Low Exponent Research Articles

On the universality of power laws for tokamak plasma predictions

Significant deviations from well established power laws for the thermal energy confinement time, obtained from extensive databases analysis as the IPB98(y,2), have been recently reported in dedicated power scans. In order to illuminate the adequacy, validity and universality of power laws as tools for predicting plasma performance, a simplified analysis has been carried out in the framework of a minimal modeling for heat transport which is, however, able to account for the interplay between turbulence and collinear effects with the input power known to play a role in experiments with significant deviations from such power laws. Whereas at low powers, the usual scaling laws are recovered with little influence of other plasma parameters, resulting in a robust power low exponent, at high power it is shown how the exponents obtained are extremely sensitive to the heating deposition, the q-profile or even the sampling or the number of points considered due to highly non-linear behavior of the heat transport. In particular circumstances, even a minimum of the thermal energy confinement time with the input power can be obtained, which means that the approach of the energy confinement time as a power law might be intrinsically invalid. Therefore plasma predictions with a power law approximation with a constant exponent obtained from a regression of a broad range of powers and other plasma parameters which can non-linearly affect and suppress heat transport, can lead to misleading results suggesting that this approach should be taken cautiously and its results continuously compared with modeling which can properly capture the underline physics, as gyrokinetic simulations.

Synthesis and Electronic Structures of Heavy Lanthanide Metallocenium Cations.

The origin of 60 K magnetic hysteresis in the dysprosocenium complex [Dy(Cpttt)2][B(C6F5)4] (Cpttt = C5H2tBu3-1,2,4, 1-Dy) remains mysterious, thus we envisaged that analysis of a series of [Ln(Cpttt)2]+ (Ln = lanthanide) cations could shed light on these properties. Herein we report the synthesis and physical characterization of a family of isolated [Ln(Cpttt)2]+ cations (1-Ln; Ln = Gd, Ho, Er, Tm, Yb, Lu), synthesized by halide abstraction of [Ln(Cpttt)2(Cl)] (2-Ln; Ln = Gd, Ho, Er, Tm, Yb, Lu). Complexes within the two families 1-Ln and 2-Ln are isostructural and display pseudo-linear and pseudo-trigonal crystal fields, respectively. This results in archetypal electronic structures, determined with CASSCF-SO calculations and confirmed with SQUID magnetometry and EPR spectroscopy, showing easy-axis or easy-plane magnetic anisotropy depending on the choice of Ln ion. Study of their magnetic relaxation dynamics reveals that 1-Ho also exhibits an anomalously low Raman exponent similar to 1-Dy, both being distinct from the larger and more regular Raman exponents for 2-Dy, 2-Er, and 2-Yb. This suggests that low Raman exponents arise from the unique spin-phonon coupling of isolated [Ln(Cpttt)2]+ cations. Crucially, this highlights a direct connection between ligand coordination modes and spin-phonon coupling, and therefore we propose that the exclusive presence of multihapto ligands in 1-Dy is the origin of its remarkable magnetic properties. Controlling the spin-phonon coupling through ligand design thus appears vital for realizing the next generation of high-temperature single-molecule magnets.

Assessment of Aerosol Characteristics and Radiative Forcing Over Northwest Himalayan Region

The study examined spectral aerosol optical depth (AOD) carried out using ground based measurements (MicrotopsII) and satellite data (MODIS&MISR) over Dehradun, part of Northwest Himalayas during January–December 2015. During premonsoon the region experiences high mean AOD500 (0.34 ± 0.09 to 0.63 ± 0.12) along with low mean Angstrom exponent (α) (0.46 ± 0.09 to 0.66 ± 0.10) attributing to the dominance of mineral dust aerosols while moderate mean AOD500 and α during monsoon and post monsoon season are (0.38 ± 0.08 to 0.54 ± 0.16) and (0.78 ± 0.1 to 0.91 ± 0.11), respectively, indicating mixed type aerosols. During winter season low mean AOD500 (0.29 ± 0.06 to 0.46 ± 0.12) and high mean α (1.12 ± 0.09 to 1.30 ±0.1) is observed due to domination of fine mode aerosols coming from anthropogenic activities and agricultural biomass burning. Aerosol transport pathways were analyzed and complimented with Hysplit air mass back trajectory. Comparison of satellite derived AOD agrees well with Microtops measurements ( ${\rm{R\,= \,0.80}}$ and 0.71 for MODIS and MISR, respectively). MODIS data were used to generate spatial and seasonal distribution of AOD over northwest Himalayans and validated over selected stations in the region. The results show that AOD values are in agreement within an error of 11%–14% over entire region. The monthly and seasonal radiative forcing (ARF) was estimated over selected stations in the region. The annual mean atmospheric ARF over Dehradun was estimated to +25.83 Wm−2, while + 30.83 Wm−2 over Patiala, and + 14.97 Wm−2 over Kullu. The ratio of Surface to TOA forcing is found to be ∼2.4 to 3.7 indicating absorbing nature of aerosols predominantly existing over Northwest Himalayas.

