Planar dynamics of a uniform beam with rigid bodies affixed to the ends

The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided

Transverse vibration and buckling of a cantilevered beam with tip body under constant axial base acceleration

The planar transverse bending behavior of a uniform cantilevered beam with rigid tip body subject to constant axial base acceleration was analyzed. The beam is inextensible and capable of small elastic transverse bending deformations only. Two classes of tip bodies are recognized: (1) mass centers located along the beam tip tangent line; and (2) mass centers with arbitrary offset towards the beam attachment point. The steady state response is studied for the beam end condition cases: free, tip mass, tip body with restricted mass center offset, and tip body with arbitrary mass center offset. The first three cases constitute classical Euler buckling problems, and the characteristic equation for the critical loads/accelerations are determined. For the last case a unique steady state solution exists. The free vibration response is examined for the two classes of tip body. The characteristic equation, eigenfunctions and their orthogonality properties are obtained for the case of restricted mass center offset. The vibration problem is nonhomogeneous for the case of arbitrary mass center offset. The exact solution is obtained as a sum of the steady state solution and a superposition of simple harmonic motions

Pink landscapes: 1/f spectra of spatial environmental variability and bird community composition

Temporal and spatial environmental variability are predicted to have reddened spectra that reveal increases in variance with the period or length sampled. However, spectral analyses have seldom been performed on ecological data to determine whether these predictions hold true in the case of spatial environmental variability. For a 50 km long continuous transect of 128 point samples across a heterogeneous cultural landscape in the Czech Republic, both habitat composition and bird species composition decomposed by standard ordination techniques did indeed exhibit reddened spectra. The values of main ordination axes have relationships between log spectral density and log frequency with slopes close to -1, indicating 1/f, or 'pink' noise type of variability that is characterized by scale invariance. However, when habitat composition was controlled for and only residuals for bird species composition were analysed, the spectra revealed a peak at intermediate frequencies, indicating that population processes that structure bird communities but are not directly related to the structure of the environment might have some typical correlation length. Spatial variability of abundances of individual species was mostly reddened as well, but the degree was positively correlated to their total abundance and niche position (strength of species-habitat association). If 'pink' noise type of variability is as generally typical for spatial environmental variability as for temporal variability, the consequences may be profound for patterns of species diversity on different spatial scales, the form of species-area relationships and the distribution of abundances within species ranges

A scheme for computing surface layer turbulent fluxes from mean flow surface observations

A physical model and computational scheme are developed for generating turbulent surface stress, sensible heat flux and humidity flux from mean velocity, temperature and humidity at some fixed height in the atmospheric surface layer, where conditions at this reference level are presumed known from observations or the evolving state of a numerical atmospheric circulation model. The method is based on coupling the Monin-Obukov surface layer similarity profiles which include buoyant stability effects on mean velocity, temperature and humidity to a force-restore formulation for the evolution of surface soil temperature to yield the local values of shear stress, heat flux and surface temperature. A self-contained formulation is presented including parameterizations for solar and infrared radiant fluxes at the surface. Additional parameters needed to implement the scheme are the thermal heat capacity of the soil per unit surface area, surface aerodynamic roughness, latitude, solar declination, surface albedo, surface emissivity and atmospheric transmissivity to solar radiation

Structure of the species-energy relationship

The relationship between energy availability and species richness (the species-energy relationship) is one of the best documented macroecological phenomena. However, the structure of species distribution along the gradient, the proximate driver of the relationship, is poorly known. Here, using data on the distribution of birds in southern Africa, for which species richness increases linearly with energy availability, we provide an explicit determination of this structure. We show that most species exhibit increasing occupancy towards more productive regions (occurring in more grid cells within a productivity class). However, average reporting rates per species within occupied grid cells, a correlate of local density, do not show a similar increase. The mean range of used energy levels and the mean geographical range size of species in southern Africa decreases along the energy gradient, as most species are present at high productivity levels but only some can extend their ranges towards lower levels. Species turnover among grid cells consequently decreases towards high energy levels. In summary, these patterns support the hypothesis that higher productivity leads to more species by increasing the probability of occurrence of resources that enable the persistence of viable populations, without necessarily affecting local population densities

On equilibrium fluctuations

This paper considers a dynamical system described by a multidimensional state vector x. A component x of x evolves according to dx/dt = f(x). Equilibrium fluctuations are fluctuations of an equilibrium solution x(t) obtained when the system is in its equilibrium state reached under a constant external forcing. The frequencies of these fluctuations range from the major frequencies of the underlying dynamics to the lowest possible frequency, the frequency zero. For such a system, the known feature of the differential operator d(·)/dt as a high-pass filter makes the spectrum of f to vanish not only at frequency zero, but de facto over an entire frequency range centered at frequency zero (when considering both positive and negative frequencies). Consequently, there is a non-zero portion of the total equilibrium variance of x that cannot be determined by the differential forcing f. Instead, this portion of variance arises from many impulse-like interactions of x with other components of x, which are received by x along an equilibrium solution over time. The effect of many impulse-like interactions can only be realized by integrating the evolution equations in form of dx/dt = f(x) forward in time. This integral effect is not contained in, and can hence not be explained by, a differential forcing f defined at individual time instances

Allegiance: Fort Sumter, Charleston, and the Beginning of the Civil War

Family Reunion The Civil War publishing field doenot lack for works on battles, regiments, and personal histories, but Dana M. Mangham’s “Oh For a Touch of the Vanished Hand is one book that explores the Civil War from the view of a genealogist first, historian second. Mangham tra...

The fatty acid transport function of fatty acid-binding proteins

The intracellular fatty acid-binding proteins (FABPs) comprise a family of 14–15 kDa proteins which bind long-chain fatty acids. A role for FABPs in fatty acid transport has been hypothesized for several decades, and the accumulated indirect and correlative evidence is largely supportive of this proposed function. In recent years, a number of experimental approaches which more directly examine the transport function of FABPs have been taken. These include molecular level in vitro modeling of fatty acid transfer mechanisms, whole cell studies of fatty acid uptake and intracellular transfer following genetic manipulation of FABP type and amount, and an examination of cells and tissues from animals engineered to lack expression of specific FABPs. Collectively, data from these studies have provided strong support for defining the FABPs as fatty acid transport proteins. Further studies are necessary to elucidate the fundamental mechanisms by which cellular fatty acid trafficking is modulated by the FABPs

South Asian summer monsoon projections constrained by the Intedacadal Pacific Oscillation

A reliable projection of future South Asian summer monsoon (SASM) benefits a large population in Asia. Using a 100-member ensemble of simulations by the Max Planck Institute Earth System Model (MPI-ESM) and a 50-member ensemble of simulations by the Canadian Earth System Model (CanESM2), we find that internal variability can overshadow the forced SASM rainfall trend, leading to large projection uncertainties for the next 15 to 30 years. We further identify that the Interdecadal Pacific Oscillation (IPO) is, in part, responsible for the uncertainties. Removing the IPO-related rainfall variations reduces the uncertainties in the near-term projection of the SASM rainfall by 13 to 15% and 26 to 30% in the MPI-ESM and CanESM2 ensembles, respectively. Our results demonstrate that the uncertainties in near-term projections of the SASM rainfall can be reduced by improving prediction of near-future IPO and other internal modes of climate variabilit