Sharp Dependence Research Articles

An interpolation result for A_1 weights with applications to fractional Poincaré inequalities

We characterize the real interpolation space between weighted \(L^1\) and \(W^{1,1}\) spaces on arbitrary domains different from \(\mathbb{R}^n\), when the weights are positive powers of the distance to the boundary multiplied by an \(A_1\) weight. As an application of this result we obtain weighted fractional Poincaré inequalities with sharp dependence on the fractional parameter \(s\) (for \(s\) close to 1) and show that they are equivalent to a weighted Poincaré inequality for the gradient.

On the thermodynamics of DNA double strand in the Peyrard-Bishop-Dauxois model

The temperature dependence of energy, partition function, entropy and free energy, describing a first-order-like phase transition of a DNA molecule is calculated based on the direct method of molecular dynamics for the classical Peyrard-Bishop-Dauxois model. It is shown that without taking into account the quantum freezing of the degrees of freedom at low temperatures, the relationship between these quantities is not determined. The latent heat of DNA melting is calculated for homogeneous PolyA/PolyT and PolyG/PolyC DNA chains. It is shown that this melting transition corresponds to a sharp temperature dependence of the heat capacity.

Unusual heat transfer dependence on boundary scattering in very long narrow conductors

When modeling heat transfer in nanoribbons, an unusually sharp dependence of the heat flux, and, consequently, the thermal conductivity coefficient, on the degree of specularity of phonon reflection from the lateral boundaries was found. From numerical calculations, it followed that the addition of minimally diffuse scattering should lead to an abrupt increase in the thermal resistance of the conductor. Given the importance of selecting optimal thermal parameters in nanotechnology, this short paper provides an analysis of the found dependencies, discusses the physical reasons for this anomalous behavior, and draws conclusions about the importance of achieving the quality of the nanoconductor interface to create thermal contacts with a given or optimal thermal conductivity.

Temporal contrast enhancement of a Ti:Sapphire laser by nonlinear Fourier filtering

Temporal cleaning of high-power infrared (IR) pulses generated by a Ti:Sapphire system is demonstrated by the use of the Nonlinear Fourier Filtering (NFF) method. In a proof-of-principle experiment suppression of up to 1000 is achieved for the temporal pedestal prior to the main pulse, with a moderate (20-25%) overall throughput. This includes the same suppression ratio for the picosecond coherent pedestal in the direct vicinity of the main pulse. Based on the instantaneous, intensity-dependent and high-order switching characteristics of NFF, excellent pulse cleaning performance is observed. The efficient, high-contrast removal of the coherent pedestal from the foot of the main pulse even if its duration is shorter than 100 fs is compared with the capability of the plasma mirror technique. Calculations are also performed, supporting the experimentally observed sharp intensity dependence of the switching process, pointing out the dominant role of the ionization-based refractive index change.

Adsorption study of the charge distribution features of highly charged smectites

The study examines the results of assessing the charge density distribution of smectite layers from the bentonite province of the Republic. Kazakhstan (Taganskoye and Dinosaurovoye fields) by alkylammonium method. The method is based on the study of the interaction of a homologous series of fatty amines with the surface of smectites. Organic cations form monomolecular and bimolecular adsorption layers on the basal surfaces. This allows the analysis of the dependence of the position of the diffraction maximum in the small-angle region on the bounding area of the organic cation and to obtain the charge density distribution over the smectite layers. The results obtained for the studied samples show a similar composition of montmorillonite: in all cases, smectites were characterized by a significant charge density with a different proportion of highly charged layers (cation exchange capacity – 120-130 mEq/100 g). The obtained data on charge distribution were compared with some adsorption and colloid-chemical characteristics of smectites, including the values of their cation exchange capacities. At the same time, such technological parameters as the effective viscosity of aqueous dispersions, despite the close charge distribution, differed significantly and showed a sharp dependence on the proportion of sodium cations in the exchange complex.