Superplasticity in a commercially extruded ZK30 magnesium alloy

The high temperature mechanical behavior of a commercial ZK30 magnesium alloy was studied by means of tensile tests at various temperatures and strain rates. This behavior was related to the complex as-received microstructure that evolves during testing to a microstructure formed by few large grains (≈ 30µm) combined with a large amount of small grains (1–5µm). Large elongations to failure up to 360% and low apparent stress exponents between 2.6 and 2.9 at low strain rates are a hint of the activation of grain boundary sliding as the controlling deformation mechanism. This is corroborated by the equiaxed microstructure after testing. The stress exponents higher than 2 are attributed to the accelerated grain growth of the dual grain size microstructure.

Optimal lower exponent for the higher gradient integrability of solutions to two-phase elliptic equations in two dimensions

We study the higher gradient integrability of distributional solutions u to the equation {{mathrm{div}}}(sigma nabla u) = 0 in dimension two, in the case when the essential range of sigma consists of only two elliptic matrices, i.e., sigma in {sigma _1, sigma _2} a.e. in Omega . In Nesi et al. (Ann Inst H Poincaré Anal Non Linéaire 31(3):615–638, 2014), for every pair of elliptic matrices sigma _1 and sigma _2, exponents p_{sigma _1,sigma _2}in (2,+infty ) and q_{sigma _1,sigma _2}in (1,2) have been found so that if uin W^{1,q_{sigma _1,sigma _2}}(Omega ) is solution to the elliptic equation then nabla uin L^{p_{sigma _1,sigma _2}}_{mathrm{weak}}(Omega ) and the optimality of the upper exponent p_{sigma _1,sigma _2} has been proved. In this paper we complement the above result by proving the optimality of the lower exponent q_{sigma _1,sigma _2}. Precisely, we show that for every arbitrarily small delta , one can find a particular microgeometry, i.e., an arrangement of the sets sigma ^{-1}(sigma _1) and sigma ^{-1}(sigma _2), for which there exists a solution u to the corresponding elliptic equation such that nabla u in L^{q_{sigma _1,sigma _2}-delta }, but nabla u notin L^{q_{sigma _1,sigma _2}}. The existence of such optimal microgeometries is achieved by convex integration methods, adapting to the present setting the geometric constructions provided in Astala et al. (Ann Scuola Norm Sup Pisa Cl Sci 5(7):1–50, 2008) for the isotropic case.

Factoring RSA moduli with primes sharing bits in the middle

We address the problem of factoring a large RSA modulus $$N=pq$$ with p and q sharing a portion of bits in the middle. New polynomial time algorithms for computing the prime decomposition of N under certain conditions are presented. As an application, several attacks against RSA system using this class of moduli with low public exponent are described. Our results suggest that such integers are not appropriate for cryptographic purposes.

