Two-dimensional supersonic nonlinear Schrodinger flow past an extended obstacle

Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schroumldinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ""ship-wave"" pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

CMB in a box: Causal structure and the Fourier-Bessel expansion

This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility gamma = e(-mu), where mu is the optical depth to Thomson scattering. We show that the contributions of order gamma(N) to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z >> 10(3), effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position (x) over right arrow = 0 and time t(0). Hence, for each multipole l there is a discrete tower of momenta k(il) (not a continuum) which can affect physical observables, with the smallest momenta being k(1l) similar to l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation-no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

Performance and molecular evaluation of an anaerobic system with suspended biomass for treating wastewater with high fat content after enzymatic hydrolysis

The effect of a lipase-rich fungal enzymatic preparation, produced by a Penicillium sp. during solid-state fermentation, was evaluated in an anaerobic digester treating dairy wastewater with 1200 mg of oil and grease/L The oil and grease hydrolysis step was carried out with 0.1% (w/v) of solid enzymatic preparation at 30 degrees C for 24 h, and resulted in a final free acid concentration eight times higher than the initial value. The digester operated in sequential batches of 48 h at 30 degrees C for 245 days, and had high chemical oxygen demand (COD) removal efficiencies (around 90%) when fed with pre-hydrolyzed wastewater. However, when the pre-hydrolysis step was removed, the anaerobic digester performed poorly (with an average COD removal of 32%), as the oil and grease accumulated in the biomass and effluent oil and grease concentration increased throughout the operational period. PCR-DGGE analysis of the Bacteria and Archaea domains revealed remarkable differences in the microbial profiles in trials conducted with and without the pre-hydrolysis step, indicating that differences observed in overall parameters were intrinsically related to the microbial diversity of the anaerobic sludge. (C) 2009 Elsevier Ltd. All rights reserved.

Parameter setting and statistical learning

Three main models of parameter setting have been proposed: the Variational model proposed by Yang (2002; 2004), the Structured Acquisition model endorsed by Baker (2001; 2005), and the Very Early Parameter Setting (VEPS) model advanced by Wexler (1998). The VEPS model contends that parameters are set early. The Variational model supposes that children employ statistical learning mechanisms to decide among competing parameter values, so this model anticipates delays in parameter setting when critical input is sparse, and gradual setting of parameters. On the Structured Acquisition model, delays occur because parameters form a hierarchy, with higher-level parameters set before lower-level parameters. Assuming that children freely choose the initial value, children sometimes will miss-set parameters. However when that happens, the input is expected to trigger a precipitous rise in one parameter value and a corresponding decline in the other value. We will point to the kind of child language data that is needed in order to adjudicate among these competing models.

Repeatability of surface EMG variables in the sternocleidomastoid and anterior scalene muscles

In this study we examined the repeatability and reliability of the surface electromyographic (sEMG) signal mean frequency (MNF), average rectified value (ARV) and conduction velocity (CV) measured for the sternocleidomastoid (SCM) and the anterior scalene (AS) muscles in nine healthy volunteers during 15-s isometric cervical flexion contractions at 50% of the maximal voluntary contraction level over 3 non-consecutive days. Repeatability and reliability estimates were obtained for the initial values and rates of change of each sEMG variable by using both the Intraclass Correlation Coefficient (ICC) and the normalised standard error of the mean (nSEM). Results from SCM indicated good levels of repeatability for the initial value and slope of ARV (ICC > 65%). For the AS, high levels of repeatability were identified for the initial value of MNF (ICC > 70%) and the slope of ARV (ICC > 75%). Values of nSEM in the range 2.8-7.2% were obtained for the initial values of MNF and CV for both SCM and AS, indicating clinically acceptable measurement precision. The low value obtained for the nSEM of the initial value of MNF for the AS, in combination with the high ICC, indicates that of all of the variables examined, this variable could offer the best normative index to distinguish between subjects with and without neck pain, and represents the sEMG variable of choice for future evaluation purposes.

Difference equations in Banach spaces

Difference equations which discretely approximate boundary value problems for second-order ordinary differential equations are analysed. It is well known that the existence of solutions to the continuous problem does not necessarily imply existence of solutions to the discrete problem and, even if solutions to the discrete problem are guaranteed, they may be unrelated and inapplicable to the continuous problem. Analogues to theorems for the continuous problem regarding a priori bounds and existence of solutions are formulated for the discrete problem. Solutions to the discrete problem are shown to converge to solutions of the continuous problem in an aggregate sense. An example which arises in the study of the finite deflections of an elastic string under a transverse load is investigated. The earlier results are applied to show the existence of a solution; the sufficient estimates on the step size are presented. (C) 2003 Elsevier Science Ltd. All rights reserved.