A bifurcation integrates information from many noisy ion channels and allows for milli-Kelvin thermal sensitivity in the snake pit organ

In various biological systems, information from many noisy molecular receptors must be integrated into a collective response. A striking example is the thermal imaging organ of pit vipers. Single nerve fibers in the organ reliably respond to milli-Kelvin (mK) temperature increases, a thousand times more sensitive than their molecular sensors, thermo-transient receptor potential (TRP) ion channels. Here, we propose a mechanism for the integration of this molecular information. In our model, amplification arises due to proximity to a dynamical bifurcation, separating a regime with frequent and regular action potentials (APs), from a regime where APs are irregular and infrequent. Near the transition, AP frequency can have an extremely sharp dependence on temperature, naturally accounting for the thousand-fold amplification. Furthermore, close to the bifurcation, most of the information about temperature available in the TRP channels' kinetics can be read out from the times between consecutive APs even in the presence of readout noise. A key model prediction is that the coefficient of variation in the distribution of interspike times decreases with AP frequency, and quantitative comparison with experiments indeed suggests that nerve fibers of snakes are located very close to the bifurcation. While proximity to such bifurcation points typically requires fine-tuning of parameters, we propose that having feedback act from the order parameter (AP frequency) onto the control parameter robustly maintains the system in the vicinity of the bifurcation. This robustness suggests that similar feedback mechanisms might be found in other sensory systems which also need to detect tiny signals in a varying environment.

Extending Schottky–Mott rule to van der Waals heterostructures of 2D Janus materials: Influence of intrinsic dipoles

The Schottky–Mott (S–M) limit based on the S–M rule is often used to evaluate the Schottky barrier height (SBH) at metal–semiconductor (MS) van der Waals (vdW) contacts but fails at the polar interfaces. In order to extend the S–M rule to the polar interfaces, we here modify the S–M equation to predict the SBH at vdW interfaces of 2D Janus materials, taking into account the effects of intrinsic and interface dipoles. The modified S–M equation is verified based on the first-principles calculations of the MoSi2As2P2/HTaSe2F vdW interfaces, showing a sharp dependence of SBH on the dipole amplitude and direction. Specifically, n-type Schottky barriers tend to form when a semiconductor contacts with a low-work-function surface of Janus metal or a metal interfaces to the high-electron-affinity surface of Janus semiconductor; otherwise, a p-type one is preferable. Interestingly, the smallest n(p)-type SBH could be attained when both intrinsic dipole directions are the same. This work demonstrates that the S–M rule can be extended to the polar interfaces and dipole engineering is an effective strategy to tune the SBH at the MS interface.

A Berry-Esseen bound with (almost) sharp dependence conditions

Suppose that the (normalised) partial sum of a stationary sequence converges to a standard normal random variable. Given sufficiently moments, when do we have a rate of convergence of n−1∕2 in the uniform metric, in other words, when do we have the optimal Berry-Esseen bound? We study this question in a quite general framework and find the (almost) sharp dependence conditions. The result applies to many different processes and dynamical systems. As specific, prominent examples, we study functions of the doubling map 2x mod 1, the left random walk on the general linear group and functions of linear processes.

Multimode fluorescence intensity ratio thermometer based on synergistic luminescence from Eu3+ to Mn4+ of SrTiO3:Eu3+-ZnTiO3:Mn4+ nanocomposites

SrTiO3:Eu3+-ZnTiO3:Mn4+ nanocomposites were successfully synthesized to obtain highly sensitive optical thermometers. The synthesized SrTiO3:Eu3+ was cubic perovskite structure, and the synthesized ZnTiO3:Mn4+ was cubic perovskite structure accompanying with hexagonal ilmenite structure. The results of X-ray diffraction and Fourier transform infrared spectra suggested that the mixture of SrTiO3:Eu3+-ZnTiO3:Mn4+ nanophosphors had no obvious change in the structure after heat treatment at 800 °C. The photoluminescence intensity of Eu3+ in SrTiO3 phosphors revealed a stable temperature dependence, while that of Mn4+ in ZnTiO3 phosphors revealed a sharp temperature dependence. The emission band ranging from 650 nm to 800 nm were separated into two bands centered at 690 nm and 714 nm, which were assigned to 4T2g→4A2g and 2Eg→4A2g transitions of Mn4+ ions in cubic perovskite and hexagonal ilmenite ZnTiO3 matrix, respectively. The maximum relative sensitivity revealed a dependence on the molar ratio between SrTiO3 and ZnTiO3. The maximum value of 3.3 %K−1 was achieved for the composites with the molar ratio of 1:3 between SrTiO3:Eu3+ and ZnTiO3:Mn4+ nanophosphors, which was higher than that of the composites before heat treatment, 3.1 %K−1. The results suggested the potential application in optical temperature probes for the composites.

