Two-dimensional approximation for tide-induced watertable fluctuations in a sloping sandy beach

The prediction of watertable fluctuations in a coastal aquifer is important for coastal management. However, most previous approaches have based on the one-dimensional Boussinesq equation, neglecting variations in the coastline and beach slope. In this paper, a closed-form analytical solution for a two-dimensional unconfined coastal aquifer bounded by a rhythmic coastline is derived. In the new model, the effect of beach slope is also included, a feature that has not been considered in previous two-dimensional approximations. Three small parameters, the shallow water parameter (epsilon), the amplitude parameter (a) and coastline parameter (beta) are used in the perturbation approximation. The numerical results demonstrate the significant influence of both the coastline shape and beach slopes on tide-driven coastal groundwater fluctuations. (c) 2004 Elsevier Ltd. All rights reserved.

A method of fundamental solutions for two-dimensional heat conduction

We investigate an application of the method of fundamental solutions (MFS) to heat conduction in two-dimensional bodies, where the thermal diffusivity is piecewise constant. We extend the MFS proposed in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction, Eng. Anal. Bound. Elem. 32 (2008), pp. 697–703] for one-dimensional heat conduction with the sources placed outside the space domain of interest, to the two-dimensional setting. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be obtained efficiently with small computational cost.

Two-dimensional viscoelastic discrete triangular system with negative-stiffness components

Potential applications of high-damping and high-stiffness composites have motivated extensive research on the effects of negative-stiffness inclusions on the overall properties of composites. Recent theoretical advances have been based on the Hashin-Shtrikman composite models, one-dimensional discrete viscoelastic systems and a two-dimensional nested triangular viscoelastic network. In this paper, we further analyze the two-dimensional triangular structure containing pre-selected negative-stiffness components to study its underlying deformation mechanisms and stability. Major new findings are structure-deformation evolution with respect to the magnitude of negative stiffness under shear loading and the phenomena related to dissipation-induced destabilization and inertia-induced stabilization, according to Lyapunov stability analysis. The evolution shows strong correlations between stiffness anomalies and deformation modes. Our stability results reveal that stable damping peaks, i.e. stably extreme effective damping properties, are achievable under hydrostatic loading when the inertia is greater than a critical value. Moreover, destabilization induced by elemental damping is observed with the critical inertia. Regardless of elemental damping, when the inertia is less than the critical value, a weaker system instability is identified.

Three-Dimensional Operational Calculi for Nonlocal Evolution Boundary Value Problems

Иван Христов Димовски, Юлиан Цанков Цанков - Построени са директни операционни смятания за функции u(x, y, t), непрекъснати в област от вида D = [0, a] × [0, b] × [0, ∞). Наред с класическата дюамелова конволюция, построението използва и две некласически конволюции за операторите ∂2x и ∂2y. Тези три едномерни конволюции се комбинират в една тримерна конволюция u ∗ v в C(D). Вместо подхода на Я. Микусински, основаващ се на конволюционни частни, се развива алтернативен подход с използване на мултипликаторните частни на конволюционната алгебра (C(D), ∗).

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). In the present work, we follow the method originally proposed by Van Vliet in LRT. The Hamiltonian in this approach is of the form: H = H°(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H° - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H°(E, B) , include the external fields without any limitation on strength. In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0 , t → ∞ , so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices.

Characterization of the volatile profile of Brazilian Merlot wines through comprehensive two dimensional gas chromatography time-of-flight mass spectrometric detection.

