Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.

Historical review of light scattering studies

This paper reviews the earlier experimental studies on light scattering in quartz near its phase transition, which ultimately laid the foundation for the basic concept of the soft mode. The theoretical work on the subject has been briefly referred to. A list of ferroelectrics in which soft mode studies have been carried out near TC using laser Raman spectroscopy is appended. Reference has also been made to the appearance of the central mode with abnormal increase in intensity at TC.

Changes in straylight and corneal light scattering in a newly diagnosed case of type 2 diabetes

Visual problems may be the first symptoms of diabetes. There have been several reports of transient changes in refraction of people newly diagnosed with diabetes. Visual acuity and refraction may be affected when there are ocular biometric changes. Small but significant biometrical changes have been found by some authors during hyperglycaemia and during reduction of hyperglycaemia.[4] Here, we describe a case of type 2 diabetes that was detected from ocular straylight and intraocular thickness measurements...

Water-ethanol mixtures by molecular dynamics and x-ray Compton scattering

Water-ethanol mixtures are commonly used in industry and house holds. However, quite surprisingly their molecular-level structure is still not completely understood. In particular, there is evidence that the local intermolecular geometries depend significantly on the concentration. The aim of this study was to gain information on the molecular-level structures of water-ethanol mixtures by two computational methods. The methods are classical molecular dynamics (MD), where the movement of molecules can be studied, and x-ray Compton scattering, in which the scattering cross section is sensitive to the electron momentum density. Firstly, the water-ethanol mixtures were studied with MD simulations, with the mixture concentration ranging from 0 to 100%. For the simulations well-established force fields were used for the water and ethanol molecules (TIP4P and OPLS-AA, respectively). Moreover, two models were used for ethanol, rigid and non-rigid. In the rigid model the intramolecular bond lengths are fixed, whereas in the non-rigid model the lengths are determined by harmonic potentials. Secondly, mixtures with three different concentrations employing both ethanol models were studied by calculating the experimentally observable x-ray quantity, the Compton profile. In the MD simulations a slight underestimation in the density was observed as compared to experiment. Furthermore, a positive excess of hydrogen bonding with water molecules and a negative one with ethanol was quantified. Also, the mixture was found more structured when the ethanol concentration was higher. Negligible differences in the results were found between the two ethanol models. In contrast, in the Compton scattering results a notable difference between the ethanol models was observed. For the rigid model the Compton profiles were similar for all the concentrations, but for the non-rigid model they were distinct. This leads to two possibilities of how the mixing occurs. Either the mixing is similar in all concentrations (as suggested by the rigid model) or the mixing changes for different concentrations (as suggested by the non-rigid model). Either way, this study shows that the choice of the force field is essential in the microscopic structure formation in the MD simulations. When the sources of uncertainty in the calculated Compton profiles were analyzed, it was found that more statistics needs to be collected to reduce the statistical uncertainty in the final results. The obtained Compton scattering results can be considered somewhat preliminary, but clearly indicative of the behaviour of the water-ethanol mixtures when the force field is modified. The next step is to collect more statistics and compare the results with experimental data to decide which ethanol model describes the mixture better. This way, valuable information on the microscopic structure of water-ethanol mixtures can be found. In addition, information on the force fields in the MD simulations and on the ability of the MD simulations to reproduce the microscopic structure of binary liquids is obtained.

Radiative transfer, interception and scattering in coniferous forests : models and applications for production ecology and remote sensing

This work develops methods to account for shoot structure in models of coniferous canopy radiative transfer. Shoot structure, as it varies along the light gradient inside canopy, affects the efficiency of light interception per unit needle area, foliage biomass, or foliage nitrogen. The clumping of needles in the shoot volume also causes a notable amount of multiple scattering of light within coniferous shoots. The effect of shoot structure on light interception is treated in the context of canopy level photosynthesis and resource use models, and the phenomenon of within-shoot multiple scattering in the context of physical canopy reflectance models for remote sensing purposes. Light interception. A method for estimating the amount of PAR (Photosynthetically Active Radiation) intercepted by a conifer shoot is presented. The method combines modelling of the directional distribution of radiation above canopy, fish-eye photographs taken at shoot locations to measure canopy gap fraction, and geometrical measurements of shoot orientation and structure. Data on light availability, shoot and needle structure and nitrogen content has been collected from canopies of Pacific silver fir (Abies amabilis (Dougl.) Forbes) and Norway spruce (Picea abies (L.) Karst.). Shoot structure acclimated to light gradient inside canopy so that more shaded shoots have better light interception efficiency. Light interception efficiency of shoots varied about two-fold per needle area, about four-fold per needle dry mass, and about five-fold per nitrogen content. Comparison of fertilized and control stands of Norway spruce indicated that light interception efficiency is not greatly affected by fertilization. Light scattering. Structure of coniferous shoots gives rise to multiple scattering of light between the needles of the shoot. Using geometric models of shoots, multiple scattering was studied by photon tracing simulations. Based on simulation results, the dependence of the scattering coefficient of shoot from the scattering coefficient of needles is shown to follow a simple one-parameter model. The single parameter, termed the recollision probability, describes the level of clumping of the needles in the shoot, is wavelength independent, and can be connected to previously used clumping indices. By using the recollision probability to correct for the within-shoot multiple scattering, canopy radiative transfer models which have used leaves as basic elements can use shoots as basic elements, and thus be applied for coniferous forests. Preliminary testing of this approach seems to explain, at least partially, why coniferous forests appear darker than broadleaved forests in satellite data.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

