Large Decay Research Articles

Remarks on the decay of Fourier coefficients to solutions of Navier-Stokes system

We first investigate the large time decay of the Fourier coefficients to the global mild solution of Navier-Stokes system with periodic boundary condition and with small enough initial data. In particular, this result ensures the fast decay of Fourier coefficients to any global solution u ∈ C ( [ 0 , ∞ [ ; H ˙ 1 2 ( T 3 ) ) u\in C([0,\infty [;\dot H^{\frac 12}({\mathbb T}^3)) of Navier-Stokes system. Then we extend this result to Navier-Stokes system with an additional low frequency damping term in the whole space. Finally, we prove that the radius of analyticity R ( t ) R(t) to this modified system with small initial data in H ˙ 1 2 ( R 3 ) \dot {H}^{\frac 12}(\mathbb {R}^3) is bounded from below by a positive constant times t , t, which makes sharp contrast with the corresponding result for the classical Navier-Stokes system that R ( t ) t − 1 2 R(t)t^{-\frac 12} is bounded from below by a positive constant.

Tuning the Excited State of Tetradentate Pd(II) and Pt(II) Complexes through Benzannulated N‐Heteroaromatic Ring and Central Metal

Comprehensive SummaryA series of tetradentate Pd(II) and Pt(II) complexes containing fused 5/6/6 metallocycles with phenyl N‐heteroaromatic benzo[d]imidazole (pbiz), benzo[d]oxazole (pboz) or benzo[d]thiazole (pbthz)‐containing ligands was developed. Systematic studies by experiments and theoretical calculations reveal that both the central metal and the benzannulated N‐heteroaromatic ring have significant influence on the electrochemical, photophysical and excited‐state properties of the Pd(II) and Pt(II) complexes. In identical condition, compared to pbiz‐based Pd(II) and Pt(II) complexes, the corresponding metal complexes with pboz and pbthz‐containing ligand show significant red‐shift emission spectra. Pd(II) complexes exhibit blue‐shift emission spectra in comparison with the corresponding Pt(II) complexes. The Pt(II) complexes possess more metal‐to‐ligand charge transfer (3MLCT) character in their T1 states, which enables the Pt(II) complexes to have much higher quantum efficiencies (ΦPL) and shorter excited‐state lifetimes (τ), resulting in large radiative decay rates (kr). Especially, Pt(pbiz) has a ΦPL of 94% with a τ of 4.0 μs in 5 wt% doped PMMA film at room temperature. Pt(pbiz)‐doped green organic light‐emitting diode (OLED) using 26mCPy as host demonstrated a peak external quantum efficiency (EQE) of 21.6% and a maximum brightness (Lmax) of 55481 cd/m2, which still maintained an EQE of 16.5% and 10.8% at 1000 and 10000 cd/m2, respectively.

Force decay of polyethylene terephthalate glycol aligner materials during simulation of typical clinical loading/unloading scenarios.

This invitro study investigated the effect of three distinct daily loading/unloading cycles on force delivery during orthodontic aligner therapy. The cycles were applied for 7days and were designed to reflect typical clinical aligner application scenarios. Flat polyethylene terephthalate glycol (PET-G) specimens (Duran®, Scheu Dental, Iserlohn, Germany) with thicknesses ranging between 0.4 and 0.75 mm were tested in athree-point-bending testing machine. Measurements comprised loading/unloading intervals of 12 h/12 h, 18 h/6 h, and 23 h/1 h, and specimens were exposed to bidistilled water during loading to simulate intraoral conditions. Avery large decay in force for the PET‑G specimens could already be observed after the first loading period, with significantly different residual force values of 24, 20, and 21% recorded for the 12 h/12 h, 18 h/6 h, and 23 h/1 h loading/unloading modes, respectively (Mann-Whitney U test, p < 0.01). In addition, further decays in force from the first to the last loading period at day7 of 13.5% (12 h/12 h), 9.7% (18 h/6 h), and 8.4% (23 h/1 h) differed significantly among the three distinct loading modes (Mann-Whitney U test, p < 0.01). Although the initial material stiffness of PET‑G is relatively high, the transmission of excessive forces is attenuated by the high material-related force decay already within afew hours after intraoral insertion.

Large Time Asymptotics for a Cubic Nonlinear Schrödinger System in One Space Dimension, II

This is a sequel to the paper "Large time asymptotics for a cubic nonlinear Schr\"odinger system in one space dimension" by the same authors. We continue to study the Cauchy problem for the two-component system of cubic nonlinear Schr\"odinger equations in one space dimension. We provide criteria for large time decay or non-decay in $L^2$ of the small amplitude solutions in terms of the Fourier transforms of the initial data.

