One-dimensional Gradient Research Articles

Static stability of a viscoelastically supported asymmetric sandwich beam with thermal gradient

The static stability of an asymmetric sandwich beam with viscoelastic core on viscoelastic supports at the ends and subjected to an axial pulsating load and a steady, one-dimensional temperature gradient is investigated by computational method. The equations of motion and associated boundary conditions are obtained using the Hamilton's energy principle. Then, these equations of motion and the associated boundary conditions are non- dimensionalised. A set of Hill's equations is obtained from the non-dimensional equations of motion by the application of the general Galerkin method. The static buckling loads are obtained from the Hill's equations. The effects of shear parameter, geometric parameters, core loss factors, and thermal gradient on the non-dimensional static buckling loads zones have been investigated.

Single-Molecule Spectroscopic Imaging Studies of Polarity Gradients Prepared by Infusion-Withdrawal Dip-Coating

Sol–gel-derived thin films incorporating a one-dimensional polarity gradient are prepared by infusion-withdrawal dip-coating (IWDC) and characterized by single-molecule spectroscopic (SMS) imaging. Nonpolar phenyltrimethoxysilane (PTMOS) and polar tetramethoxysilane (TMOS) are used as precursor silanes during IWDC. Sessile drop water contact angle measurements demonstrate the presence of a wettability gradient in the resulting films, on macroscopic length scales. Raman maps of the phenyl C–H stretch at 3059 cm–1 confirm gradient formation. Material polarity is assessed by SMS imaging, using Nile Red as a polarity-sensitive probe. Polarity data are obtained by recording fluorescence videos of single-molecule emission simultaneously in two spectral bands (590 ± 20 and 640 ± 20 nm). The pairs of fluorescence spots produced by each molecule are identified and analyzed using automated spot-tracking software. The local film polarity is quantified via the Clausius–Mossotti factors calculated from the single-mole...

One-dimensional nonlocal and gradient elasticity: Assessment of high order approximation schemes

We investigate the application and performance of high-order approximation techniques to one-dimensional nonlocal elastic rods. Governing equations and corresponding discrete forms are derived for the integro-differential formulation proposed by Eringen and the laplacian-based strain gradient formulation developed by Aifantis and coworkers. Accuracy and convergence rate of the numerical solutions obtained with Lagrange, Hermite, B-spline finite elements and C∞ generalized finite elements are assessed against the corresponding analytical solutions.

Equilibrium Fluctuations for a Non Gradient Energy Conserving Stochastic Model

In this paper we study the equilibrium energy fluctuation field of a one-dimensional reversible non gradient model. We prove that the limit fluctuation process is governed by a generalized Ornstein-Uhlenbeck process, whose covariances are given in terms of the diffusion coefficient.The fact that the conserved, quantity (energy) is not a linear functional of the coordinates of the system: introduces new difficulties of a geometric nature when adapting the non gradient method introduced by Varadhan.

Controllable Growth of Functional Gradient ZnO Material Using Chemical Vapor Deposition

As a kind of semiconductor material, the morphology of zinc oxide directly affects its physical properties. By adjusting the ratio of the reaction source and the rate of the incoming gas flow, we obtained one-dimensional nanowire and two-dimensional nanoflag-like functional gradient material (FGM) using chemical vapor deposition (CVD) method. Compared with the one-dimensional nanowires, the growth of the two-dimensional ZnO FGM not only c-oriented, but other directions are also appeared. Photoluminescence results show that the FGM has a higher visible/UV emission intensity ratio than the nanowires for several orders of magnitudes. Meanwhile, the growth mechanism of these nanostructures were discussed in details.

Ratcheting and Transitions: Short Granular Chain in a Gradient of Vibration

We report our experimental work on a one-dimensional gradient of vibration with a short granular chain. The system exhibits transitions of ratcheting dynamics from passive monotonic creeping against the gradient, to rapid stochastic head swinging with a reversed bias in its direction, and to seemingly random fluctuations. The spontaneously emerged spatial pattern reflects bifurcations of the state of the chain. Evidence from counterpart experiments using uniform vibrations confirms a nonmonotonic development of accessible modes behind the transitions, whereas the reversed ratcheting reflects an interesting dialogue between the size of the object and the spatial gradient.