Neutron Scattering and Molecular Dynamics Evidence for Levitation Effect in Nanopores

Neutron Scattering and Molecular Dynamics Evidence for Levitation Effect in Nanopores ... Neutron scattering measurements and molecular dynamics simulations have been carried out on the three isomers of pentane (neopentane (neo), isopentane (iso), and n-pentane (n-)) adsorbed in zeolite NaY. ... In order to understand this surprising dependence, the dimensionless levitation parameter, γ, for atomic systems may be modified to suit molecular systems.

Brillouin Scattering by Phonons Renormalized by Two-Magnon Excitations in Ferromagnetic Dielectrics

Brillouin scattering by one-phonon-two-magnon interacting excitations in ferromagnetic dielectrics is discussed. The basic light scattering mechanism is taken to be the modulation of the density-dependent optical dielectric polarizability of the medium by the dynamic strain field generated by the longitudinal acoustic (LA) phonons. The renormalization effects arising from the scattering of phonons by the two-magnon creation-annihilation processes have, however, been taken into account. Via these interactions, the Brillouin components corresponding to the two-magnon excitations are reflected indirectly in the spectrum of the phonon scattered light as line-broadening of the otherwise relatively sharp Brillouin doublet. The present mechanism is shown to be dominant in a clean saturated ferromagnetic dielectric with large magneto-strictive coupling constant, and with the magnetic ions in the orbitally quenched states. Following the linear response theory, an expression has been derived for the spectral density of the scattered light as a function of temperature, scattering angle, and the strength of the externally applied magnetic field. Some estimates are given for the line-width and line-shift of the Brillouin components for certain typical choice of parameters involved. The results are discussed in relation to some available calculations on the ultrasonic attenuation in ferromagnetic insulators at low temperatures.

Analyticity of the charge-monopole scattering amplitude

We study the analyticity in cosθ of the exact quantum-mechanical electric-charge-magnetic-monopole scattering amplitude by ascribing meaning to its formally divergent partial-wave expansion as the boundary value of an analytic function. This permits us to find an integral representation for the amplitude which displays its analytic structure. On the physical sheet we find only a branch-point singularity in the forward direction, while on each of the infinitely many unphysical sheets we find a logarithmic branch-point singularity in the backward direction as well as the same forward structure.

Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

Acute fluid shifts influence the assessment of serum vitamin D status in critically ill patients

Introduction Recent reports have highlighted the prevalence of vitamin D deficiency and suggested an association with excess mortality in critically ill patients. Serum vitamin D concentrations in these studies were measured following resuscitation. It is unclear whether aggressive fluid resuscitation independently influences serum vitamin D. Methods Nineteen patients undergoing cardiopulmonary bypass were studied. Serum 25(OH)D3, 1α,25(OH)2D3, parathyroid hormone, C-reactive protein (CRP), and ionised calcium were measured at five defined timepoints: T1 - baseline, T2 - 5 minutes after onset of cardiopulmonary bypass (CPB) (time of maximal fluid effect), T3 - on return to the intensive care unit, T4 - 24 hrs after surgery and T5 - 5 days after surgery. Linear mixed models were used to compare measures at T2-T5 with baseline measures. Results Acute fluid loading resulted in a 35% reduction in 25(OH)D3 (59 ± 16 to 38 ± 14 nmol/L, P < 0.0001) and a 45% reduction in 1α,25(OH)2D3 (99 ± 40 to 54 ± 22 pmol/L P < 0.0001) and i(Ca) (P < 0.01), with elevation in parathyroid hormone (P < 0.0001). Serum 25(OH)D3 returned to baseline only at T5 while 1α,25(OH)2D3 demonstrated an overshoot above baseline at T5 (P < 0.0001). There was a delayed rise in CRP at T4 and T5; this was not associated with a reduction in vitamin D levels at these time points. Conclusions Hemodilution significantly lowers serum 25(OH)D3 and 1α,25(OH)2D3, which may take up to 24 hours to resolve. Moreover, delayed overshoot of 1α,25(OH)2D3 needs consideration. We urge caution in interpreting serum vitamin D in critically ill patients in the context of major resuscitation, and would advocate repeating the measurement once the effects of the resuscitation have abated.