Ionic screening in bulk and under confinement.

Recent experiments have shown that the repulsive force between atomically flat, like-charged surfaces confining room-temperature ionic liquids or concentrated electrolytes exhibits an anomalously large decay length. In our previous publication [J. Zeman, S. Kondrat, and C. Holm, Chem. Commun. 56, 15635 (2020)], we showed by means of extremely large-scale molecular dynamics simulations that this so-called underscreening effect might not be a feature of bulk electrolytes. Herein, we corroborate these findings by providing additional results with more detailed analyses and expand our investigations to ionic liquids under confinement. Unlike in bulk systems, where screening lengths are computed from the decay of interionic potentials of mean force, we extract such data in confined systems from cumulative charge distributions. At high concentrations, our simulations show increasing screening lengths with increasing electrolyte concentration, consistent with classical liquid state theories. However, our analyses demonstrate that-also for confined systems-there is no anomalously large screening length. As expected, the screening lengths determined for ionic liquids under confinement are in good quantitative agreement with the screening lengths of the same ionic systems in bulk. In addition, we show that some theoretical models used in the literature to relate the measured screening lengths to other observables are inapplicable to highly concentrated electrolytes.

Effects of dark energy on dynamic phase transition of charged AdS black holes

Searching for the effect of quintessence dark energy on the kinetics of black hole phase transition, we investigate in detail the dynamic phase transition of charged AdS black holes surrounded by quintessence in this paper. Based on the Gibbs free energy landscape, we obtain the analytic expression of the corresponding Gibbs free energy. As shown in $G_L-r_+$ curve at the phase transition temperature, there exist double wells with the same depth, providing further support on the finding in the former literature. By numerically solving the Fokker-Planck equation with both the initial condition and reflecting boundary condition imposed, we probe the probabilistic evolution of charged AdS black holes surrounded by quintessence. The peak denoting the initial black hole state gradually decreases while the other peak starts to grow from zero, approaching to be a stationary distribution in the long time limit with two peaks denoting the large and small black holes respectively. We also study the first passage process of charged AdS black holes surrounded by quintessence and discuss the relevant quantities. We resolve the Fokker-Planck equation by adding the absorbing boundary condition for the intermediate transition state. It is shown intuitively that the peaks located at the large (small) black hole decay very rapidly, irrespective of the initial black hole state. In all the procedures above, we have compared the cases with different choices of the state parameter of quintessence dark energy $\omega_q$. The larger $\omega_q$ is, the faster the initial black hole state decays, showing the effect of quintessence dark energy. To the best of our knowledge, it is the first probe on the influence of dark energy on the dynamic phase transition of charged AdS black hole.

Liquid Phase‐Induced Solid Solution Phase Mechanisms for Highly Stable and Ultrafast Energy Storage

AbstractPhase transitions induce large changes of the lattice parameters, and thus have negative effects on the electrochemical energy storage of electrode materials. In contrast, solid solution phase energy storage mechanisms can ensure smaller shrinkage/expansion of the structure, and therefore better cyclability and fast reaction kinetics of the electrode materials. In this work, the liquid phase is found to control the energy storage mechanisms of K2.55Zn3.08[Fe(CN)6]2·0.28H2O (KZnHCF). Via in situ characterization techniques, phase‐transition and a solid solution phase hybrid mechanism with large chemical structural decay are observed in electrolytes with low K+ concentration, while only a solid solution phase type with a highly stable structure occurs in 5.0 m KCF3SO3 and 3.0 m KCF3SO3+2.0 m Zn(CF3SO3)2 electrolytes. Consequently, the solid solution phase ionic storage mechanism ensures a high rate capability at 20 A g−1 (capacity retention of 66.6%) and a long cyclability of 10 000 cycles (capacity retention of 93.7%) of the KZnHCF cathode.