Temperature dependent properties of heat treated aluminium alloys

The mechanical properties of different aluminium alloys used in the manufacture of power train automotive parts were studied. The alloys were cast in wedge shape ingots that promote a one-dimensional solidification gradient. Tensile samples were machined from bars that were cast with different degrees of microstructural refining and were heat treated at times and temperatures that depended on their composition. The mechanical properties were measured from samples that had been held for 200 h within the temperature range of 25 to 300°C. It was found that the increase of Cu in alloys of the Si–Mg type alloys enhanced the mechanical properties above room temperature. The best properties were found in the Al–Cu alloy.

Influence of Allosteric Regulators on Individual Steps in the Reaction Catalyzed by Mycobacterium tuberculosis 2-Hydroxy-3-oxoadipate Synthase

Allosteric regulation often controls key branch points in metabolic processes. Mycobacterium tuberculosis 2-hydroxy-3-oxoadipate synthase (HOAS), a thiamin diphosphate (ThDP)-dependent enzyme, produces 2-hydroxy-3-oxoadipate using 2-ketoglutarate and glyoxylate. The proposed chemical mechanism in analogy with other ThDP-dependent carboligases involves multiple ThDP-bound covalent intermediates. Acetyl coenzyme A is an activator, and GarA, a forkhead association domain-containing protein known to regulate glutamate metabolism, is an allosteric inhibitor of HOAS. Steady state kinetics using assays to study the first half and the full catalytic cycle suggested that the regulators act at different steps in the overall mechanism. To explore the modes of regulation and to test the effects on individual catalytic steps, we performed circular dichroism (CD) studies using a non-decarboxylatable 2-ketoglutarate analog and determined the distribution of ThDP-bound covalent intermediates during the steady state of the HOAS reaction using one-dimensional (1)H gradient carbon heteronuclear single quantum coherence NMR. The results suggest that acetyl coenzyme A acts as a mixed V and K type activator and predominantly affects the predecarboxylation steps. GarA does not inhibit the formation of the predecarboxylation analog and does not affect the accumulation of the postdecarboxylation covalent intermediate derived from 2-ketoglutarate; however, it decreases the abundance of the product ThDP adduct in the HOAS pathway. Thus, the two regulators act on different halves of the catalytic cycle in an unusual regulatory regime.

Defining Relatives

This article uses a case study of scientific English from the seventeenth to the nineteenth centuries to test the traditional demarcation between restrictive and nonrestrictive adnominal relatives and to reconsider appropriate methods for analyzing such historical data. After an initial classification of some 1,160 clauses from the ARCHER corpus using the traditional dichotomy, alternative proposals for analyzing relative clauses are reviewed in the light of problematic examples. The concept of “aspective” relatives is adopted: those having most of the formal and pragmatic hallmarks of restrictive relatives while not strictly restrictive in the set-theoretic sense. We identify these with the clauses in present-day English that are not restrictive but that Huddleston, Pullum, and Peterson include under the heading “integrated.” We add a fourth, minor type, “continuative.” Nevertheless our data present problems even for a four-way classification. We demonstrate how some analytic difficulties are the result of changes in text-type-specific style and conventions over time, plus general diachronic change, but also that some examples genuinely resist hard-and-fast classification. We therefore treat our classes as overlapping bands on a one-dimensional gradient, testing the revised classification in detail on our seventeenth-century data. The overlaps are less numerous than any of the three main types (restrictive, aspective, and nonrestrictive), but they help to reduce the number of unclear cases from over a quarter of the total in our initial classification to a mere 1 percent. We distinguish carefully between vagueness (underspecified examples where the interpretation is in no doubt) and ambiguity (involving a choice between interpretations that depends on missing information). We suggest that our classification might be more widely applicable to the study of relative clauses. By and large, modern Sprachgefühl can be used cautiously alongside other, more objective tests to classify relatives in historical scientific texts—a point of more general theoretical relevance.

One-dimensional nonlocal and gradient elasticity: Closed-form solution and size effect

The equivalence between nonlocal and gradient elasticity models is investigated by making reference to one-dimensional boundary value problems equipped with two integral stress–strain laws proposed by Eringen (Nonlocal Continuum Field Theories (2002)). Corresponding closed-form solutions are derived through a procedure for the reduction of integral to differential equations. The reproduction of size effects in micro/nano rods is discussed. The differential formulation associated with the local/nonlocal model is shown to correspond to the strain-gradient formulation proposed by Aifantis (Mech. Mater. 35 (2003) 259–280).