Specific absorption rate in quasispherical and elongated aggregates of magnetite nanoparticles: Experimental characterization and numerical simulation

Assemblies of magnetite nanoparticles created by the ultrasonic mechanocavitation in a viscous liquid have been obtained for use in magnetic hyperthermia. The magnetite nanoparticles inherit the perfect crystal structure of the original coarse-grained magnetite powder, with characteristic sizes of 0.2–8 μm, and have a high saturation magnetization, Ms = 92 emu/g, close to the value of pure magnetite. Measurements of the specific absorption rate (SAR) of assemblies in an alternating (ac) magnetic field showed a significant dependence of SAR on the nanoparticle concentration, as well as on the shape of particle macroaggregates. A 4-fold increase in the SAR of elongated clusters of particles oriented parallel to the action of ac magnetic field was found in comparison with an assembly of quasi-spherical clusters. In addition a sharp dependence of the SAR of an assembly of elongated clusters on the ac magnetic field direction with respect to the cluster orientation axis was revealed. The results obtained are in qualitative agreement with the results of numerical simulation of dense clusters of magnetic nanoparticles based on the solution of the stochastic Landau-Lifshitz equation.

Preferential destruction of NH2-bearing complex interstellar molecules via gas-phase proton-transfer reactions.

Complex, nitrogen-bearing interstellar molecules, especially amines, are targets of particular interest for detection in star- and planet-forming regions, due to their possible relevance to prebiotic chemistry. However, these NH2-bearing molecules are not universally detected in sources where other, oxygen-bearing complex organic molecules (COMs) are often plentiful. Nevertheless, recent astrochemical models have often predicted large abundances for NH2-bearing complex organics, based on their putative production on dust grains. Here we investigate a range of new gas-phase proton-transfer reactions and their influence on the destruction of COMs. As in past studies, reactions between protonated COMs and ammonia (NH3) are found to be important in prolonging gas-phase COM lifetimes. However, for molecules with proton affinities (PA) greater than that of ammonia, proton-transfer reactions result in drastic reductions in abundances and lifetimes. Ammonia acts as a sink for proton transfer from low-PA COMs, while passing on protons to high-PA species; dissociative recombination with electrons then destroys the resulting ions. Species strongly affected include methylamine (CH3NH2), urea (NH2C(O)NH2) and others bearing the NH2 group. The abundances of these species show a sharp time dependence, indicating that their detectability may rest on the precise chemical age of the source. Rapid gas-phase destruction of glycine (NH2CH2COOH) in the models suggests that its future detection may be yet more challenging than previously hoped.

Uniform titania-supported Ce(iii) carbonate cluster catalysts for degradation of reactive oxygen species.

We report the synthesis of uniform 2.5 ± 0.4 nm diameter Ce(iii) carbonate clusters deposited on the surface of TiO2 nanoparticles and characterize them using HAADF-STEM and EELS, as well as UV-Vis and FTIR spectroscopies. This material is a highly proficient catalytic antioxidant for the degradation of photocatalytically generated reactive oxygen species (ROS). We observed an unusual U-shaped pH-dependence in its photoprotection catalytic activity, with an optimum function in the near-neutral pH range of 7.7 ± 0.7. This sharp pH dependence is not observed in previously reported bulk Ce(iii) carbonate materials, and it is also not a consequence of Ce(iii) carbonate cluster decomposition. However, it is consistent with a tandem reaction sequence consisting of a biomimetic superoxide dismutase and catalase function, which is dependent on a balance of protons and hydroxide anions for function. Our dissolution-deposition approach for synthesizing nanoscale Ce(iii) carbonate clusters on TiO2 should be generalizable to other carbonates and metal-oxide supports.

Ammonium Metavanadate Fabricated by Selective Precipitation of Impurity Chemicals on Inorganic Flocculants

High purity ammonium metavanadate (NH4VO3) is the most vital chemical to produce V2O5, VO2, VN alloy, VFe alloy and VOSO4, which have some prospective applications for high strength steel, smart window, infrared detector and imaging, large scale energy storage system. NH4VO3 is usually produced by spontaneous crystallization from the aqueous solution due to its sharp dependence of solubility on the temperature. However, hazardous chemicals in industrial effluent, include phosphorate, silicate and arsenate, causing severe damage to the environment. In this work, these impurities are selectively precipitated onto inorganic flocculants, while the vanadate dissolved in an aqueous solution keeps almost undisturbed. Therefore, high purity NH4VO3 is produced by the crystallization from the purified solution. By screening various flocculants and precipitating parameters, polyaluminum sulfate with an optimal amount of 50 g/L, is demonstrated to selectively remove phosphorate, silicate and arsenate, corresponding to the removing efficiency of 93.39%, 97.11% and 88.31%, respectively. NH4VO3 from the purified solution holds a purity of 99.21%, in comparison with 98.33% in the product from the crude solution. This purifying technology cannot only produce NH4VO3 with high added value, but also reduce the environmental pollution of waste liquid.

