Exact Mapping Research Articles

Hydrogeological characteristics of some deep siphonal springs in Serbia and Montenegro karst

In terms of hydrogeological, engineering-geological, and hydrotechnical tapping in karst in relation to ground waters, karst channels, springs and ponors, speleodiving is the only research method which enables direct observation, studying and exact geological mapping of karst channels and caverns. Data collected during speleodiving research contribute considerably to the analysis of karst evolution process in the given region, which is very important in evaluating the depth of karstification and determining the main direction of the groundwater flow. In the past 30 years in Serbia and Montenegro, speleodivers have investigated over 40 siphonal springs, active cave channels and ponors, of which more than 20 are proof of deep siphonal circulation in karstic aquifers. The karstic springs are the most interesting phenomenon from a hydrogeological view point, and their investigations need particular attention. Most of significant karstic springs are on the rims of erosion basins—perimeters of karst poljes, river valleys, sea coasts and contact areas between karst aquifers and hydrogeological barriers. General characteristics of the spring regime are the direct correlation between precipitation and spring discharge. Moreover, the hydrogeological regime of these springs also depends on the size of the catchment area, karstic aquifer retardation capacity, total porosity, as well as lithological and structural characteristics.

Critical exponents for higher-representation sources in 3D SU(3) gauge theory from CFT

We establish an exact mapping between the multiplication table of the irreducible representations of SU(3) and the fusion algebra of the two-dimensional conformal field theory in the same universality class of 3D SU(3) gauge theory at the deconfining point. In this way the Svetitsky-Yaffe conjecture on the critical behaviour of Polyakov lines in the fundamental representation naturally extends to whatever representation one considers. As a consequence, the critical exponents of the correlators of these Polyakov lines are determined. Monte Carlo simulations with sources in the symmetric two-index representation, combined with finite-size scaling analysis, compare very favourably with these predictions.

Non-perturbative renormalization group for simple fluids

We present a new non-perturbative renormalization group for classical simple fluids. The theory is built in the Grand Canonical ensemble and also in the framework of two equivalent scalar field theories. The exact mapping between the three renormalization flows is established rigorously. In the Grand Canonical ensemble the theory may be seen as an extension of the Hierarchical Reference Theory [Adv. Phys. 44, 211 (1995)] but, however, does not suffer from its shortcomings at subcritical temperatures. In the framework of a new canonical field theory for the liquid state developed with that aim, our construction identifies with the effective average action approach developed recently [Phys. Rep. 363 (2002)].

K-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects

We develop the theory of the -core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the -core percolation is an unusual, hybrid phase transition with a jump emergence of the k-core as at a first order phase transition but also with a critical singularity as at a continuous transition. We describe the properties of the -core, explain the meaning of the order parameter for the k-core percolation, and reveal the origin of the specific critical phenomena. We demonstrate that a so-called "corona" of the k-core plays a crucial role (corona is a subset of vertices in the k-core which have exactly neighbors in the -core). It turns out that the k-core percolation threshold is at the same time the percolation threshold of finite corona clusters. The mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point. We show that a random removal of even one vertex from the k-core may result in the collapse of a vast region of the k-core around the removed vertex. The mean size of this region diverges at the critical point. We find an exact mapping of the k-core percolation to a model of cooperative relaxation. This model undergoes critical relaxation with a divergent rate at some critical moment.

Erfolgreiche Ablation einer rechts-lateralen akzessorischen Leitungsbahn unter kombiniertem Einsatz einer langen intrakardialen Schleuse und eines intrakoronaren Mapping-Katheters in der rechten Kranzarterie

We present a patient with an accessory pathway difficult to ablate in the right free wall. Two prolonged and failed attempts at radiofrequency catheter ablation of this accessory pathway in other institutions led to a third attempt in our hospital. Successful outcome of accessory pathway ablation was achieved by mapping the right free wall using an intracoronary catheter in the right coronary artery. A long vascular sheeth was introduced in the right femoral vein, manipulated into the tricuspid anulus, which allowed a stable catheter position with adequate tissue contact of the ablation catheter at the target site. The combination of exact mapping and adequate tissue contact of the ablation catheter as described above facilitated successful outcome in this patient. Further investigation is necessary to determine the role of this technique as first choice therapy in patients prone to develop recurrence of accessory pathway conduction or primary failure of catheter ablation.