HTPB/AP계 고체 추진제의 연소속도 증진 방안 연구

본 논문에서는 HTPB/AP/Al계 추진제의 성능 개선을 위한 연소속도와 압력지수를 제어하기 위하여 연소특성에 관한 AP입자 사이즈 비율과 연소촉매로 사용된 Butacene 함량의 영향을 조사하였다. 23%의 <TEX>$28{\mu}m$</TEX> Al과 3%의 Butacene을 포함하는 추진제 조성에서 연소속도와 압력지수는 <TEX>$9{\mu}m$</TEX> AP 입자의 함량이 증가함에 따라 증가하였다. 그리고 Butacene을 함유하는 추진제는 비교적 낮은 압력지수 특성을 보임으로써 Butacene의 함량이 증가함에 따라 연소속도도 증가하였다. 그러나 Butacene의 함량에 의한 압력지수의 변화는 크게 나타나지 않았다. In this paper, in order to control the burning rate and pressure exponent of HTPB/AP/Al based propellant for the improvement of performance, the effect of the size ratio of AP particles and various contents of Butacene as burning catalyst on combustion properties was investigated. In the propellant formulation with both <TEX>$28{\mu}m$</TEX> Al of 23% and Butacene of 3%, the burning rate and pressure exponent were increased with increasing the contents of <TEX>$9{\mu}m$</TEX> AP particles. And the burning rate was increased with increasing the contents of Butacene with showing the relatively low pressure exponent in the propellant containing Butacene. However, the significant variations of pressure exponent by contents of Butacene were not observed.

Modeling of chemical reactions between polyatomic molecules for atmospheric entry simulations with direct simulation Monte Carlo

For the simulation of atmospheric entry maneuvers at Mars and Saturn’s Titan, the chemistry modeling of polyatomic molecules is implemented in the direct simulation Monte Carlo method within the reactive plasma flow solver PICLas. An additional reaction condition as well as the consideration of the vibrational degrees of freedom is described in the context of the total collision energy model. The treatment of reverse exchange and recombination reactions is discussed, where the low temperature exponent of the Arrhenius fit for methane dissociation limited the calculation of the reaction probability at relevant temperatures. An alternative method based on the equilibrium constant is devised. The post-reaction energy redistribution is performed under the assumption of equipartition of the remaining collisional energy. The implementation is verified for several reaction paths with simple reservoir simulations. Finally, the feasibility of the new chemistry model is demonstrated by a simulation of a trajectory point of Huygens probe at Titan.

Characterization of Aging Behavior of Butacene® Based Composite Propellants by Loss Factor Curves

AbstractButacene® is a polymeric binder with ferrocenyl groups chemically bonded to HTPB backbone. Through incorporation in the AP−Al composite propellant formulation, it leads to high burning rates (BR) &gt;20 mm/s at 7 MPa, and low pressure exponents n&lt;0.5, allowing more flexibility to the rocket design, keeping the characteristics (process, mechanical properties, pot‐life) of HTPB binder formulations together with a lower vulnerability (IM) contribution by Butacene®. The key molecular level characteristic of such HTPB based elastomeric binder systems of solid composite rocket propellants (SCRP) is the glass‐rubber transition region, which is mainly defined by the molecular mobility of the components in the polymeric network during the transition from energy to entropy elasticity with respect to temperature. The molecular rearrangement regions or binder mobility fractions related to the glass‐rubber transition of such composite propellants during storage are important in terms of in‐service time estimations. They are detectable by dynamic mechanical analysis (DMA). Formulations with and without Butacene® were prepared and analyzed using the loss factor curves obtained by torsion DMA. A special modelling with so named Exponentially Modified Gaussian (EMG) distribution was used to define and quantify sub‐transition regions in the loss factor curve. SEM images revealed the network formation connected with AP bonding, which correlate to the tensile results. DMA loss factors revealed a strong oxidation with Butacene® containing formulations during aging. Burning rates of the formulations show slight increases with aging.

Domain growth dynamics in (K, Na)NbO 3 ferroelectric thin films

(K,Na)NbO3 (KNN) based lead-free materials have gained great progress and drawn much attention recently, due to their attractive piezoelectric performance and the demand for environmental protection. As is known, domain motion is essential for piezoelectric output; however, there is limited understanding on this topic for KNN. In the present study, the domain growth process of the KNN thin film is studied by piezoresponse force microscopy (PFM). The domain size shows a linear dependence on the pulse voltage and a complex dependence, unlike the commonly accepted logarithmic relationship, on the pulse duration. Meanwhile, a power decay relationship between the domain wall velocity and the domain size is observed. The extremely low dynamical exponent proves that our sample is influenced by extremely strong pinning effects caused by defects, resulting in the uncommon pulse duration dependence of domain size.