Twinning Enhances Efficiencies of Metallic Catalysts toward Electrolytic Water Splitting

AbstractTwinning is demonstrated to be an effective way of enhancing efficiencies of metallic catalysts toward electrolytic water splitting. Dendritic Cu possessing dense coherent nanotwin (NT) boundaries (NTCu‐5nm) is successfully prepared with an organic‐assisted electrodeposition at high pulse current densities. NT boundaries significantly improve electrocatalytic efficiencies and stability of NTCu‐5nm over nanocrystalline Cu (NCCu), reducing overpotentials at 10 mA cm−2 for the oxygen evolution reaction (OER) from 378 to 281 mV and from 235 to 88 mV for the hydrogen evolution reaction (HER), with a small chronoamperometric decay of 5% after 100 h continuous overall water splitting at an ultrahigh initial current density of 500 mA cm−2, largely outperforming the large chronoamperometric decay of 27% for only 1 h operation of the NCCu//NCCu couple. The defective twin boundaries enable formation of active CuIIIO2− at low overpotentials, thus enhancing OER performance. The synergistic geometric and electronic effects induced by the twin boundaries result in shifts in Gibbs free energies of hydrogen adsorption (ΔGH) toward the apex of a volcano plot of exchange current density versus ΔGH, leading to the remarkable improvement in HER activity.

Temperature increase drives critical slowing down of fish ecosystems.

Fish ecosystems perform ecological functions that are critically important for the sustainability of marine ecosystems, such as global food security and carbon stock. During the 21st century, significant global warming caused by climate change has created pressing challenges for fish ecosystems that threaten species existence and global ecosystem health. Here, we study a coastal fish community in Maizuru Bay, Japan, and investigate the relationships between fluctuations of ST, abundance-based species interactions and salient fish biodiversity. Observations show that a local 20% increase in temperature from 2002 to 2014 underpins a long-term reduction in fish diversity (∼25%) played out by some native and invasive species (e.g. Chinese wrasse) becoming exceedingly abundant; this causes a large decay in commercially valuable species (e.g. Japanese anchovy) coupled to an increase in ecological productivity. The fish community is analyzed considering five temperature ranges to understand its atemporal seasonal sensitivity to ST changes, and long-term trends. An optimal information flow model is used to reconstruct species interaction networks that emerge as topologically different for distinct temperature ranges and species dynamics. Networks for low temperatures are more scale-free compared to ones for intermediate (15-20°C) temperatures in which the fish ecosystem experiences a first-order phase transition in interactions from locally stable to metastable and globally unstable for high temperatures states as suggested by abundance-spectrum transitions. The dynamic dominant eigenvalue of species interactions shows increasing instability for competitive species (spiking in summer due to intermediate-season critical transitions) leading to enhanced community variability and critical slowing down despite higher time-point resilience. Native competitive species whose abundance is distributed more exponentially have the highest total directed interactions and are keystone species (e.g. Wrasse and Horse mackerel) for the most salient links with cooperative decaying species. Competitive species, with higher eco-climatic memory and synchronization, are the most affected by temperature and play an important role in maintaining fish ecosystem stability via multitrophic cascades (via cooperative-competitive species imbalance), and as bioindicators of change. More climate-fitted species follow temperature increase causing larger divergence divergence between competitive and cooperative species. Decreasing dominant eigenvalues and lower relative network optimality for warmer oceans indicate fishery more attracted toward persistent oscillatory states, yet unpredictable, with lower cooperation, diversity and fish stock despite the increase in community abundance due to non-commercial and venomous species. We emphasize how changes in species interaction organization, primarily affected by temperature fluctuations, are the backbone of biodiversity dynamics and yet for functional diversity in contrast to taxonomic richness. Abundance and richness manifest gradual shifts while interactions show sudden shift. The work provides data-driven tools for analyzing and monitoring fish ecosystems under the pressure of global warming or other stressors. Abundance and interaction patterns derived by network-based analyses proved useful to assess ecosystem susceptibility and effective change, and formulate predictive dynamic information for science-based fishery policy aimed to maintain marine ecosystems stable and sustainable.

Aligned natural inflation in the Large Volume Scenario

We embed natural inflation in an explict string theory model and derive observables in cosmology. We achieve this by compactifying the type IIB string on a Calabi-Yau orientifold, stabilizing moduli via the Large Volume Scenario, and configuring axions using D7-brane stacks. In order to obtain a large effective decay constant, we employ the Kim-Nilles-Peloso alignment mechanism, with the required multiple axions arising naturally from generically anisotropic bulk geometries. The bulk volumes, and hence the axion decay constants, are stabilized by generalized one-loop corrections and subject to various conditions: the Kähler cone condition on the string geometry; the convex hull condition of the weak gravity conjecture; and the constraint from the power spectrum of scalar perturbations. We find that all constraints can be satisfied in a geometry with relatively small volume and thus heavy bulk axion mass. We also covariantize the convex hull condition for the axion-dilaton-instanton system and verify the normalization of the extremal bound.