Second order shear lag theory

The standard shear lag theory for elastic aligned short-fibre composites is extended to allow for a gradient of overall strain. The result is a one-dimensional strain gradient theory of the Toupin–Mindlin type. All parameters are the same as in the standard theory, and in the limits of weak strain gradients, large fibre aspect ratios or low elastic modulus ratios, the standard theory is recovered. The gradient effect is illustrated by a simple one-dimensional boundary value problem: a vertical composite rod fixed at both ends and loaded by gravity. The fibre length significantly affects the solution when the fibres are rigid and their length is near the rod length; but otherwise the effect is weak.

In situ nondestructive sediment characterization and resuspendability evaluation of concentrated aqueous paliperidone palmitate suspensions in prefilled syringes by low-field one-dimensional pulsed-field gradient NMR profilometry

This work aims to demonstrate the usefulness of a low-field one-dimensional pulsed-field gradient NMR (1D pfg NMR) profilometry technique to enable in situ nondestructive sediment characterization and resuspendability quantification of concentrated prefilled injectable suspensions. Aqueous paliperidone palmitate suspensions were used as model samples and low-intensity centrifugation was evaluated as a long-term gravity simulation approach. The low-field 1D pfg NMR technique allowed a detection zone of 2.5 cm in height for water content measurement of syringe samples using a Teflon syringe holder. Thus, the sediment compactness could be deduced from its water content. Quantitative evaluation of resuspendability was realized by front tracking of the NMR profile signals, which yielded the exponential sediment volume decay constant as a resuspendability quantification parameter. The study shows that both active ingredient particle size distribution and storage temperature had significant effects on the sedimentation rate and the resuspendability of the suspensions. The centrifugation method proved to be useful as a long-term gravity simulation and screening method, although the results should be interpreted with caution due to its higher acceleration and compression force imposed on the active ingredient particles.

Mass Spectrometric Characterization of the Sarcoplasmic Reticulum from Rabbit Skeletal Muscle by On-membrane Digestion

The sarcoplasmic reticulum from skeletal muscle constitutes an elaborate membrane system that contains a considerable number of integral and very large proteins that exist in highly complex supramolecular clusters. Conventional proteomics using two-dimensional gel electrophoresis greatly underestimates the presence of these proteins. Here, we have applied one-dimensional gradient gels and on-membrane digestion to overcome this technical problem. Mass spectrometric analysis has determined the presence of 31 distinct protein species in the sarcoplasmic reticulum, including key Ca2+-handling proteins such as the ryanodine receptor, Ca2+-ATPase, calsequestrin and sarcalumenin. Immunoblotting confirmed the relative position of these Ca2+-regulatory elements in analytical gel replicas. Interestingly, aldolase and phosphofructokinase were found to be present in the purified sarcoplasmic reticulum, supporting the idea of a close physical coupling between the glycolytic pathway and the energy-dependent sarcoplasmic reticulum. Hence, on-membrane digestion is highly suitable as the method of choice for studying integral and high-molecular-mass proteins in proteomic studies.

A facile and efficient approach for pore-opening detection of anodic aluminum oxide membranes

The well aligned porous anodic aluminum oxide (AAO) membrane is fabricated by a two-step anodization method. The oxide barrier layer of AAO membrane must be removed to get through-hole membrane for synthesizing nanowires and nanotubes of metals, semiconductors and conducting polymers. Removal of the barrier layer of oxide and pore-extending is of significant importance for the preparation of AAO membrane with through-hole pore morphology and desired pore diameter. The conventional method for pore opening is that AAO membrane after removing of aluminum substrate is immersed in chemical etching solution, which is completely empirical and results in catastrophic damage for AAO membrane frequently. A very simple and efficient approach based on capillary action for detecting pore opening of AAO membrane is introduced in this paper, this method can achieve the detection for pore opening visually and control the pore diameter precisely to get desired morphology and the pore diameter of AAO membrane. Two kinds of AAO membranes with different pore shape were obtained by different pore opening methods. In addition, one-dimensional gradient gold nanowires are also fabricated by electrodeposition based on AAO membranes.