Mappings between reaction–diffusion and kinetically constrained systems:A+A ↔ A and the Fredrickson–Andersen model have upper critical dimensiondc = 2

We present an exact mapping between two simple spin models: the Fredrickson–Andersen(FA) model and a model of annihilating random walks with spontaneous creation from thevacuum, A + A ↔ 0. We discuss the geometric structure of the mapping and its consequences for symmetriesof the models. Hence we are able to show that the upper critical dimension of the FAmodel is two, and that critical exponents are known exactly in all dimensions.These conclusions also generalize to a mapping between A + A ↔ 0 and the reaction–diffusion system in which the reactions are branching and coagulation,A + A ↔ A. We discuss the relation of our analysis to earlier work, and explain why themodels considered do not fall into the directed percolation universality class.

Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures

Correlation functions related to the dynamic density response of the one-dimensional Bose gas in the model of Lieb and Liniger are calculated. An exact Bose-Fermi mapping is used to work in a fermionic representation with a pseudopotential Hamiltonian. The Hartree-Fock and generalized random phase approximations are derived and the dynamic polarizability is calculated. The results are valid to first order in 1/\gamma where \gamma is Lieb-Liniger coupling parameter. Approximations for the dynamic and static structure factor at finite temperature are presented. The results preclude superfluidity at any finite temperature in the large-\gamma regime due to the Landau criterion. Due to the exact Bose-Fermi duality, the results apply for spinless fermions with weak p-wave interactions as well as for strongly interacting bosons.

Phonon effects in tunnelling through a double quantum dot molecule

Phonon effects in tunnelling through a double quantum dot molecule are investigated by use of a recently developed technique, which is based on an exact mapping of a many-body electron-phonon interaction problem onto a multichannel one-body problem. The molecule is sandwiched between two ideal electrodes and the electron at each dot of the molecule interacts independently with Einstein phonons. Single-electron transmission rates through the molecule are computed and the nonlinear spectrum obtained shows a structure with many more satellite peaks due to the excitations of phonons. The strength of resonant peaks is found to be strongly dependent on the number of excited phonons. The effects of electron-phonon interaction on the current and shot noise, depending on the voltage bias applied at the two electrodes as well as the potential energy of the molecule, are discussed.

Topological mass mechanism and exact fields mapping

We present a class of mappings between models with topological mass mechanism and purely topological models in arbitrary dimensions. These mappings are established by directly mapping the fields of one model in terms of the fields of the other model in closed expressions. These expressions provide the mappings of their actions as well as the mappings of their propagators. For a general class of models in which the topological model becomes the BF model the mappings present arbitrary functions which otherwise are absent for Chern-Simons like actions. This work generalizes the results of [1] for arbitrary dimensions.

Exact mappings between fermionic Ising spin-glass and classical spin-glass models

We present in this paper exact analytical expressions for the thermodynamical properties and Green functions of a certain family of fermionic Ising spin-glass models with Hubbard interaction, by noticing that their Hamiltonian is a function of the number operator only. The thermodynamical properties are mapped to the classical Ghatak-Sherrington spin-glass model while the the Density of States (DoS) is related to its joint spin-field distribution. We discuss the presence of the pseudogap in the DoS with the help of this mapping.

Fractional-filling Mott domains in two-dimensional optical superlattices

Ultracold bosons in optical superlattices are expected to exhibit fractional-filling insulating phases for sufficiently large repulsive interactions. On strictly one-dimensional systems, the exact mapping between hard-core bosons and free spinless fermions shows that any periodic modulation in the lattice parameters causes the presence of fractional-filling insulator domains. Here, we focus on two recently proposed realistic two-dimensional structures where such mapping does not hold, i.e., the two-leg ladder and the trimerized kagom\'e lattice. Based on a cell strong-coupling perturbation technique, we provide quantitatively satisfactory phase diagrams for these structures, and give estimates for the occurrence of the fractional-filling insulator domains in terms of the intercell to intracell hopping amplitude ratio.