Myoelectric manifestations of sternocleidomastoid and anterior scalene muscle fatigue in chronic neck pain patients

Objective: This study compares myoelectric manifestations of fatigue of the sternocleidomastoid (SCM) and anterior scalene (AS) muscles between 10 chronic neck pain subjects and 10 normal matched controls. Methods: Surface electromyography (sEMG) signals were recorded from the sternal bead of SCM and AS muscles bilaterally during submaximal isometric cervical flexion contractions at 25 and 50% of the maximum voluntary contraction (MVC). The mean frequency, average rectified value and conduction velocity of the sEMG signal were calculated to quantify myoelectric manifestations of muscle fatigue. Results: For both the SCM and AS muscles, the Mann-Whitney U test indicated that the initial value and slope of the mean frequency in neck pain patients were greater than in healthy subjects (P < 0.05). This was significant both at 25 and 50% of MVC. Conclusions: These results suggest: (a) a predominance of type-II fibres in the neck pain patients and/or (b) greater fatigability of the superficial cervical flexors in neck pain patients. These results are in agreement with previous muscle biopsy studies in subjects with neck pain, which identified transformation of slow-twitch type-I fibres to fast-twitch type-IIB fibres, as well as the clinical observation of reduced endurance in the cervical flexors in neck pain patients. (C) 2003 Elsevier Science Ireland Ltd. All rights reserved.

Real-time rheology of actively growing bacteria

The population growth of a Staphylococcus aureus culture, an active colloidal system of spherical cells, was followed by rheological measurements, under steady-state and oscillatory shear flows. We observed a rich viscoelastic behavior as a consequence of the bacteria activity, namely, of their multiplication and density-dependent aggregation properties. In the early stages of growth (lag and exponential phases), the viscosity increases by about a factor of 20, presenting several drops and full recoveries. This allows us to evoke the existence of a percolation phenomenon. Remarkably, as the bacteria reach their late phase of development, in which the population stabilizes, the viscosity returns close to its initial value. Most probably, this is caused by a change in the bacteria physiological activity and in particular, by the decrease of their adhesion properties. The viscous and elastic moduli exhibit power-law behaviors compatible with the "soft glassy materials" model, whose exponents are dependent on the bacteria growth stage. DOI: 10.1103/PhysRevE.87.030701.

Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis

In this paper, we discuss the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrödinger equation and Heisenberg uncertainty principles are structured within local fractional operators.

A one-dimensional prescribed curvature equation modeling the corneal shape

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

Living bacteria rheology: Population growth, aggregation patterns, and collective behaviour under diferente shear flows

The activity of growing living bacteria was investigated using real-time and in situ rheology-in stationary and oscillatory shear. Two different strains of the human pathogen Staphylococcus aureus-strain COL and its isogenic cell wall autolysis mutant, RUSAL9-were considered in this work. For low bacteria density, strain COL forms small clusters, while the mutant, presenting deficient cell separation, forms irregular larger aggregates. In the early stages of growth, when subjected to a stationary shear, the viscosity of the cultures of both strains increases with the population of cells. As the bacteria reach the exponential phase of growth, the viscosity of the cultures of the two strains follows different and rich behaviors, with no counterpart in the optical density or in the population's colony-forming units measurements. While the viscosity of strain COL culture keeps increasing during the exponential phase and returns close to its initial value for the late phase of growth, where the population stabilizes, the viscosity of the mutant strain culture decreases steeply, still in the exponential phase, remains constant for some time, and increases again, reaching a constant plateau at a maximum value for the late phase of growth. These complex viscoelastic behaviors, which were observed to be shear-stress-dependent, are a consequence of two coupled effects: the cell density continuous increase and its changing interacting properties. The viscous and elastic moduli of strain COL culture, obtained with oscillatory shear, exhibit power-law behaviors whose exponents are dependent on the bacteria growth stage. The viscous and elastic moduli of the mutant culture have complex behaviors, emerging from the different relaxation times that are associated with the large molecules of the medium and the self-organized structures of bacteria. Nevertheless, these behaviors reflect the bacteria growth stage.

A one-dimensional prescribed curvature equation modeling the corneal shape.