Long-range decay of pair correlations and nematic ordering in a two-dimensional system of Gay-Berne mesogens

Isothermal-isobaric(NPT) Monte-Carlo simulation has been used to investigate the nature of pair-correlations and ordering in a two-Dimensional system of soft ellipses with aspect ratio κ=3 interacting via the Gay-Berne potential. The system is found to exhibit an isotropic phase (with exponential decay of orientational correlations) and a nematic phase (with algebraic decay of orientational correlations) as we suitably change temperature and pressure. The large distance decay exponent of the orientational correlations is found to converge around an universal value of 0.5 with the increase in pressure along an isotherm. The algebraic decay of orientational correlation in the low temperature phase shows that the nematic lacks true-long range orientational order. This has been substantiated by the system size dependence of the nematic order parameter. We have found the emergence of localized nematic patches separated by disclinations on increasing the pressure in the isotropic phase. No abrupt change is observed in pressure-density plot corresponding to the isotherms studied in this work.

Regularity of the Vlasov–Poisson–Boltzmann System Without Angular Cutoff

In this paper we study the regularity of the non-cutoff Vlasov-Poisson-Boltzmann system for plasma particles of two species in the whole space $\mathbb{R}^3$ with hard potential. The existence of global-in-time nearby Maxwellian solutions is known for soft potential from [15]. However the smoothing effect of these solutions has been a challenging open problem. We establish the global existence and regularizing effect to the Cauchy problem for hard potential with large time decay. Hence, the solutions are smooth with respect to $(t,x,v)$ for any positive time $t>0$. This gives the regularity to Vlasov-Poisson-Boltzmann system, which enjoys a similar smoothing effect as Boltzmann equation. The proof is based on the time-weighted energy method building also upon the pseudo-differential calculus.

On interference effects in top-philic decay chains

Sizeable exotic Higgs boson production through gluon fusion via top quark loops is correlated with large Higgs decay probabilities into top quark final states, if these are kinematically accessible. It is known that gg→S→tt¯ is particularly susceptible to signal-background interference effects that can significantly impact discovery sensitivities. In such an instance, identifying more robust signatures to enhance the discovery sensitivity becomes necessary, shifting phenomenological focus to final states that show a reduced destructive signal-background interference. In this work, we discuss the phenomenological relevance of signal-signal and signal-background interference effects for decay chains. In particular, we identify asymmetric cascade decays in models of scalar extensions of the SM Higgs sector as new promising candidates. In parallel, characteristic interference patterns can provide a formidable tool for indirect CP spectroscopy of BSM sectors if a discovery is made in the future. This motivates associated searches at present and future colliders as robust discovery modes of new physics, in addition to serving as a sensitive tool for the reconstruction of the underlying UV electroweak potential.

Rejection- and importance-sampling-based perfect simulation for Gibbs hard-sphere models

AbstractCoupling-from-the-past (CFTP) methods have been used to generate perfect samples from finite Gibbs hard-sphere models, an important class of spatial point processes consisting of a set of spheres with the centers on a bounded region that are distributed as a homogeneous Poisson point process (PPP) conditioned so that spheres do not overlap with each other. We propose an alternative importance-sampling-based rejection methodology for the perfect sampling of these models. We analyze the asymptotic expected running time complexity of the proposed method when the intensity of the reference PPP increases to infinity while the (expected) sphere radius decreases to zero at varying rates. We further compare the performance of the proposed method analytically and numerically with that of a naive rejection algorithm and of popular dominated CFTP algorithms. Our analysis relies upon identifying large deviations decay rates of the non-overlapping probability of spheres whose centers are distributed as a homogeneous PPP.

One-pot solvothermal preparation of graphene encapsulated SnO nanospheres composites for enhanced lithium storage

SnO based material is one of the most promising anode materials for lithium-ion batteries owing to its high theoretical capacity. However, the difficult synthesis process, large volume expansion and rapid capacity decay, etc., limited its further application. Herein, graphene encapsulated SnO nanospheres, self-assembled from numerous nano-sized secondary nanoparticles, have been successfully synthesized through an efficient one-pot solvothermal method within three hours. The graphene encapsulation and secondary particle assembly structure effectively improves the conductivity of SnO, shortens the ion transmission path and reduces its volume expansion during cycling, thus achieving cycle stability. SnO/G-3 H composite delivers a discharge capacity of 1307 mA h g −1 after 700 cycles at 800 mA g −1 , and maintained an enhanced rate capability of 423 mA h g −1 at 3000 mA g −1 . This simple, economic, and environmental-friendly synthesis route can be extended to the preparation of other transition metal oxide materials.