Exact results of a mixed spin-1/2 and spin- S Ising model on a bathroom tile (4–8) lattice: Effect of uniaxial single-ion anisotropy

Effect of uniaxial single-ion anisotropy upon magnetic properties of a mixed spin-1/2 and spin- S ( S ⩾ 1 ) Ising model on a bathroom tile (4–8) lattice is examined within the framework of an exact star-triangle mapping transformation. Particular attention is focused on the phase diagrams established for several values of the quantum spin number S. It is shown that the mixed-spin bathroom tile lattice exhibits very similar phase boundaries as the mixed-spin honeycomb lattice whose critical points are merely slightly enhanced with respect to the former ones. The influence of uniaxial single-ion anisotropy upon the total magnetization vs. temperature dependence is particularly investigated as well.

Magnetic properties of a mixed spin- [formula omitted] and spin- [formula omitted] Ising model with an uniaxial and biaxial crystal-field potential

Magnetic properties of a mixed spin- 1 2 and spin- 3 2 Ising model on honeycomb lattice are investigated within the framework of an exact star-triangle mapping transformation. The particular attention is focused on the effect of uniaxial and biaxial crystal-field potentials that basically influence a magnetic behavior of the spin- 3 2 atoms. Our results for basic thermodynamic quantities as well as dynamical time-dependent autocorrelation function indicate a spin tunneling between | ± 3 2 〉 and | ∓ 1 2 〉 states in two different magnetically ordered phases OP 1 and OP 2, respectively.

Correlation between clinical and histological features in a pig model of choroidal neovascularization

To analyse the histological changes in the retina and the choroid in a pig model of choroidal neovascularization (CNV) and to correlate these findings with fundus photographic and fluorescein angiographic features. CNV was induced by surgical removal of the retinal pigment epithelium (RPE) and perforation of Bruch's membrane in four pig eyes. In addition, two eyes had an amniotic membrane implanted in the subretinal space. Retinal landmarks such as arterioles, crossing of vessels and the optic nerve were used to obtain an exact mapping of histological findings on colour fundus photographs (FPs) and fluorescein angiograms (FAs). We analysed the appearance on the FPs and FAs of the following histological features: CNV, hypo/hyperpigmented RPE, and pathological changes to the retina and choroid. CNV was found in all eyes and correlated to areas with late staining but no leakage in the FAs. Areas of hypopigmented RPE were identified and corresponded to window defects in the FAs. Where fibrovascular tissue was covered with hyperpigmented RPE, blocked fluorescence was found on the FAs. The implanted amniotic membrane showed staining but no leakage in the FAs. In a pig model of surgically induced CNV, histological mapping was used to make clinicopathological correlations of the following lesion components: CNV, window defects, blocked fluorescence. Our findings give a more solid foundation for interpretation of fluorescein angiograms in pig models.

Thermodynamic properties of a tetramer Ising-Heisenberg bond-alternating chain as a model system forCu(3−Chloropyridine)2(N3)2

Thermodynamic properties of a tetramer ferro-ferro-antiferro-antiferromagnetic Ising-Heisenberg bond alternating chain are investigated by the use of an exact mapping transformation technique. Exact results for the magnetization, susceptibility and specific heat in the zero as well as nonzero magnetic field are presented and discussed in detail. The results obtained from the mapping are compared with the relevant experimental data of Cu(3-Clpy)$_2$(N$_3$)$_2$ (3-Clpy=3-Chloropyridine).

Role of solvent for globular proteins in solution

The properties of the solvent affect the behavior of the solution. We propose a model that accounts for the contribution of the solvent free energy to the free energy of globular proteins in solution. For the case of an attractive square-well potential, we obtain an exact mapping of the phase diagram of this model without solvent to the model that includes the solute-solvent contribution. In particular we find for appropriate choices of parameters upper critical points, lower critical points, and even closed loops with both upper and lower critical points similar to those found before [Macromolecules 36, 5843 (2003)]. In the general case of systems whose interactions are not attractive square wells, this mapping procedure can be a first approximation to understand the phase diagram in the presence of solvent. We also present simulation results for both the square-well model and a modified Lennard-Jones model.

