Role of Internal Motions and Molecular Geometry on the NMR Relaxation of Hydrocarbons

The role of internal motions and molecular geometry on $^1$H NMR relaxation times $T_{1,2}$ in hydrocarbons is investigated using MD (molecular dynamics) simulations of the autocorrelation functions for in{\it tra}molecular $G_R(t)$ and in{\it ter}molecular $G_T(t)$ $^1$H-$^1$H dipole-dipole interactions arising from rotational ($R$) and translational ($T$) diffusion, respectively. We show that molecules with increased molecular symmetry such as neopentane, benzene, and isooctane show better agreement with traditional hard-sphere models than their corresponding straight-chain $n$-alkane, and furthermore that spherically-symmetric neopentane agrees well with the Stokes-Einstein theory. The influence of internal motions on the dynamics and $T_{1,2}$ relaxation of $n$-alkanes are investigated by simulating rigid $n$-alkanes and comparing with flexible (i.e. non-rigid) $n$-alkanes. Internal motions cause the rotational and translational correlation-times $\tau_{R,T}$ to get significantly shorter and the relaxation times $T_{1,2}$ to get significantly longer, especially for longer-chain $n$-alkanes. Site-by-site simulations of $^1$H's along the chains indicate significant variations in $\tau_{R,T}$ and $T_{1,2}$ across the chain, especially for longer-chain $n$-alkanes. The extent of the stretched (i.e. multi-exponential) decay in the autocorrelation functions $G_{R,T}(t)$ are quantified using inverse Laplace transforms, for both rigid and flexible molecules, and on a site-by-site bases. Comparison of $T_{1,2}$ measurements with the site-by-site simulations indicate that cross-relaxation (partially) averages-out the variations in $\tau_{R,T}$ and $T_{1,2}$ across the chain of long-chain $n$-alkanes. This work also has implications on the role of nano-pore confinement on the NMR relaxation of fluids in the organic-matter pores of kerogen and bitumen

NMR Spin-Rotation Relaxation and Diffusion of Methane

The translational-diffusion coefficient $D_T$ and the spin-rotation contribution to the $^1$H NMR relaxation time $T_{1J}$ for methane (CH$_4$) are investigated using MD (molecular dynamics) simulations, over a wide range of densities $\rho$ and temperatures $T$, spanning the liquid, supercritical, and gas phases. The simulated $D_T$ agree well with measurements, without any adjustable parameters in the interpretation of the simulations. A minimization technique is developed to compute the angular-velocity for non-rigid spherical molecules, which is used to simulate the autocorrelation function $G_{\!J}(t)$ for spin-rotation interactions. With increasing $D_T$ (i.e. decreasing $\rho$), $G_{\!J}(t)$ shows increasing deviations from the single-exponential decay predicted by the Langevin theory for hard spheres, and the deviations are quantified using inverse Laplace transforms of $G_{\!J}(t)$. $T_{1J}$ is derived from $G_{\!J}(t)$ using the kinetic model "km" for gases ($T_{1J}^{km}$), and the diffusion model "dm" for liquids ($T_{1J}^{dm}$). $T_{1J}^{km}$ shows better agreement with $T_1$ measurements at higher $D_T$, while $T_{1J}^{dm}$ shows better agreement with $T_1$ measurements at lower $D_T$. $T_{1J}^{km}$ is shown to dominate over the MD simulated $^1$H-$^1$H dipole-dipole relaxation $T_{1RT}$ at high $D_T$, while the opposite is found at low $D_T$. At high $D_T$, the simulated spin-rotation correlation-time $\tau_J$ agrees with the kinetic collision time $\tau_K$ for gases, from which a new relation $1/T_{1J}^{km} \propto D_T$ is inferred, without any adjustable parameters

Modelling multiscale aspects of colorectal cancer

Colorectal cancer (CRC) is responsible for nearly half a million deaths annually world-wide [11]. We present a series of mathematical models describing the dynamics of the intestinal epithelium and the kinetics of the molecular pathway most commonly mutated in CRC, the Wnt signalling network. We also discuss how we are coupling such models to build a multiscale model of normal and aberrant guts. This will enable us to combine disparate experimental and clinical data, to investigate interactions between phenomena taking place at different levels of organisation and, eventually, to test the efficacy of new drugs on the system as a whole

A person-centred problem

It has become commonly expected that the “personhood” of people with dementia should be recognised, understood in the relational sense that is now widely adopted in healthcare practices. Despite its broad acceptance, however, the concept of personhood remains problematic in dementia care, as a result both of the theoretical challenges it poses and the practices that arise from it. This work employs the technique of ethnographic observation of residents, family members, and care staff of an aged care facility to explore the ways in which various modalities of the “self” are displayed in persons with dementia. The results provide insights into the moral and ontological impact of personhood on the systems that structure and influence interactions involving people with dementia. We conclude that privileging a preserved identity in dementia, and delivering care that conforms to contemporary “person-centred” expectations may limit recognition of the fluid, ongoing selfhood of people with dementia and that a reconsideration of this focus may enable us to expand our understanding of, and our responses to, their changing experiences