Basal metabolic rate in free-living tropical birds: the influence of phylogenetic, behavioral, and ecological factors.

The majority of our knowledge of avian energetics is based on studies of birds from temperate and high latitudes. Using the largest existing sample of wild-caught Old World tropical species, we showed that birds from Southern Vietnam had lower basal metabolic rate (BMR) than temperate species. The strongest dissimilarity between tropical and temperate species was the low scaling exponent in the allometric relation between BMR and body mass in tropical birds (the regression slope was 0.573). The passerine migrants to temperate and high latitudes had higher BMR than tropical sedentary passerines. Body mass alone accounted for 93% of the variation in BMR (body mass ranged from 5 to 252 g). Contrary to some other studies, we did not find evidence besides the above mentioned that phylogeny, taxonomy, behavior, or ecology have a significant influence on BMR variation among tropical birds.

Kinetics of sub-spinodal dewetting of thin films of thickness dependent viscosity

An alternative explanation of the time varying and very low growth exponents in dewetting of polymer films like polystyrene films is presented based on non-linear simulations. The kinetics of these films is explored within the framework of experimentally observed thickness dependent viscosity. These films exhibit sub-spinodal dewetting via formation of satellite holes in between primary dewetted holes under favorable conditions of excess intermolecular forces and film thicknesses. We find that conditions responsible for sub-spinodal dewetting concurrently lead to remarkable changes in the kinetics of dewetting of even primary holes. For example, the radius of the hole grows in time with a power-law growth exponent sequence of , in contrast to the usual ∼4/5. This is due to the cumulative effect of reduced rim mobility due to thickness dependent viscosity and hindrance created by satellite holes.

Identification of the steady-state creep behavior of Zircaloy-4 claddings under simulated Loss-Of-Coolant Accident conditions based on a coupled experimental/numerical approach

The secondary creep behavior of Zircaloy-4 (Zr-4) claddings under simulated Loss-Of-Coolant Accident (LOCA) conditions was investigated. A coupled experimental / numerical approach is developed to determine the steady-state creep constitutive law’s parameters. The test matrix targets thermal mechanical conditions for which several creep mechanisms are expected to take place (phase transition zone of Zr-4).Ballooning tests were performed on tubular specimens. A heterogeneous thermal mechanical loading was applied to the specimen. The resulting thermal and kinematics fields were measured using full-field optical measurements. Then a Finite Element model was updated to determine a constitutive Norton creep law fitting the kinematic fields measured by way of digital image correlation (DIC). The following methodology enables a significant reduction in the number of tests used for the mapping of creep mechanisms depending on stress and temperature conditions. The results of nine experiments covering stresses from 7 to 45 MPa and temperatures varying from 745 to 850 °C are detailed. In the α-phase domain, the transition from low Norton exponents (∼ 1) to higher ones (∼ 4-5) is observed at a von Mises stress of 26 MPa. The activation energies are consistent in the α-phase domain. For modeling purposes, several tests (T < 810 °C) were then correlated. Three constitutive laws, depending on the stress and creep-rate levels, were determined. Norton exponent and activation energy consistent with the superplasticity observed by Garde et al. were identified in the early stage of the two-phase domain.

Long-term ground deformation patterns of Bucharest using multi-temporal InSAR and multivariate dynamic analyses: a possible transpressional system?

The aim of this exploratory research is to capture spatial evolution patterns in the Bucharest metropolitan area using sets of single polarised synthetic aperture radar (SAR) satellite data and multi-temporal radar interferometry. Three sets of SAR data acquired during the years 1992–2010 from ERS-1/-2 and ENVISAT, and 2011–2014 from TerraSAR-X satellites were used in conjunction with the Small Baseline Subset (SBAS) and persistent scatterers (PS) high-resolution multi-temporal interferometry (InSAR) techniques to provide maps of line-of-sight displacements. The satellite-based remote sensing results were combined with results derived from classical methodologies (i.e., diachronic cartography) and field research to study possible trends in developments over former clay pits, landfill excavation sites, and industrial parks. The ground displacement trend patterns were analysed using several linear and nonlinear models, and techniques. Trends based on the estimated ground displacement are characterised by long-term memory, indicated by low noise Hurst exponents, which in the long-term form interesting attractors. We hypothesize these attractors to be tectonic stress fields generated by transpressional movements.

