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ABSTRACT. There is considered a **layered** heterogeneous poroelastic isotropic **medium** with physical parameters characterized by piecewise constant functions of the depth only. We derive a mathematical algorithm for calculating reflected/transmitted poroelastic **waves** across all temporal frequencies. To define the frequency effect we use the dynamic permeability expression proposed by Johnson, Koplik and Dashen; **in** the time domain, this coefficient introduces order 1/2 shifted fractional time derivative involving a convolution product. The algorithm proposed is based on the formalism introduced by Ursin. The algorithm is tested numerically **in** a 1D-case. The numerical experiments confirm the effectiveness of the proposed algorithm **in** identifying the main wave events **in** both low frequency and high frequency regimes **in** the reservoir and laboratory scales.

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The case of the transmission/concentrator elements [2], when the ultrasound **waves** pass through one **medium** (usual alloy aluminum or titan) and the case of ultrasound **piezoelectric** transducer [3], when the ultrasound **waves** pass through two mediums (usual alloy aluminum # **piezoelectric** element).

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Shear **waves** SH propagation **in** **piezoelectric** composite under the influence of initial stress is investigated analytically and numerically. The dispersion equation of shear **waves** propagation **in** direction normal to the layering is obtained **in** presence of initial stress. Numer‐ ical solutions were obtained for evaluating the effect of stress on dimensionless frequency and phase velocity. The effect of stress on stop band is discussed **in** this study. It can be concluded from the results that initial stress has significant effect on propagation charac‐ teristics of shear **waves**. The variation of initial stress has small effect on the phase velocity of shear **waves**. This study provides insight for development of **piezoelectric** composite structure under the influence of initial stress.

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20. Danoyan Z.N, Atoyan L.H., Danoyan N.Z. Shear horizontal electro-magneto-elastic surface **waves** **in** a **layered** **piezoelectric** structure **in** the presence of an electric or ЦКРnОЭТМ ЬМrООn. ,,TopТМКХ ProЛХОЦЬ oП ConЭТnuuЦ MОМСКnТМЬ’’. TСО proМООНТnРЬ oП international Conference, 4-8 October 2010, Dilijan, Armenia, pp. 266-271.

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The paper is devoted to develop a new scheme to calculate imped- ance matrices for axial-symmetric foundations embedded **in** half- space **medium**. The half-space **medium** can be approximated by increasing thickness of one layer stratum on rigid bedrock due to the effect of material damping. However, as thickness increases, the numerical problem will arise. This problem is caused by the numerical contamination by some negligible reflection **waves** from rigid bedrock. **In** reality, the effect of these reflection **waves** on impedance is getting small as the thickness of the one layer stra- tum increases. Therefore, the scheme will employ the solutions for one layer stratum with suppressing these reflection **waves** to gen- erate the impedance for the case of half-space. The numerical results by the presented scheme are compared with the results by other scheme **in** order to show that the new numerical scheme is effective and the solutions **in** **layered** **medium** can be extended to obtain the results for the cases of **layered** half-space **medium**. Some numerical results of torsional, vertical, horizontal, coupling and rocking impedances with different embedded depths will be presented and comments on the numerical scheme will be given.

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The experimental study of graphene triggered a grow- ing attention to its electronic properties,[14] because the honeycomb lattice defines a band structure [19] with two nodal points **in** the Brillouin zone which determines a relativistic Dirac-type electronic dynamics [18] (creat- ing links with certain theories of particle physics). These properties are responsible for unusual phenomena, such as the fractional Hall effect,[13, 20, 7, 16] which al- lows the possibility for magnetic catalysis of an excitonic **gap**,[6, 5, 10, 9, 8, 11] ferromagnetism and superconduc- tivity. [12]