Spectroscopy of a driven solid-state qubit coupled to a structured environment

We study the asymptotic dynamics of a driven spin-boson system where the environment is formed by a broadened localized mode. Upon exploiting an exact mapping, an equivalent formulation of the problem in terms of a quantum two-state system (qubit) coupled to a harmonic oscillator which is itself Ohmically damped, is found. We calculate the asymptotic population difference of the two states in two complementary parameter regimes. For weak damping and low temperature, a perturbative Floquet-Born-Markovian master equation for the qubit-oscillator system can be solved. We find multi-photon resonances corresponding to transitions in the coupled quantum system and calculate their line-shape analytically. In the complementary parameter regime of strong damping and/or high temperatures, non-perturbative real-time path integral techniques yield analytic results for the resonance line shape. In both regimes, we find very good agreement with exact results obtained from a numerical real-time path-integral approach. Finally, we show for the case of strong detuning between qubit and oscillator that the width of the $n$-photon resonance scales with the $n$-th Bessel function of the driving strength in the weak-damping regime.

Reentrant transitions of a mixed-spin Ising model on the diced lattice

Magnetic behaviour of a mixed spin-1/2 and spin-1 Ising model on the diced lattice is studied using an exact star-triangle mapping transformation. It is found that the uniaxial as well as biaxial single-ion anisotropy acting on the spin-1 sites may potentially cause a reentrant transition with two consecutive critical points. Contrary to this, the effect of next-nearest-neighbour interaction between the spin-1/2 sites possibly leads to a reentrant transition with three critical temperatures in addition to the one with two critical points only. The shape of the total magnetization versus temperature dependence is particularly investigated for the case of ferrimagnetically ordered system.

Path Concentration Distribution of Toluene using Remote Sensing FTIR and One-Dimensional Reconstruction Method

A one-dimensional mapping technique coupled with Open-Path remote sensing FTIR was presented in this article. This technique was applied to one of the air toxic volatile organic compounds (VOCs)-toluene. The Path Integrated Concentrations (PICs) of toluene in different path lengths along one beam path were fitted by polynomial fitting method with degrees from 3 to 7. The 6th degree polynomial fitting showed the best fitting result. Moreover, the methods of reconstructing path concentration distribution along the beam path by applying a Gaussian model and the derivative of 6th degree polynomial fitting function were established in this article. The reconstructed concentrations of toluene along the beam path by the two methods were experimentally close. Results showed that the concentration peaks were at 1.05 and 2.40 m from the instrument by applying the Gaussian model with the maximum concentration of 0.85 and 3.19 ppm, and at 0.99 and 2.49 m from the instrument with the maximum concentration of 0.78 and 2.80 ppm by applying the 6th polynomial fitting function. It was obvious that the reconstruction results by these two methods were very close. This approach could be appreciated for its fast calculation, exact peak location orientation and concentration flow tendency mapping. In can be concluded that this method can provide the path concentration distributions of much more releasing gases in a briefly and intuitionistic way. The remote sensing FTIR coupled with these mathematical reconstruction techniques can be applied to the real world environmental and industrial hygiene monitoring, thus works as an alert system for the VOCs pollution.

Fractional-filling loophole insulator domains for ultracold bosons in optical superlattices

The zero-temperature phase diagram of a Bose-Einstein condensate confined in realistic one-dimensional $\ell$-periodic optical superlattices is investigated. The system of interacting bosons is modeled in terms of a Bose-Hubbard Hamiltonian whose site-dependent local potentials and hopping amplitudes reflect the periodicity of the lattice partition in $\ell$-site cells. Relying on the exact mapping between the hard-core limit of the boson Hamiltonian and the model of spinless noninteracting fermions, incompressible insulator domains are shown to exist for rational fillings that are predicted to be compressible in the atomic limit. The corresponding boundaries, qualitatively described in a {\it multiple-site} mean-field approach, are shown to exhibit an unusual loophole shape. A more quantitative description of the loophole domain boundaries at half filling for the special case $\ell$ = 2 is supplied in terms of analytic strong-coupling expansions and quantum Monte Carlo simulations.