investigate form factors of local operators in a multi-component quantum nonlinear Schrödinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using the coordinate Bethe Ansatz solution and establish a connection with the finite volume matrix elements. In the two-component models we derive a set of recursion relations for the ‘magnonic form factors’, which are the matrix elements on the nested Bethe Ansatz states. In certain simple cases (involving states with only one spin-impurity), we obtain explicit solutions for the recursion relations.

Моделирование демпфирующей способности графитизированных чугунов

The statistical model is designed in order to assess the relative contribution to the energy dissipation parameters of graphite in-clusions, which include the volume fraction, size, form factor and specific interphase surface "inclusion-matrix". Estimation of the parameters of graphite inclusions in cast irons is carried out using automated image analyzer and software package.

Can High Density 3D Through Silicon Stacking Replace Lithography-Driven CMOS Scaling as the Engine for the Semiconductor Industry?

High density 3D Through Silicon Stacking (TSS) offers opportunities for form factor miniaturization, cost reduction, and performance and energy improvement for advanced semiconductor systems. We will explore the value propositions for TSS compared to CMOS scaling to consider if TSS could replace lithography-driven CMOS scaling as the engine for the semiconductor industry. TSS can provide major reduction in volume form factor compared to 2D CMOS scaling. As the industry moves to advanced lithography and complex device structures at 16nm and below, the cost improvement resulting from CMOS scaling is expected to diminish. The cost reduction opportunities of TSS compared to traditional System on Chip (SOC) solutions enabled by lithography-driven CMOS scaling will be explored. The realized technology value propositions are strongly dependent on the specific system architecture and application. Architectural and software innovation enabled by HD 3D TSS and Architectural Pathfinding could provide an additional vector for continuing the improvements from semiconductor miniaturization.

Lüscher's μ-term and finite volume bootstrap principle for scattering states and form factors

We study the leading order finite size correction (Lüscher's μ-term) associated to moving one-particle states, arbitrary scattering states and finite volume form factors in ( 1 + 1 ) -dimensional integrable models. Our method is based on the idea that the μ-term is intimately connected to the inner structure of the particles, i.e., their composition under the bootstrap program. We use an appropriate analytic continuation of the Bethe–Yang equations to quantize bound states in finite volume and obtain the leading μ-term (associated to symmetric particle fusions) by calculating the deviations from the predictions of the ordinary Bethe–Yang quantization. Our results are compared to numerical data of the E 8 scattering theory obtained by truncated fermionic space approach. As a by-product it is shown that the bound state quantization does not only yield the correct μ-term, but also provides the sum over a subset of higher order corrections as well.

Pion polarizabilities and volume effects in lattice QCD

We use chiral perturbation theory to study the extraction of pion electromagnetic polarizabilities from lattice QCD. Chiral extrapolation formulae are derived for partially quenched QCD, and quenched QCD simulations. On a torus, volume dependence of electromagnetic current correlators is complicated by $SO(4)$ breaking, as well as photon zero-mode interactions. We determine finite volume corrections to the Compton scattering tensor of pions. We argue, however, that such results cannot be used to ascertain volume corrections to polarizabilities determined in lattice QCD with background field methods. Connection is lacking because small momentum expansions are not permitted in finite volume. Our argument also applies to form factors. Volume effects for background field calculations of electromagnetic moments cannot be deduced from finite volume form factors.

Form factors in finite volume I: Form factor bootstrap and truncated conformal space

We describe the volume dependence of matrix elements of local fields to all orders in inverse powers of the volume (i.e., only neglecting contributions that decay exponentially with volume). Using the scaling Lee–Yang model and the Ising model in a magnetic field as testing ground, we compare them to matrix elements extracted in finite volume using truncated conformal space approach to exact form factors obtained using the bootstrap method. We obtain solid confirmation for the form factor bootstrap, which is different from all previously available tests in that it is a non-perturbative and direct comparison of exact form factors to multi-particle matrix elements of local operators, computed from the Hamiltonian formulation of the quantum field theory. We also demonstrate that combining form factor bootstrap and truncated conformal space is an effective method for evaluating finite volume form factors in integrable field theories over the whole range in volume.