Acceleration of Nonradiative Charge Recombination Reactions at Larger Distances in Kinked Donor-Bridge-Acceptor Molecules.

Photoinduced electron transfer in donor-bridge-acceptor (D-B-A) molecular systems can occur via tunneling over long distances (rDA) of well over 10 Å. We commonly observe decreasing rates of electron transfer with increasing distances, a result of a decrease in the electronic coupling of the donor and acceptor moiety. In the study of D-B-A molecules with Ru(bpy)32+ as a bridge/core, Kuss-Petermann and Wenger observed the opposite trend (J. Am. Chem. Soc.2016, 138, 1349); a maximum rate constant of electron transfer was observed at an intermediate electron transfer distance. Within the high-temperature limit of the classical Marcus equation, their observation was qualitatively explained by a sharp distance dependence of outer sphere (or solvent) reorganization energy, as predicted by Sutin and co-workers (J. Am. Chem. Soc.1984, 106, 6858), and almost distance-independent electronic couplings. Here, we report another example of such an underexplored behavior with three kinked D-B-A systems of rDA ∼ 10-19 Å, showing increasing rates of nonradiative charge recombination with increasing rDA. The three D-B-A systems are based on boron dipyrromethene and triphenylamine as electron acceptor and donor groups, respectively, with aryl bridges where the donor and acceptor moieties are connected at meso-positions. These D-B-A molecules exhibit radiative electron transfer reactions (or charge-transfer emission), which enables us to experimentally determine the solvent reorganization energy and the electronic couplings. The analysis of charge-transfer emission that explicitly considers electron-vibration coupling, in conjunction with the temperature-dependent analysis and computational method, revealed that the solvent reorganization energy indeed increases with distance, and at the same time, the electronic coupling decreases with distance expectedly. Therefore, under the right conditions for solvent reorganization energy and electronic coupling values, our results show that we can observe the acceleration of electron transfer reactions with increasing distance, even when we have the expected distance dependence of electronic coupling. This work indicates that the acceleration of electron transfer with increasing distance may be achieved with a fine-tuning of molecular design.

NN¯ production in e+e− annihilation near the threshold revisited

Production of $p\bar{p}$ and $n\bar{n}$ pairs in $e^{+}e^{-}$ annihilation near the threshold of the process is discussed with account for the new experimental data appeared recently. Since a significant part of these new data was obtained at energies noticeably exceeding the threshold, we also take into account the form factor describing the amplitude of $N\bar{N}$ pair production at small distances. The effective optical potential, which describes a sharp dependence of the $N\bar{N}$ production cross sections near the threshold, consists of the central potential for $S$ and $D$ waves and the tensor potential. These potentials differ for the states with isospin $I=0$ and $I=1$ of $N\bar{N}$ pair. The optical potential describes well $N\bar{N}$ scattering phases, the cross sections of $p\bar{p}$ and $n\bar{n}$ production in $e^{+}e^{-}$ annihilation near the threshold, the electromagnetic form factors $G_{E}$ and $G_{M}$ for protons and neutrons, as well as the cross sections of the processes $e^{+}e^{-}\to6\pi$ and $e^{+}e^{-}\to K^{+}K^{-}\pi^{+}\pi^{-}$.

Grain-size effects on the temperature-dependent elastocaloric cooling performance of polycrystalline NiTi alloy

Grain-size (GS) effects on the temperature-dependent elastocaloric cooling performance of NiTi with the average GS of 11, 22, 30, 45 and 70 nm are investigated over a temperature range from -50 ℃ to 80 ℃. It is found that GS refinement is conducive to improving the thermal stability of superelasticity and the associated elastocaloric effect, while the trade-off between cooling temperature drop ΔT and effective working temperature span Tspan, more or less, is inevitable regardless of GS. The large ΔT of the 70 nm-GS specimen, which is characterized by sharp first-order martensitic transformation and strong temperature dependence of the transformation stress dσtr/dT (= 5.7 MPa/℃), is restricted to a narrow Tspan (= 19 ℃). Tspan can be widened by five times via reducing GS to 11 nm but at the expense of a significant sacrifice in ΔT, as the combined result of high strength and small dσtr/dT (= 0.9 MPa/℃). Among the five microstructures, the 30 nm-GS one achieves a favorable compromise between ΔT and Tspan owing to the mild transformation nature together with robust mechanical properties. Consequently, its ΔT can reach 50% – 440% of that of the 70 nm-GS counterpart and the resultant cooling efficiency can be enhanced by a factor of half to six. The work demonstrates that GS engineering is a feasible approach for reconciling various elastocaloric cooling metrics of the NiTi refrigerant.