Determinants of outcome in critically ill patients

Assessment of the outcome of critical illness is complex. Severity scoring systems and organ dysfunction scores are traditional tools in mortality and morbidity prediction in intensive care. Their ability to explain risk of death is impressive for large cohorts of patients, but insufficient for an individual patient. Although events before intensive care unit (ICU) admission are prognostically important, the prediction models utilize data collected at and just after ICU admission. In addition, several biomarkers have been evaluated to predict mortality, but none has proven entirely useful in clinical practice. Therefore, new prognostic markers of critical illness are vital when evaluating the intensive care outcome. The aim of this dissertation was to investigate new measures and biological markers of critical illness and to evaluate their predictive value and association with mortality and disease severity. The impact of delay in emergency department (ED) on intensive care outcome, measured as hospital mortality and health-related quality of life (HRQoL) at 6 months, was assessed in 1537 consecutive patients admitted to medical ICU. Two new biological markers were investigated in two separate patient populations: in 231 ICU patients and 255 patients with severe sepsis or septic shock. Cell-free plasma DNA is a surrogate marker of apoptosis. Its association with disease severity and mortality rate was evaluated in ICU patients. Next, the predictive value of plasma DNA regarding mortality and its association with the degree of organ dysfunction and disease severity was evaluated in severe sepsis or septic shock. Heme oxygenase-1 (HO-1) is a potential regulator of apoptosis. Finally, HO-1 plasma concentrations and HO-1 gene polymorphisms and their association with outcome were evaluated in ICU patients. The length of ED stay was not associated with outcome of intensive care. The hospital mortality rate was significantly lower in patients admitted to the medical ICU from the ED than from the non-ED, and the HRQoL in the critically ill at 6 months was significantly lower than in the age- and sex-matched general population. In the ICU patient population, the maximum plasma DNA concentration measured during the first 96 hours in intensive care correlated significantly with disease severity and degree of organ failure and was independently associated with hospital mortality. In patients with severe sepsis or septic shock, the cell-free plasma DNA concentrations were significantly higher in ICU and hospital nonsurvivors than in survivors and showed a moderate discriminative power regarding ICU mortality. Plasma DNA was an independent predictor for ICU mortality, but not for hospital mortality. The degree of organ dysfunction correlated independently with plasma DNA concentration in severe sepsis and plasma HO-1 concentration in ICU patients. The HO-1 -413T/GT(L)/+99C haplotype was associated with HO-1 plasma levels and frequency of multiple organ dysfunction. Plasma DNA and HO-1 concentrations may support the assessment of outcome or organ failure development in critically ill patients, although their value is limited and requires further evaluation.

Too ill to will? deathbed wills: assessing testamentary capacity near the end of life

Assessing testamentary capacity in the terminal phase of an illness or at a person's deathbed is fraught with challenges for both doctors and lawyers. Numerous issues need to be considered when assessing capacity for a will. These issues are exacerbated when such an assessment needs to be undertaken at the bedside of a dying patient. The nature and severity of the illness, effects on cognition of the terminal illness, effects of medication, urgency, psychological and emotional factors, interactions with carers, family and lawyers, and a range of other issues confound and complicate the assessment of capacity. What is the doctor's role in properly assessing capacity in this context and how does this role intersect with the legal issues? Doctors will play an increasing role in assessing testamentary capacity in this setting. The ageing of society, more effective treatment of acute illness and, often, the prolongation of dying are only some of the factors leading to this increasing need. However, despite its importance and increasing prevalence, the literature addressing this challenging practical area is scarce and offers limited guidance. This paper examines these challenges and discusses some practical approaches.

Acute renal failure in critically ill patients : With special reference to prediction of outcome

Acute renal failure (ARF) is a clinical syndrome characterized by rapidly decreasing glomerular filtration rate, which results in disturbances in electrolyte- and acid-base homeostasis, derangement of extracellular fluid volume, and retention of nitrogenous waste products, and is often associated with decreased urine output. ARF affects about 5-25% of patients admitted to intensive care units (ICUs), and is linked to high mortality and morbidity rates. In this thesis outcome of critically ill patients with ARF and factors related to outcome were evaluated. A total of 1662 patients from two ICUs and one acute dialysis unit in Helsinki University Hospital were included. In study I the prevalence of ARF was calculated and classified according to two ARF-specific scoring methods, the RIFLE classification and the classification created by Bellomo et al. (2001). Study II evaluated monocyte human histocompatibility leukocyte antigen-DR (HLA-DR) expression and plasma levels of one proinflammatory (interleukin (IL) 6) and two anti-inflammatory (IL-8 and IL-10) cytokines in predicting survival of critically ill ARF patients. Study III investigated serum cystatin C as a marker of renal function in ARF and its power in predicting survival of critically ill ARF patients. Study IV evaluated the effect of intermittent hemodiafiltration (HDF) on myoglobin elimination from plasma in severe rhabdomyolysis. Study V assessed long-term survival and health-related quality of life (HRQoL) in ARF patients. Neither of the ARF-specific scoring methods presented good discriminative power regarding hospital mortality. The maximum RIFLE score for the first three days in the ICU was an independent predictor of hospital mortality. As a marker of renal dysfunction, serum cystatin C failed to show benefit compared with plasma creatinine in detecting ARF or predicting patient survival. Neither cystatin C nor plasma concentrations of IL-6, IL-8, and IL-10, nor monocyte HLA-DR expression were clinically useful in predicting mortality in ARF patients. HDF may be used to clear myoglobin from plasma in rhabdomyolysis, especially if the alkalization of diuresis does not succeed. The long-term survival of patients with ARF was found to be poor. The HRQoL of those who survive is lower than that of the age- and gender-matched general population.