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Introduction: High prevalence of learning disabilities resulting **in** poor academic performance has already been described **in** Neurofibromatosis type 1. Learning process depends on the ability to listen, understand and separate the relevant parts of speech from background noise, regardless of the physical environment. It is known that much of the language is learned by hearing which is considered a functional system responsible for receiving sound information and convert them into specific transduction signals along the nerve fibers to the cortex. When there is a weak performance **in** one or more auditory abilities, it is much more difficult to learn without special assistance, even with normal intelligence, motivation and health. Objectives: Verify the neurological processing of the auditory information and its possible association with language and learning disabilities **in** patients with NF1. Methods: Descriptive-comparative study with 25 patients with NF1 (14 female and 11 male) and 22 controls (15 female and 7 male) aged 10 to 34 years. We analyzed the performance **in** auditory behavioral tests: sound localization (SL), sequential verbal memory (SVM), sequential non-verbal memory (SNVM), frequency patterns (FP), duration patterns (DP), **Gap** **in** Noise (GIN), speech **in** noise (SN), synthetic sentence identification with ipsilateral competing message (SSI – ICM) and contralateral competing message (SSI – CCM), dichotic digits (DD), staggered spondaic word (SSW) and dichotic nonverbal (DNV), **in** addition to analyze the results **in** the School Performance Test (TDE), phonologic and syntactic awareness. The statistical tools used were: t-Test, Mann- Whitney test, Fisher’s Exact test and the Pearson correlations. Probability values <0.05 were considered statistically significant. Results: Differences between NF1 and control groups were found **in** the tests: SVM, SNVM, FP, DP, GIN, SN RE and LE, SSI ICM, DD RE and LE, SSW RE and LE, SSI CCM **in** the LE ratios speech/noise -40 dB, DNV attention to RE and **in** the phonologic awareness. Positive correlations were observed between the dichotic tests and the school performance subtests. The PF and PD showed positive correlation with the phonologic awareness test. Conclusion: Patients with NF1 displayed auditory processing disorders associated to language and learning disabilities.

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A quantidade de proteína imobilizada pode ser determinada se a relação de Sauerbrey for válida. Como referido anteriormente a frequência de ressonância é afectada por efeitos viscoelásticos tanto do meio líquido como do filme adsor- vido [9]. A análise por espectroscopia de impedância permite quantificar essas **in**- terferências, sendo possível aplicar correcções à frequência de ressonância de modo a obter a massa real adsorvida. A imobilização de GST–scFv4BL levou ao aumento de resistência com dependência da concentração de anticorpo (fig. 3.3(b)). Este resultado está de acordo com o anteriormente obtido em sensores de 5 MHz [10], su- gerindo que o filme proteico apresenta um carácter viscoelástico e que a frequência de ressonância foi sobrestimada. A figura 3.3(a) apresenta os valores de varia- ção de frequência de ressonância obtidos com oscilador e os valores de frequência corrigidos (eq. 1.22) tendo em conta a variação de resistência para cada concentra- ção (fig. 3.3(b)). A viscoelasticidade do filme influenciou a resposta do oscilador com aumentos da variação de frequência na ordem dos 20 − 30%, o que significa que para a concentração de 100 µg/mL de anticorpo a massa real adsorvida é 30% menor. Assim, é possível estimar a massa a equação de Sauerbrey à frequência corrigida o valor de massa de anticorpo imobilizado foi de 1.3 µg/cm 2 . Este valor

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The cultivar BRS Pampeira is recommended for sowing **in** six rice-producing regions of the RS state, the west frontier being the preferred region, where it showed greater adaptability to the favorable environment. **In** registration with the Ministry of Agriculture, Livestock and Supply (MAPA), the cultivar was also recommended to the states of Goiás and Mato Grosso do Sul (midwest region); Tocantins, Pará and Roraima (north region); Maranhão, Piauí, Ceará, Rio Grande do Norte, Paraíba, Pernambuco, Alagoas and Sergipe (northeast region).

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Lp0/Lt"0 then Dep0Dip0/¸. **In** accordance with Eq. 11 we obtain: ¸"10 6 RQ. When (ep0)"0 and Lp0/Ltip0/tx, then txi105t0(t0"year 22). **In** these conditions we can suggest that p0 depends weakly on time and position. **In** this case we can use p0 as a constant **in** the equations for perturbed quantities.

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From a crystallographic point of view, the graphene is a triangular Bravais lattice with a diamond-shaped unit tile consisting of two sites so one gets the honeycomb structure. The electronic propagation **in** such a perfect crystal is described by Bloch **waves** (a generalization to lattices of the ordinary plane **waves** **in** free space). The corresponding Bloch wave vector k spans the so-called Brillouin zone and the way the energy of these Bloch **waves** depends on k is encoded **in** the band structure. The very unique feature of the graphene band structure is that the two lowest-energy bands, known as the valence and the conduction band touch at two isolated points located at the corners of the Brillouin zone. **In** the immediate vicinity of these degeneracy points, known as the Dirac points, the band structure is a cone. **In** natural graphene samples, there is exactly one electron per site, and thus, at zero temperature, all levels **in** the valence band are filled (a situation known as half-filling). As a result, the energy of the last occupied level precisely slices the band structure at the Dirac points. The low-energy excitations of this system are then described by the massless two-dimensional Weyl-Dirac equation and their energy dispersion relation v k F is that of

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These days, oil companies are interested **in** the process of thermodiffusion for more efficient extraction of oil from oil deposits. The spontaneous movement of the particles from high concentration region to the low concentration region is defined as diffusion and it occurs **in** response to a concentration gradient expressed as the change **in** the concentration due to change **in** position. The thermodiffusion **in** elastic solids is due to coupling of fields of temperature, mass diffusion and that of strain **in** addition to heat and mass exchange with environment.