Wine aroma is an important characteristic and may be related to certain specific parameters, such as raw material and production process. The complexity of Merlot wine aroma was considered suitable for comprehensive two-dimensional gas chromatography (GCGC), as this technique offers superior performance when compared to one-dimensional gas chromatography (1D-GC). The profile of volatile compounds of Merlot wine was, for the first time, qualitatively analyzed by HS-SPME-GCxGC with a time-of-flight mass spectrometric detector (TOFMS), resulting in 179 compounds tentatively identified by comparison of experimental GCxGC retention indices and mass spectra with literature 1D-GC data and 155 compounds tentatively identified only by mass spectra comparison. A set of GCGC experimental retention indices was also, for the first time, presented for a specific inverse set of columns. Esters were present in higher number (94), followed by alcohols (80), ketones (29), acids (29), aldehydes (23), terpenes (23), lactones (16), furans (14), sulfur compounds (9), phenols (7), pyrroles (5), C13-norisoprenoids (3), and pyrans (2). GCxGC/TOFMS parameters were improved and optimal conditions were: a polar (polyethylene glycol)/medium polar (50% phenyl 50% dimethyl arylene siloxane) column set, oven temperature offset of 10ºC, 7 s as modulation period and 1.4 s of hot pulse duration. Co-elutions came up to 138 compounds in 1D and some of them were resolved in 2D. Among the coeluted compounds, thirty-three volatiles co-eluted in both 1D and 2D and their tentative identification was possible only due to spectral deconvolution. Some compounds that might have important contribution to aroma notes were included in these superimposed peaks. Structurally organized distribution of compounds in the 2D space was observed for esters, aldehydes and ketones, alcohols, thiols, lactones, acids and also inside subgroups, as occurred with esters and alcohols. The Fischer Ratio was useful for establishing the analytes responsible for the main differences between Merlot and non-Merlot wines. Differentiation among Merlot wines and wines of other grape varieties were mainly perceived through the following components: ethyl dodecanoate, 1-hexanol, ethyl nonanoate, ethyl hexanoate, ethyl decanoate, dehydro-2-methyl-3(2H)thiophenone, 3-methyl butanoic acid, ethyl tetradecanoate, methyl octanoate, 1,4 butanediol, and 6-methyloctan-1-ol.

Condensed phase combustion travelling waves with sequential exothermic or endothermic reactions

The one-dimensional propagation of a combustion wave through a premixed solid fuel for two-stage kinetics is studied. We re-examine the analysis of a single reaction travelling-wave and extend it to the case of two-stage reactions. We derive an expression for the travelling wave speed in the limit of large activation energy for both reactions. The analysis shows that when both reactions are exothermic, the wave structure is similar to the single reaction case. However, when the second reaction is endothermic, the wave structure can be significantly different from single reaction case. In particular, as might be expected, a travelling wave does not necessarily exist in this case. We establish conditions in the limiting large activation energy limit for the non-existence, and for monotonicity of the temperature profile in the travelling wave.

Proton-transfer versus nontransfer in compounds of the diazo-dye precursor 4-(phenyldiazenyl) aniline (aniline yellow) with strong organic acids: the 5-sulfosalicylate and the dichroic benzenesulfonate salts, and the 1:2 adduct with 3,5-dinitrobenzoic

The structures of two 1:1 proton-transfer red-black dye compounds formed by reaction of aniline yellow [4-(phenyldiazenyl)aniline] with 5-sulfosalicylic acid and benzenesulfonic acid, and a 1:2 nontransfer adduct compound with 3,5-dinitrobenzoic acid have been determined at either 130 or 200 K. The compounds are 2-(4-aminophenyl)-1-phenylhydrazin-1-ium 3-carboxy-4-hydroxybenzenesulfonate methanol solvate, C12H12N3+.C7H5O6S-.CH3OH (I), 2-(4-aminophenyl)-1-hydrazin-1-ium 4-(phenydiazinyl)anilinium bis(benzenesulfonate), 2C12H12N3+.2C6H5O3S-, (II) and 4-(phenyldiazenyl)aniline-3,5-dinitrobenzoic acid (1/2) C12H11N3.2C~7~H~4~N~2~O~6~, (III). In compound (I) the diaxenyl rather than the aniline group of aniline yellow is protonated and this group subsequently akes part in a primary hydrogen-bonding interaction with a sulfonate O-atom acceptor, producing overall a three-dimensional framework structure. A feature of the hydrogen bonding in (I) is a peripheral edge-on cation-anion association involving aromatic C--H...O hydrogen bonds, giving a conjoint R1/2(6)R1/2(7)R2/1(4)motif. In the dichroic crystals of (II), one of the two aniline yellow species in the asymmetric unit is diazenyl-group protonated while in the other the aniline group is protonated. Both of these groups form hydrogen bonds with sulfonate O-atom acceptors and thee, together with other associations give a one-dimensional chain structure. In compound (III), rather than proton-transfer, there is a preferential formation of a classic R2/2(8) cyclic head-to-head hydrogen-bonded carboxylic acid homodimer between the two 3,5-dinitrobenzoic acid molecules, which in association with the aniline yellow molecule that is disordered across a crystallographic inversion centre, result in an overall two-dimensional ribbon structure. This work has shown the correlation between structure and observed colour in crystalline aniline yellow compounds, illustrated graphically in the dichroic benzenesulfonate compound.