Toroidal Alfvén eigenmodes with nonlinear gyrokinetic and fluid hybrid models

Alfvén eigenmodes may be important in driving fast particle transport in magnetic confinement fusion devices, with potentially deleterious results. To explain and predict this behaviour, numerical simulations are necessary. In order to predict transport, modes must be simulated through to their nonlinear saturated state. In this work, the first simulations of non-linear wave-particle interaction between an energetic particle population and a Toroidal Alfvén Eigenmode are performed in which fluctuations responding self-consistently to modification of the fast particle profile are calculated with gyrokinetic treatment of all plasma species. Results from two such gyrokinetic codes are compared with new results from non-perturbative and perturbative fluid-gyrokinetic hybrid codes. There is a power-law relationship between the saturated magnetic perturbation amplitude, δB∕B0, and the linear mode growth rate, γL. All models show a transition from a higher to a lower exponent regime with increasing γL. Measured values of the higher exponent from different codes fall in a range between 1.45 and 1.79, while the lower exponent falls in a range between 0.47 and 0.79. There is a consistent difference of 1.0 between the higher and lower exponents independent of the model. The absolute level of saturated δB∕B0 is determined by the damping rate. In the fluid-gyrokinetic hybrid codes, an ad-hoc damping is applied, while in the gyrokinetic case the measured damping is consistent with the estimated rate of physical electron Landau damping.

Softening Mechanisms of the AISI 410 Martensitic Stainless Steel Under Hot Torsion Simulation

This study investigated the softening mechanisms of the AISI 410 martensitic stainless steel during torsion simulation under isothermal continuous in the temperature range of 900 to 1150 °C and strain rates of 0.1 to 5.0s-1. In the first part of the curves, before the peak, the results show that the critical (ec) and peak (ep) strains are elevated for higher strain rate and lower temperatures contributing for higher strain hardening rate (h). Moreover, this indicated that dynamic recrystallization (DRX) and dynamic recovery (DRV) are not effective in this region. After the peak, the reductions in stresses are associated to the different DRX/DRV competitions. For lower temperatures and higher strain rates there is a delay in the DRX while the DRV is acting predominantly (with low Avrami exponent (n) and high t0.5). The steady state was reached after large strains showing DRX grains, formation of retained austenite and the presence of chromium carbide (Cr23C6) and ferrite δ at the martensitic grain boundaries. These contribute for impairing the toughness and ductility on the material. The constitutive equations at the peak strain indicated changes in the deformation mechanism, with variable strain rate sensitivity (m), which affected the final microstructure.

A new stylolite classification scheme to estimate compaction and local permeability variations

We modeled the geometrical roughening of bedding-parallel, mainly layer-dominated stylolites in order to understand their structural evolution, to present an advanced classification of stylolite shapes and to relate this classification to chemical compaction and permeability variations at stylolites. Stylolites are rough dissolution seams that develop in sedimentary basins during chemical compaction. In the Zechstein 2 carbonate units, an important lean gas reservoir in the southern Permian Zechstein basin in Germany, stylolites influence local fluid flow, mineral replacement reactions and hence the permeability of the reservoir. Our simulations demonstrate that layer-dominated stylolites can grow in three distinct stages: an initial slow nucleation phase, a fast layer-pinning phase and a final freezing phase if the layer is completely dissolved during growth. Dissolution of the pinning layer and thus destruction of the stylolite's compaction tracking capabilities is a function of the background noise in the rock and the dissolution rate of the layer itself. Low background noise needs a slower dissolving layer for pinning to be successful but produces flatter teeth than higher background noise. We present an advanced classification based on our simulations and separate stylolites into four classes: (1) rectangular layer type, (2) seismogram pinning type, (3) suture/sharp peak type and (4) simple wave-like type. Rectangular layer type stylolites are the most appropriate for chemical compaction estimates because they grow linearly and record most of the actual compaction (up to 40mm in the Zechstein example). Seismogram pinning type stylolites also provide good tracking capabilities, with the largest teeth tracking most of the compaction. Suture/sharp peak type stylolites grow in a non-linear fashion and thus do not record most of the actual compaction. However, when a non-linear growth law is used, the compaction estimates are similar to those making use of the rectangular layer type stylolites. Simple wave-like stylolites are not useful for compaction estimates, since their growth is highly non-linear with a very low growth exponent. In the case where sealing material is collected at the tooth during dissolution, stylolites can act as barriers for local fluid flow as they intensify sealing capabilities of pinning layers. However, the development of teeth and spikes offsets and thus destroys continuous stylolite seams so that the permeability across the stylolite becomes very heterogeneous and they are no continuous barriers. This behavior is best shown in rectangular layer and seismogram pinning type stylolites that develop efficient fluid barriers at teeth tips but destroy sealing capabilities of layers by offsetting them at the flank, leading to a permeability anisotropy along 2-D stylolite planes. Suture/sharp peak stylolites can create fluid barriers if they collect enough sealing material. However, if the collecting material does not seal or if spikes offset the sealing material the stylolite leaks. We propose that our classification can be used to realistically estimate chemical compaction in reservoirs and gives an indication on how heterogeneous the permeability of stylolites can be.