Estimation and optimization of the peak capacity of one-dimensional gradient high performance liquid chromatography using a long monolithic silica capillary column

An estimation of the performance and optimization of gradient HPLC conditions using various columns for maximum total peak capacity was studied for “one-shot proteomics”[1] which involves one-dimensional gradient HPLC, connected to an electrospray ionization (ESI)-mass spectrometry (MS), using a monolithic silica-C18 capillary column (350cm long and 100μm internal diameter) and an over 40h shallow gradient elution with one injection. Optimization of such special one-dimensional HPLC has been a tedious task if carried out with a trial-and-error approach due to the extremely long analysis time for each run. Here, the optimized separation conditions including the column type, either particle-packed or monolithic, and the column length with a fixed gradient time are proposed by calculating the peak capacity obtainable using a long column and a long gradient time that may promote the “one-shot proteomics” approach. For instance, conventional conditions at less than 20MPa can be adapted for a 40h gradient elution for the proteomics experiment, and a ca. 3m long monolithic silica-C18 capillary column was identified as the optimized medium indicated by our model with peak capacity theory. To verify this model experimentally, the numbers of identified peptides and proteins were investigated with a nano LC/MS/MS system coupled with a 3m monolithic silica-C18 capillary column by using various elution times. The experimental results showed that the numbers of identified peptides and proteins were maximized and reached a plateau with a gradient time of several tens of hours, which indicated that our model to optimize one dimensional HPLC conditions with a long column could be verified and useful.

Discrete gradient algorithms of high order for one-dimensional systems

We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories in the phase space. The accuracy of our integrators is higher by several orders of magnitude as compared with the standard discrete gradient scheme (modified midpoint rule) and, what is more, our schemes have very high accuracy even for large time steps.

Nonlinear Dynamic Response of Functionally Graded Rectangular Plates under Different Internal Resonances

The nonlinear dynamic response of functionally graded rectangular plates under combined transverse and in-plane excitations is investigated under the conditions of 1 : 1, 1 : 2 and 1 : 3 internal resonance. The material properties are assumed to be temperature-dependent and vary along the thickness direction. The thermal effect due to one-dimensional temperature gradient is included in the analysis. The governing equations of motion for FGM rectangular plates are derived by using Reddy's third-order plate theory and Hamilton's principle. Galerkin's approach is utilized to reduce the governing differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms, which are then solved numerically by using 4th-order Runge-Kutta algorithm. The effects of in-plane excitations on the internal resonance relationship and nonlinear dynamic response of FGM plates are studied.

Temperature gradient analyzers for compact high-resolution X-ray spectrometers

Compact high-resolution X-ray spectrometers with a one-dimensional temperature gradient at the analyzer crystal are considered. This gradient, combined with the use of a position-sensitive detector, makes it possible to relax the usual Rowland-circle condition, allowing increased space at the sample position for a given energy resolution or arm radius. Thus, for example, it is estimated that approximately meV resolution is possible with a 3 m analyzer arm and 200 mm clearance between the sample and detector. Simple analytic formulae are provided, supported by excellent agreement with ray-tracing simulations. One variation of this method also allows the detector position sensitivity to be used to determine momentum transfer, effectively improving momentum resolution without reducing (slitting down) the analyzer size. Application to medium-resolution ( approximately 10-100 meV) inelastic X-ray scattering spectrometers with large angular acceptance is discussed, where this method also allows increased space at the sample. In some cases the application of a temperature gradient can improve the energy resolution even with a single-element detector.

An analytic solution for one-dimensional dissipational strain-gradient plasticity

An analytic solution is developed for the one-dimensional dissipational slip gradient equation, first described by Gurtin.. [ " On the plasticity of single crystals; free energy, microforces, plastic strain-gradients", J.Mech. Phys. Solids 48 (200) 989-1036] and then investigate numerically by Annand et al, ["A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results". J. Mech.Phys. Solids 53 (2005) 1798-1826]. However, we find that the analytic solution is incompatible with the zero-sliprate boundary condition ("clamped boundary condition") postulated by these authors, and is in fact excluded by the theory. As a consequence, the analytic solution agrees with the numerical results except near the boundary. The equation also admits a series of higher mode solutions where the numerical result corresponds to (a particular case of) the fundamental mode. Anand et al also established that the one-dimensional dissipational gradients strengthen the material, but this proposition only holds if zero-sliprate boundary conditions can be imposed, which we have shown cannot be done. Hence the possibility remains open that dissipational gradient weakening may also occur. doi:10.1017/S1446181109000066

Properties of C 1-smooth mappings with one-dimensional gradient range

We find necessary and sufficient conditions for a curve in ℝm×n to be the gradient range of a C1-smooth function υ: Ω ⊂ ℝn → ℝm. We show that this curve has tangents in a weak sense; these tangents are rank 1 matrices and their directions constitute a function of bounded variation. We prove also that in this case v satisfies an analog of Sard’s theorem, while the level sets of the gradient mapping ▿υ: Ω → ℝm×n are hyperplanes.