X-ray computed tomography

X-ray computed tomography (CT) is a medical imaging technique that produces images of trans-axial planes through the human body. When compared with a conventional radiograph, which is an image of many planes superimposed on each other, a CT image exhibits significantly improved contrast although this is at the expense of reduced spatial resolution.----- A CT image is reconstructed mathematically from a large number of one dimensional projections of the chosen plane. These projections are acquired electronically using a linear array of solid-state detectors and an x ray source that rotates around the patient.----- X-ray computed tomography is used routinely in radiological examinations. It has also be found to be useful in special applications such as radiotherapy treatment planning and three-dimensional imaging for surgical planning.

Isopropylaminium 2-carboxy-4, 5-dichlorobenzoate

In the structure of the 1:1 proton-transfer compound of isopropylamine with 4,5-dichlorophthalic acid, C3H10N+·C8H3Cl2O4-, the three cation H-atom donors associate with three separate carboxyl O-atom anion acceptors, giving conjoint cyclic R44(12), R44(16) hydrogen-bonding cation-anion interactions in a one-dimensional ribbon structure. In the anions, the carboxyl groups lie slightly out of the plane of the benzene ring [maximum deviations = 0.439 (1) for a carboxylic acid O atom and 0.433 (1) Å for a carboxylate O atom]. However, the syn-related proton of the carboxylic acid group forms the common short intramolecular O-HOcarboxyl hydrogen bond.

Hydrogen bonding in the water stabilized structure of the modified unsymmetrically substituted viologen chromophore, N-ethyl-N'-(2-phosphonomethyl)-4,4'-bipyridylium dichloride

The crystal structure of the modified unsymmetrically N, N'-substituted viologen chromophore, N-ethyl- N'-(2-phosphonoethyl)-4, 4'-bipyridinium dichloride 0.75 hydrate. (1) has been determined. Crystals are triclinic, space group P-1 with Z = 2 in a cell with a = 7.2550(1), b = 13.2038(5), c = 18.5752(7) Å, α = 86.495(3), β = 83.527(2), γ = 88.921(2)o. The two independent but pseudo-symmetrically related cations in the asymmetric unit form one-dimensional hydrogen-bonded chains through short homomeric phosphonic acid O-H...O links [2.455(4), 2.464(4)A] while two of the chloride anions are similarly strongly linked to phosphonic acid groups [O-H…Cl, 2.889(4), 2.896(4)Å]. The other two chloride anions together with the two water molecules of solvation (one with partial occupancy) form unusual cyclic hydrogen-bonded bis(Cl...water) dianion units which lie between the layers of bipyridylium rings of the cation chain structures with which they are weakly associated.

4-Methylpyridinium 2-carboxy-4,5-dichlorobenzoate

In the structure of the 1:1 proton-transfer compound of 4-methylpyridine (\g-picoline) with 4,5-dichlorophthalic acid, C6H8N+ C8H3Cl2O4- . H2O, determined at 200 K, the 4,5-dichlorophthalate anions are bridged by the water molecule through O--H...O~carboxyl~ hydrogen bonds, giving zig-zag chains which extend along the c axial direction of the unit cell. The 4-methylpyridine cations are linked to the chains through single N--H...O~water~ hydrogen bonds and occupy the voids within the chains in the one-dimensional structure. The anions have the common 'planar' conformation with the short intramolecular O--H...O(carboxyl) hydrogen bond.

Guanidinium 2-phenylacetate

In the structure of CH6N3+ C8H7O2-, the guanidinium cation gives three cyclic hydrogen-bonding interactions with O acceptors of three independent phenylacetate anions, one R2/2(8) and two R1/2(6), giving one-dimensional columnar structures which extend down the 4~2~ axis in the tetragonal cell. Within these structures there are 86.5A^3^ solvent accessible voids.

Adaptive instantaneous frequency estimation: Techniques and algorithms

This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications. Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis. In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise. Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise. Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized. For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis. A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H. An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent