MATHEMATICA notebook for computing tetrahedral finite element shape functions and matrices for the Helmholtz equation

A MATHEMATICA notebook to compute the elements of the matrices which arise in the solution of the Helmholtz equation by the finite element method (nodal approximation) for tetrahedral elements of any approximation order is presented. The results of the notebook enable a fast computational implementation of finite element codes for high order simplex 3D elements reducing the overheads due to implementation and test of the complex mathematical expressions obtained from the analytical integrations. These matrices can be used in a large number of applications related to physical phenomena described by the Poisson, Laplace and Schrodinger equations with anisotropic physical properties.

Effect of enzymatic hydrolysis on some physicochemical properties of root and tuber granular starches

A hidrólise enzimática do amido pode fornecer informações importantes sobre sua estrutura granular. Amidos de mandioca, batata-doce, mandioquinha-salsa e batata foram hidrolisados por α-amilase bacteriana a 37 °C durante 48 horas, e algumas propriedades físico-químicas dos resíduos da hidrólise foram determinadas. O amido de mandioca foi o mais suscetível à enzima com 20,9% de hidrólise, enquanto o amido de batata foi o mais resistente com 5,9%. O tamanho médio dos grânulos variou de 10,8 a 23,4 μm para os amidos de mandioquinha-salsa e batata, respectivamente. Amidos de mandioca e batata-doce apresentaram um padrão de difração de raio-X tipo A, enquanto os amidos de mandioquinha-salsa e batata mostraram padrão tipo B. Todos os amidos nativos mostraram superfície granular lisa e, após hidrólise, os amidos de mandioca, batata-doce e mandioquinha-salsa mostraram alguns grânulos bastante degradados, enquanto o amido de batata apresentou sutil sinal de degradação. O teor de amilose dos amidos diminuiu com a hidrólise para os amidos de mandioca, batata-doce e mandioquinha-salsa, permanecendo inalterado para o amido de batata. Como esperado, a viscosidade intrínseca e as propriedades de pasta diminuíram para todos os amidos hidrolisados. Não houve diferença significativa entre as propriedades térmicas dos amidos nativos e hidrolisados. Estes resultados sugeriram que a hidrólise ocorreu nas áreas cristalinas e amorfas dos grânulos. O padrão de difração do tipo B e o grande tamanho dos grânulos do amido de batata podem ter contribuído para a maior resistência deste amido à hidrólise.

Interpolating EFGM for computing continuous and discontinuous electromagnetic fields

Purpose - This paper proposes an interpolating approach of the element-free Galerkin method (EFGM) coupled with a modified truncation scheme for solving Poisson's boundary value problems in domains involving material non-homogeneities. The suitability and efficiency of the proposed implementation are evaluated for a given set of test cases of electrostatic field in domains involving different material interfaces.Design/methodology/approach - the authors combined an interpolating approximation with a modified domain truncation scheme, which avoids additional techniques for enforcing the Dirichlet boundary conditions and for dealing with material interfaces usually employed in meshfree formulations.Findings - the local electric potential and field distributions were correctly described as well as the global quantities like the total potency and resistance. Since, the treatment of the material interfaces becomes practically the same for both the finite element method (FEM) and the proposed EFGM, FEM-oriented programs can, thus, be easily extended to provide EFGM approximations.Research limitations/implications - the robustness of the proposed formulation became evident from the error analyses of the local and global variables, including in the case of high-material discontinuity.Practical implications - the proposed approach has shown to be as robust as linear FEM. Thus, it becomes an attractive alternative, also because it avoids the use of additional techniques to deal with boundary/interface conditions commonly employed in meshfree formulations.Originality/value - This paper reintroduces the domain truncation in the EFGM context, but by using a set of interpolating shape functions the authors avoided the use of Lagrange multipliers as well Mathematics in Engineering high-material discontinuity.

A simple prescription for computing the stress-energy tensor

A non-variational technique for computing the stress-energy tensor is presented. The prescription is used, among other things, to obtain the correct field equations for Prasanna's highly nonlinear electrodynamics.

Comparison of hexamethyidisilazane and critical point drying treatments for SEM analysis of anaerobic biofilms and granular sludge

We present a fast procedure for scanning electron microscopy (SEM) analysis in which hexamethyldisilazane (HMDS) solvent, instead of the critical point drying, is used to remove liquids from a microbiological specimen. The results indicate that the HMDS solvent is suitable for drying samples of anaerobic cells for examination by SEM and does not cause cell structure disruption.

On computing discriminants of subfields of Q(zeta(pr))

The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(Q(zeta(n))/Q), the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K. By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of Q(zeta(p)r), where p is an odd prime and r is a positive integer. (C) 2002 Elsevier B.V. (USA).

On the dissimilarity between the algorithms for computing the symmetric energy-momentum tensor in ordinary field theory and general relativity

The recipe used to compute the symmetric energy-momentum tensor in the framework of ordinary field theory bears little resemblance to that used in the context of general relativity, if any. We show that if one stal ts fi om the field equations instead of the Lagrangian density, one obtains a unified algorithm for computing the symmetric energy-momentum tensor in the sense that it can be used for both usual field theory and general relativity.

Algorithm for computing the propagator for higher derivative gravity theories

A simple algorithm for computing the propagator for higher derivative gravity theories based on the Barnes-Rivers operators is presented. The prescription is used, among other things, to obtain the propagator for quadratic gravity in an unconventional gauge. We also find the propagator for both gravity and quadratic gravity in an interesting gauge recently baptized the Einstein gauge [Hitzer and Dehnen, Int. J. Theor. Phys. 36 (1997), 559].

N-methyl-D-aspartate channel and consciousness: From signal coincidence detection to quantum computing

Research on Blindsight, Neglect/Extinction and Phantom limb syndromes, as well as electrical measurements of mammalian brain activity, have suggested the dependence of vivid perception on both incoming sensory information at primary sensory cortex and reentrant information from associative cortex. Coherence between incoming and reentrant signals seems to be a necessary condition for (conscious) perception. General reticular activating system and local electrical synchronization are some of the tools used by the brain to establish coarse coherence at the sensory cortex, upon which biochemical processes are coordinated. Besides electrical synchrony and chemical modulation at the synapse, a central mechanism supporting such a coherence is the N-methyl-D-aspartate channel, working as a 'coincidence detector' for an incoming signal causing the depolarization necessary to remove Mg 2+, and reentrant information releasing the glutamate that finally prompts Ca 2+ entry. We propose that a signal transduction pathway activated by Ca 2+ entry into cortical neurons is in charge of triggering a quantum computational process that accelerates inter-neuronal communication, thus solving systemic conflict and supporting the unity of consciousness. © 2001 Elsevier Science Ltd.

On computing discriminants of subfields of ℚ (ζp r)

The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(ℚ(ζn)/ℚ), the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K. By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of ℚ(ζpr), where p is an odd rime and r is a positive integer. © 2002 Elsevier Science USA.

Granular cell tumour (Abrikossoff's tumour): Case series

This case series describes three unreported cases of an uncommon benign neoplasm named Abrikossoff's tumour or granular cell tumour (GCT). This mesenchymal neoplasm apparently arises from neural or Schwann cell origin with benign and malignant forms. All cases presented here were unique nodules on oral mucosa, coming out from the connective tissue, and occurring in women with age ranging from 30 to 42 years. The histological aspects of the GCT showed large granular cells arranged in groups and nests of connective tissue separating pseudoepitheliomatous overlying surface. This feature can possibly be misunderstood with squamous cell carcinoma. The differentiation between malignant and benign GCT is evaluated by the presence of metastases which is considered the only reliable criterion for malignancy. © 2005 Elsevier Ltd. All rights reserved.

Pré-oxidação e adsorção em carvão ativado granular para remoção dos herbicidas Diuron e Hexazinona de água subterrânea

The cultivation of sugarcane demands the use of herbicides such as Diuron and Hexazinone. Some supply wells from Ribeirão Preto, SP, Brazil, built in the Guarani Aquifer are located in recharge points, and the presence of sandy Quartzarenic Neosol in these areas increases the vulnerability of the groundwater to contamination from herbicides This paper reports the water quality monitored in some wells located in the recharge area and the removal of Diuron and Hexazinone by means of adsorption in granular activated carbon (GAC), preceded or not by preoxidation with chlorine and chlorine dioxide in a pilot plant. The results indicated that Diuron was more strongly adsorbed than Hexazinone and that the saturation time of the GAC in the test with preoxidation was shorter than in the test without preoxidation, which may have occurred mainly due to the formation of by-products that competed with the adsorption of the herbicides.