The stochastic axiverse

In addition to spectacular signatures such as black hole superradiance and the rotation of CMB polarization, the plenitude of axions appearing in the string axiverse may have potentially dangerous implications. An example is the cosmological overproduction of relic axions and moduli by the misalignment mechanism, more pronounced in regions where the signals mentioned above may be observable, that is for large axion decay constant. In this work, we study the minimal requirements to soften this problem and show that the fundamental requirement is a long period of low-scale inflation. However, in this case, if the inflationary Hubble scale is lower than around O(100) eV, no relic DM axion is produced in the early Universe. Cosmological production of some axions may be activated, via the misalignment mechanism, if their potential minimum changes between inflation and today. As a particular example, we study in detail how the maximal-misalignment mechanism dilutes the effect of dangerous axions and allows the production of axion DM in a controlled way. In this case, the potential of the axion that realises the mechanism shifts by a factor ∆θ = π between the inflationary epoch and today, and the axion starts to oscillate from the top of its potential. We also show that axions with masses ma ∼ O(1 − 100) H0 realising the maximal-misalignment mechanism generically behave as dark energy with a decay constant that can take values well below the Planck scale, avoiding problems associated to super-Planckian scales. Finally, we briefly study the basic phenomenological implications of the mechanism and comment on the compatibility of this type of maximally-misaligned quintessence with the swampland criteria.

Microcapsule synthesis and evaluation on fatigue and healing of microcapsule-based asphalt by the entropy and TOPSIS method

ABSTRACT Encapsulation is a promising approach to enhance the self-healing ability of asphalt materials. In this study, microcapsules encapsulated waste engine oil was synthesised to improve the self-healing ability of asphalt. The factors affecting the synthesis of microcapsules, especially emulsification and core shell ratio, were investigated through a micro-observation. Dynamic mechanical properties of microcapsule-based asphalts were analysed. Fatigue and healing properties of asphalt binder were evaluated using the entropy and TOPSIS method. Results showed that a combination of sodium dodecyl sulphate and Span-60 showed better emulsification and the optimised dosage of emulsifier was 1.5 wt%. Increasing emulsifying speed, or decreasing core shell ratio, improved encapsulation efficiency. Addition of microcapsules decreased the asphalt stiffness at low frequency and the fatigue resistance of microcapsule-based asphalt went through relatively large decay when microcapsule addition exceeded 4 wt%. Three healing indexes increased with the addition of microcapsules. By entropy weight and the Technique for Order Preference by Similarity to an Ideal Solution analysis, healing index relating to fatigue life shows a larger entropy weight than others and asphalt with 2 wt% microcapsules perform better with respect to fatigue and healing properties.

Smoothing estimates of the Vlasov-Poisson-Landau system

In this work, we consider the smoothing effect of Vlasov-Poisson-Landau system for both hard and soft potential. In particular, we prove that any classical solutions becomes immediately smooth with respect to all variables. We also give a proof on the global existence to Vlasov-Poisson-Landau system with optimal large time decay. These results give the regularity to Vlasov-Poisson-Landau system. The proof is based on the time-weighted energy method building upon the Pseudodifferential calculus.

On the modified Poisson–Boltzmann closure for primitive model electrolytes at high concentration

The modified Poisson-Boltzmann closure is applied to the Kirkwood hierarchy of integral equations to investigate high concentration primitive model electrolytes. Two approximations are considered in the two sphere fluctuation potential problem. The derived damped oscillatory mean electrostatic potentials suggest that this closure should be of use in providing a basis for understanding the large experimental decay lengths found at high electrolyte concentrations.

Perceptions of dental therapy students regarding the teaching and training with dental amalgam, in a dental school in KwaZulu-Natal, South Africa

Dental amalgam has been used as a restorative material in dentistry for the past 150 years. This material has been used to restore posterior teeth throughout the world and is also used in South Africa. Dental amalgam has been the material of choice for patients presenting with large tooth decay areas, including the loss of cuspal areas. The reason for this is that dental amalgam was always considered strong and durable. Compared to alternate dental materials, this material could also withstand the significant forces associated with chewing and biting. Dental amalgam is also considered more cost-effective than alternate dental materials such as conventional glass ionomers, resin-modified glass ionomers, resin composite and ceramic restorations, making it more feasible and material of choice in lower economic countries, including South Africa.