An analytic approach to projectile motion in a linear resisting medium

The time of flight, range and the angle which maximizes the range of a projectile in a linear resisting medium are expressed in analytic form in terms of the recently defined Lambert W function. From the closed-form solutions a number of results characteristic to the motion of the projectile in a linear resisting medium are analytically confirmed, and asymptotic and approximate expressions valid within the weak and strong damping limits are developed. The problem provides an accessible account of the increasingly applicable Lambert W function and highlights much of the important mathematics associated with this simple yet rapidly emerging ‘implicitly’ elementary function.     

EXPERIMENTAL AND NUMERICAL METHOD FOR DETERMINING TEMPERATURE DISTRIBUTION IN A WOOD CUTTING TOOL

A 2-D boundary-element model was used to solve the steady-state heat conduction problem in a wood cutting tool. Cutting experiments were conducted in order to measure temperatures at remote locations on the tool rake face and at the tool/holder interface. The tool/holder interface temperatures were used as inputs into the boundary-element model. Heat input into the tool was adjusted until predicted temperatures on the rake face agreed with experimental results. The proportion of the machining power conducted into the tool as heat was determined as a function of the cutting geometry, specific cutting energy, and cutting speed.     

An Euler–Bernoulli Beam with Dynamic Frictionless Contact: Penalty Approximation and Existence

In this work, we consider the dynamic frictionless Euler–Bernoulli equation with the Signorini contact conditions along the length of a thin beam. The existence of solutions is proved based on the penalty method. Employing energy functional with the penalty method, we bound integral of contact forces over space and time. Hölder continuity of the fundamental solution plays an important role in the convergence theory.     

The absorption spectrum of 12C2D2 in the 10000–12500 cm−1 spectral region

The absorption spectrum of dideuteroacetylene has been recorded by intracavity laser absorption spectroscopy (ICLAS) in the 10 200–12 500cm^?1 spectral region. Among 25 absorption bands of ¹²C₂D₂ rotationally analysed in this spectral region, 17 are newly observed. They include one II_u-Σ⁺ _g and thirteen Σ⁺ _u-Σ⁺ _g bands starting from the vibrational ground state and eleven hot bands from the V ₄ = 1 and V ₅ = 1 lower states. The rotational structure of two excited levels is affected by a strongly J-dependent interaction with a perturber which induces intensity transfer to extra lines. The coupling is identified as a I-resonance interaction with δ_u dark states and the vibrational assignment of the perturbers is discussed. Two Σ-Σ bands of the ¹²C¹³ CD₂ species, present in natural abundance in the sample, could also be identified and rotationally analysed. Most of the corresponding excited vibrational levels of ¹²C₂D₂ were unambiguously assigned using the polyad model [Herman, M., el idrissi, M. I., Pisarchik, A., Campargue, A., Gaillot, A.-C., Biennier, L., di lonardo, G. and Fusina, L., 1998, J. chem. Phys., 108, 1377] which allows vibrational energies and B _V rotational constants to be predicted. In particular the previously highlighted 1/244 anharmonic resonance is confirmed by energy and intensity features in several {(V ₁, V ₂, V ₃, V ₄ = 0, V ₅ = 0),(V ₁ ?1, V ₂ + 1, V ₃ V ₄ = 2, V ₅ = 0)} dyads. Significant deviations between predicted and experimental energy levels are observed for a few levels and discussed.     

Halogen bonding in DNA base pairs

Halogen bonding (R-X···Y) is a qualitative analogue of hydrogen bonding that may prove useful in the rational design of artificial proteins and nucleotides. We explore halogen-bonded DNA base pairs containing modified guanine, cytosine, adenine and thymine nucleosides. The structures and stabilities of the halogenated systems are compared to the normal hydrogen bonded base pairs. In most cases, energetically stable, coplanar structures are identified. In the most favorable cases, halogenated base pair stabilities are within 2 kcal mol(-1) of the hydrogen bonded analogues. Among the halogens X = Cl, Br, and I, bromine is best suited for inclusion in these biological systems because it possesses the best combination of polarizability and steric suitability. We find that the most stable structures result from a single substitution of a hydrogen bond for a halogen bond in dA:dT and dG:dC base pairs, which allows 1 or 2 hydrogen bonds, respectively, to complement the halogen bond.     

Structural and chemical properties of the nitrogen-rich energetic material triaminoguanidinium 1-methyl-5-nitriminotetrazolate under pressure

The structural and chemical properties of the bi-molecular, hydrogen-bonded, nitrogen-rich energetic material triaminoguanidinium 1-methyl-5-nitriminotetrazolate C(3)H(12)N(12)O(2) (TAG-MNT) have been investigated at room pressure and under high pressure isothermal compression using powder x-ray diffraction and Raman and infrared spectroscopy. A stiffening of the equation of state and concomitant structural relaxation between 6 and 14 GPa are found to correlate with Raman mode disappearances, frequency discontinuities, and changes in the pressure dependence of modes. These observations manifest the occurrence of a reversible martensitic structural transformation to a new crystalline phase. The onset and vanishing of Fermi resonance in the nitrimine group correlate with the stiffening of the equation of state and phase transition, suggesting a possible connection between these phenomena. Beyond 15 GPa, pressure induces irreversible chemical reactions, culminating in the formation of a polymeric phase by 60 GPa.     

2′-Fluoro-3-deazaaristeromycin

The carbocyclic nucleoside 3-deazaaristeromycin has shown biological promise but a library of its derivatives upon which to expand this property is lacking. To address this situation, the synthesis of the two diastereomers of 2′-fluoro-3-deazaaristeromycin is described in a multistep convergent process that calls upon d-ribose for construction of the cyclopentyl fluoro units.     

Simultaneous measurement of X‐ray diffraction and ferroelectric polarization data as a function of applied electric field and frequency

The characteristics of a new ferroelectric measurement system at the European Synchrotron Radiation Facility are presented. The electric‐field‐induced phase transitions of Pb(Mg_1/3Nb_2/3)O₃–xPbTiO₃ are determined viain situ measurements of electric polarization within the synchrotron diffraction beamline. Real‐time data collection methods on single‐crystal samples are employed as a function of frequency to determine the microstructural origin of piezoelectric effects within these materials, probing the dynamic ferroelectric response.     

Single- and multi-scan femtosecond laser writing for selective chemical etching of cross section patternable glass micro-channels

We report on the fabrication of three dimensional micro-fluidic channels in fused silica glass using a combination of femtosecond laser writing and hydrofluoric acid wet etching to flexibly create various cross-sectional profiles of highly uniform shape and smooth vertical walls. The laser power, polarization, focusing depth, scanning angle and scanning speed were systematically studied with single- and multi-scan configurations to assess optimum micro-channel formation including etch rate, surface roughness, and stress-induced crack formation. We introduce the formation of vertical access-ports that extend the buried channel formation to unlimited length without tapering or distortion of the channel cross-sectional shape.     

Fourier transform microwave spectroscopy of the reactive intermediate monoiodosilylene,HSiI and DSiI

The pure rotational spectra of three silicon isotopologues of HSiI and two isotopologues of DSiI have been recorded by pulsed-jet Fourier transform microwave (FTMW) spectroscopy. Neon was passed over dry ice cooled H₃SiI or D₃SiI and introduced into the pulsed valve of the FTMW spectrometer. The monoiodosilylenes HSiI and DSiI were produced in situ with a 1000 V DC-discharge nozzle. Only a-type transitions occur in monoiodosilylene from 6 to 26 GHz. We observe K_a = 0 a-type transitions for H²⁸SiI, H²⁹SiI, H³⁰SiI, and D²⁹SiI, and both K_a = 0 and 1 a-type transitions for D²⁸SiI. Rotational constants, centrifugal distortion constants, iodine nuclear quadrupole coupling constants, and nuclear spin–molecular rotation constants were measured.