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

Study on the changes of soil chemical characteristics as result of prescribed fire

Every year, particularly during the summer period, the Portuguese forests are devastated by forest fire that destroys their ecosystems. So in order to prevent these forest fires, public and private authorities frequently use methods for the reduction of combustible mass as the prescribed fire and the mechanical vegetation pruning. All of these methods of prevention of forest fires alter the vegetation layer and/or soil [1-2]. This work aimed the study of the variation of some chemical characteristics of soil that suffered prescribed fire. The studied an area was located in the Serra of Cabreira (Figure 1) with 54.6 ha. Twenty sampling points were randomly selected and samples were collected with a shovel before, just after the prescribed fire, and 125 and 196 days after that event. The parameters that were studied were: pH, soil moisture, organic matter and iron, magnesium and potassium total concentration. All the analysis followed International Standard Methodologies. This work allowed to conclude that: a) after the prescribed fire; i) the pH remained practically equal to the the initial value; ii) occurred a slight increase of the average of the organic matter contents and iron total contents; b) at the end of the sampling period compared to the initial values; i) the pH didn´t change significantly; ii) the average of the contents of organic matter decreased; and iii) the average of the total contents of Fe, Mg and K increased.

Remediação Ambiental

A agricultura é uma das atividades mais antigas realizadas pelo Homem, sendo de grande importância para a obtenção tanto de bens alimentares como de bens para outros fins. No entanto desde o início constatou-se que as culturas eram afetadas por pragas e doenças que levavam à perda das colheitas. Este motivo deu origem à necessidade de nesses termos surgiu a aplicação de substâncias com o objetivo de proteger as colheitas. Os pesticidas são substâncias naturais ou sintéticas, aplicadas com o objetivo de proteger as plantas eliminando pragas e doenças. Para além da potencial toxicidade destas substâncias, em alguns casos a sua degradação no meio ambiente por microrganismos, hidrólise, radiação solar, etc. dá origem a produtos de degradação tanto ou mais tóxicos que os próprios pesticidas. A utilização deste tipo de substâncias acarreta problemas, visto a sua aplicação ser feita de forma a compensar perdas que ocorrem por meio de degradação, lixiviação, entre outros processos. Este tipo de aplicação leva a que haja contaminação do meio ambiente por parte dos pesticidas, pondo em risco tanto a saúde humana como os restantes seres vivos. A utilização de ciclodextrinas no encapsulamento destes compostos tem como objetivo aumentar a estabilidade do composto e promover a sua libertação de forma controlada. No presente trabalho pretende-se efetuar um estudo comparativo sobre a fotodegradação do herbicida terbutilazina e do fungicida pirimetanil livres e quando encapsulados com 2- hidroxipropil-β- ciclodextrina. De forma a quantificar os pesticidas ao longo do estudo foi utilizado o método analítico de HPLC de fase reversa. Os resultados permitiram constatar que a terbutilazina é fotoquimicamente estável, nas condições aplicadas, visto que ao fim de 75 dias de as soluções de pesticida livre em água desionizada e em água do rio apresentarem ainda 98% do pesticida inicial e as soluções de pesticida encapsulado em água desionizada e em água do rio apresentarem ainda 98% do pesticida inicial. Neste caso particular não foi possível, no intervalo de tempo considerado, avaliar a influência do encapsulamento no processo de fotodegradação da terbutilazina. Dada a baixa fotodegradação observada optou-se pela adição de peróxido de hidrogénio às soluções de controlo e 35 mM de HP-β-CD e acetona às soluções de 0 mM e 17,5 mM de HP-β-CD, para tentar promover a degradação do pesticida. Através dos resultados obtidos constatou-se que particularmente para as soluções onde foi adicionada acetona houve um aumento da velocidade de degradação no entanto esta ainda ocorria de forma lenta e muito semelhante quer para o pesticida livre quer para o encapsulado. Relativamente ao estudo da fotodegradação do pirimetanil verificou-se que ao fim de 4 dias de irradiação as soluções de pesticida livre apresentavam já alguma degradação do pesticida e tendo o período de irradiação uma duração de 53 dias foi possível para este pesticida determinar os parâmetros cinéticos em algumas das soluções. Quanto as soluções de água desionizada e água do rio com pirimetanil livre ambas apresentaram degradação do pesticida verificando-se uma cinética de reação de 1ª ordem com constantes de 0,0018 dias-1 e de 0,0060 dias-1 respetivamente. Para a solução de água desionizada com pirimetanil encapsulado não foi detetada degradação do pesticida, já para a solução com pirimetanil encapsulado em água do rio verificou-se a existência de degradação que correspondeu a uma cinética de degradação de 1ª ordem com uma constante de 0,0013 dias-1. Através dos resultados obtidos pode-se concluir que o encapsulamento do pirimetanil com 2-hidroxipropil-β-ciclodextrina é vantajoso visto diminuir a quantidade de pesticida utilizado e aumentar a eficácia do controlo das pragas.