The 3-D kinematics of water masers around the semiregular variable RT Virginis

We report observations of water masers around the semiregular variable RT Virginis (RT Vir), which have been made with the Very Long Baseline Array (VLBA) of the National Radio Astronomy Observatory (NRAO) at five epochs, each separated by three weeks of time. We detected about 60 maser features at each epoch. Overall, 61 features, detected at least twice, were tracked by their radial velocities and proper motions. The 3-D maser kinematics exhibited a circumstellar envelope that is expanding roughly spherically with a velocity of about 8 km/s. Asymmetries in both the spatial and velocity distributions of the maser features were found in the envelope, but less significant than that found in other semiregular variables. Systematic radial-velocity drifts of individual maser features were found with amplitudes of <= 2 km/s/yr. For one maser feature, we found a quadratic position shift with time along a straight line on the sky. This apparent motion indicates an acceleration with an amplitude of 33 km/s/yr, implying the passage of a shock wave driven by the stellar pulsation of RT Vir. The acceleration motion is likely seen only on the sky plane because of a large velocity gradient formed in the accelerating maser region. We estimated the distance to RT Vir to be about 220 pc on the basis of both the statistical parallax and model-fitting methods for the maser kinematics.Comment: 18 pages, 8 figures. Accepted to appear in the Astrophysical Journa

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the NMR autocorrelation function for intramolecular dipole pairs assume single-exponential decay, yet the calculated autocorrelation of realistic systems display a rich, multi-exponential behavior resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational and translational diffusion in the same framework. We recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker-Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction, and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole-pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict NMR dipole-dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Pad{\'e}-Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory

The Spitzer c2d Survey of Large, Nearby, Interstellar Clouds. IX. The Serpens YSO Population as Observed with IRAC and MIPS

We discuss the combined IRAC/MIPS c2d Spitzer Legacy observations of the Serpens star-forming region. We describe criteria for isolating bona fide YSOs from the extensive background of extragalactic objects. We then discuss the properties of the resulting high-confidence set of 235 YSOs. An additional 51 lower confidence YSOs outside this area are identified from the MIPS data and 2MASS photometry. We present color-color diagrams to compare our observed source properties with those of theoretical models for star/disk/envelope systems and our own modeling of the objects that are well represented by a stellar photosphere plus circumstellar disk. These objects exhibit a wide range of disk properties, from many with actively accreting disks to some with both passive disks and even possibly debris disks. The YSO luminosity function extends down to at least a few times 10^(-3) L_☉ or lower. The lower limit may be set more by our inability to distinguish YSOs from extragalactic sources than by the lack of YSOs at very low luminosities. We find no evidence for variability in the shorter IRAC bands between the two epochs of our data set, Δt ~ 6 hr. A spatial clustering analysis shows that the nominally less evolved YSOs are more highly clustered than the later stages. The background extragalactic population can be fitted by the same two-point correlation function as seen in other extragalactic studies. We present a table of matches between several previous infrared and X-ray studies of the Serpens YSO population and our Spitzer data set. The clusters in Serpens have a very high surface density of YSOs, primarily with SEDs suggesting extreme youth. The total number of YSOs, mostly Class II, is greater outside the clusters

Penn State University NSF GK-12 Project: Using Web-Based Education and Interaction with K-12 and College Freshman to Promote Science and Engineering

Penn State University has hosted an NSF-sponsored GK-12 Outreach project for the past five years, and has just begun the second phase of the project. The Penn State project utilizes the talents of many science and engineering graduate students as teachers, mentors and role models for the K-12 classrooms. The project focuses on developing skills of students in the areas of science, technology, engineering and mathematics through the use of Advanced Transportation Technologies. A new project component was devised and implemented-the interaction of K-12 students with college freshman via a website project. The college freshmen were asked to create a website describing a component of Clean Energy , which was to include an assessment tool to provide feedback on their website. When possible, the college freshmen were encouraged to use active learning and inquiry-based learning concepts. This was encouraged so that the college freshman had an opportunity to practice developing scientific inquiry as a skill through a presentation, and provided the K-12 classroom students a unique opportunity to learn through inquiry. The K-12 students were invited to participate in the research by reviewing and critiquing these websites through feedback via the website to the college freshman. The feedback could take many forms, including specific comments and critique along with a creative assessment tool that the college freshman decided to present with their subject materials. This paper will review the educational outcomes garnered by the students, and provide feedback and analysis from the K-12 and college freshman participants