Analytical expression of the Eshelby tensor for arbitrary polygonal inclusions in two-dimensional elasticity

Abstract We derive the analytical expression of the Eshelby tensor field for inclusions of arbitrary polygonal shape. Differently from previous contributions in the literature, the formula proved in the paper has a particularly compact expression since it is based on the analytical evaluation of integrals depending by lower exponents of the scalar product of the vector connecting the source and observation points. Moreover, the formula is directly expressed as function of the coordinates defining the vertices of the polygon, thus avoiding the use of complex variables and anomalies. The effectiveness of the proposed formulation is numerically assessed by comparing the results provided by its implementation in a Matlab code with available results specifically contributed by different authors for weakly non-circular inclusions.

Interpreting anomalous low-strength and low-stiffness of nanoporous gold: Quantification of network connectivity

The strength and elastic modulus of macroscopic nanoporous Au samples are much lower than that predicted by using Gibson-Ashby scaling laws. Here we attribute this discrepancy to a lowered network connectivity in nanoporous structure, and propose to modify the scaling equations (for both strength and stiffness) by introducing a concept of effective relative density. It is presented that the effective relative density can be determined by measuring the elasticity of nanoporous Au; under this scenario, the corrected strengths of Au nano-ligaments agree (on the order of magnitude) well with the previous data for similar-sized Au nanowires or nanopillars, which confirms our hypotheses. This study also revealed a low power-law exponent of size-dependent strength for Au nano-ligaments (β = −0.34) compared with that of Au submicron-pillars machined by focused ion beam (FIB) (β = −0.61), which may be related to the critical roles of surface defects played in deformation. A ratio between effective relative density and relative density is suggested to quantify the network connectivity in nanoporous structure, which decreases rapidly during structure coarsening – it explains why most previous nanoporous Au samples, which more or less experienced coarsening, were unexpectedly soft. Current study also leads to some general strategies for syntheses of strong and stiff nanoporous metals.

Interfacial diffusion aided deformation during nanoindentation

Nanoindentation is commonly used to quantify the mechanical response of material surfaces. Despite its widespread use, a detailed understanding of the deformation mechanisms responsible for plasticity during these experiments has remained elusive. Nanoindentation measurements often show stress values close to a material’s ideal strength which suggests that dislocation nucleation and subsequent dislocation activity dominates the deformation. However, low strain-rate exponents and small activation volumes have also been reported which indicates high temperature sensitivity of the deformation processes. Using an order parameter aided temperature accelerated sampling technique called adiabatic free energy dynamics [J. B. Abrams and M. E. Tuckerman, J. Phys. Chem. B, 112, 15742 (2008)], and molecular dynamics we have probed the diffusive mode of deformation during nanoindentation. Localized processes such as surface vacancy and ad-atom pair formation, vacancy diffusion are found to play an important role during indentation. Our analysis suggests a change in the dominant deformation mode from dislocation mediated plasticity to diffusional flow at high temperatures, slow indentation rates and small indenter tip radii.