Wavelet representation of singular integral operators

This article develops a novel approach to the representation of singular integral operators of Calderón–Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is realized as a finite sum of averages of wavelet projections of either cancellative or noncancellative type, which are themselves Calderón–Zygmund operators. Both properties are out of reach for the established dyadic-probabilistic technique. Unlike their dyadic counterparts, our representation reflects the additional kernel smoothness of the operator being analyzed. Our representation formulas lead naturally to a new family of T(1) theorems on weighted Sobolev spaces whose smoothness index is naturally related to kernel smoothness. In the one parameter case, we obtain the Sobolev space analogue of the \(A_2\) theorem; that is, sharp dependence of the Sobolev norm of T on the weight characteristic is obtained in the full range of exponents. In the bi-parametric setting, where local average sparse domination is not generally available, we obtain quantitative \(A_p\) estimates which are best known, and sharp in the range \(\max \{p,p'\}\ge 3\) for the fully cancellative case.

Supertransport by Superclimbing Dislocations in He4 : When All Dimensions Matter

The unique superflow-through-solid effect observed in solid ^{4}He and attributed to the quasi-one-dimensional superfluidity along the dislocation cores exhibits two extraordinary features: (i) an exponentially strong suppression of the flow by a moderate increase in pressure and (ii) an unusual temperature dependence of the flow rate with no analogy to any known system and in contradiction with the standard Luttinger liquid paradigm. Based on ab initio and model simulations, we argue that the two features are closely related: Thermal fluctuations of the shape of a superclimbing edge dislocation induce large, correlated, and asymmetric stress fields acting on the superfluid core. The critical flux is most sensitive to strong rare fluctuations and hereby acquires a sharp temperature dependence observed in experiments.

Methods for the calibration of bone conduction transducers at frequencies from 5 to 20 kHz.

Techniques for standardizing the output of bone conduction transducers over the 5-20 kHz range are presented. The techniques include definitions of the standard artificial mastoid (AM) impedance and force sensitivity in that high-frequency range using an impedance head coupled to a vibration source. The AM impedance is shown to vary with the contact area of the vibration source. The AM force sensitivity does not vary with the contact area but does exhibit sharp frequency dependences over the 14-20 kHz range. The sharp frequency dependence complicates the use of the AM force sensor as a stand-alone calibration device at these high frequencies. An alternative calibration scheme that uses an accelerometer interposed between the vibrator and the AM impedance is described. Comparisons of the two schemes demonstrate that the accelerometer method produces more consistent results. Comparisons of the force and acceleration output of one bone conduction vibrator at high frequencies suggest those outputs depend on the driven load. The loads used in the two calibration schemes are compared to what is known of the impedance of the skin-covered head.

Absorption and stationary fluorescent spectra of molecular sensors in solution: A computational study

In this study we report the application and the extension of a theoretical-computational method for the modelling of absorption and stationary emission (electronic) spectra of flexible and easily polarizable chromophores embedded in complex environments. The method, similar but computationally less expensive than the most popular Quantum Mechanics/Molecular Mechanics (QM/MM) approaches, is based on a combination of Molecular Dynamics simulations, Quantum-Chemical calculations and elementary statistical mechanics. As a test case we have addressed, in the present study, the spectral features of two solvated chromophores, experimentally shown by our group to be very sensitive to the solvent (environment) polarity, formed by a 4-[4-(1-dimethylamino)phenyl]-pyridine moiety linked to an uracil group through an alkyl spacer of different lengths. The method, despite the involved approximations and intrinsic drawbacks, is able of reproducing both the absorption and emission spectra of the above system as well as the sharp dependency of the spectral observables on the environment polarity. In this respect it might represent an efficient tool, alternative to more accurate QM/MM-based approaches, in cases where their application could be made computationally very expensive.