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wireless communication known as an electric current method. The writers gave an overview of studies that had been conducted **in** the undersea communication and detection and through experimental analysis were able to conclude that propagation range **in** the **medium** at this frequency can be expanded, only if the current output is increased, without increasing the power output [76]. The experiment was carried out **in** the Mystic Lakes **in** Massachusetts, the relative permittivity and conductivity of the lake are 81 and 0.06 S/m respectively. The measured electric field patterns at a distance of 50 m below the surface of the water from the transmitting antenna are quite directional. These were compared with the computed field patterns and their results are similar, with which the conclusion is drawn that traveling wave antenna can be appropriately used for subsurface communication **in** the lake and also that at 144 MHz bands, and that water behaves like a dielectric **medium** at this frequency. **In** [77], Davis et al presented results of research and experimental validation on SQUIDS antennas operating at ELF bands to demonstrate the feasibility of using the antenna **in** an underwater environment as well as overcoming the sub-problems associated with its performance. Each of these problems was typically analyzed through measurements and the conclusion as presented by the team shows that SQUIDs antenna is potentially capable to be used as an extremely sensitive ELF RF receiving element on a mobile platform. **In** addition, the antenna has the ability to operate at a depth of 100 m below the water surface and can also deal with anticipated buoy motions through motion-processing method. **In** the same year, J. R. Wait presented propagation of ELF electromagnetic **waves** for Surface ELF Antenna For Addressing REmotely-deployed Receivers (SEAFARER), research **in** this band had actually been a fertile field of investigation for many years. The project came to address some grays area of Project Sanguine that was fraught with some controversies. **In** principle the two projects are very alike as the frequency of operation for antennas for this project is the same as that of Project Sanguine. Only that **in** the latter project power requirements were better estimated, but the US Navy was not able to explain the influence of either project on physical and biological environments. Also, this project has striking similarities and fascinating developments with an early investigation by Nicola Tesla [78].

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We study the band structure of elastic **waves** propagating **in** a nano-**piezoelectric** phononic crystal consisting of a polymeric matrix reinforced by BaTiO 3 inclusions **in** square, rectangular, triangular, honeycomb and Kagomé lattices. We also investigate the influence of inclusion cross section geometry - circular, hollow circular, square and rotated square with a 45º angle of rotation with respect to x and y axes. Plane wave expansion method is used to solve the governing equations of motion of a **piezoelectric** solid based on classical elasticity theory, ignoring nanoscopic size effects, considering two-dimensional periodicity and wave propagation **in** the xy plane. Complete band gaps between XY and Z modes are observed for all inclusions and the best performance is for circular inclusion **in** a triangular lattice. Piezoelectricity influences significantly the band gaps for hollow circular inclusion **in** lower frequencies. We suggest that nano-**piezoelectric** phononic crystals are feasible for elastic vibration management **in** GHz.

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We apply Christodoulou’s framework, developed to study the Einstein-scalar field equations **in** spherical symmetry, to the linear wave equation **in** de Sitter spacetime, as a first step towards the Einstein-scalar field equations with positive cosmological constant. We obtain an integro-differential evolution equation which we solve by taking initial data on a null cone. As a corollary we obtain elementary derivations of expected properties of linear **waves** **in** de Sitter spacetime: boundedness **in** terms of (characteristic) initial data, and a Price law establishing uniform exponential decay, **in** Bondi time, to a constant.

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These phenomena have been investigated for the simple isotropic semi-space as well as the complicated systems of multilayered anisotropic media. A detailed review **in** this respect is given by Nayfeh (1995). Qi (1994) investigated the influence of viscous fluid loading on the propagation of leaky Rayleigh **waves** **in** the presence of heat conduction effects. Wu and Zhu (1995) suggested an alternative approach to the treatment of Qi (1994). They presented solutions for the dispersion relations of leaky Rayleigh **waves** **in** the absence of heat conduction effects. Zhu and Wu (1995) used this technique to study Lamb **waves** **in** submerged and fluid coated plates. Nayfeh and Nagy (1997) formulated the exact characteristic equations for leaky **waves** propagating along the inter- faces of systems which involve isotropic elastic solids loaded with viscous fluids, including half- spaces and finite thickness fluid layers.

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