Existence of multi-solitary waves with logarithmic relative distances for the NLS equation

We construct 2-solitary wave solutions with logarithmic distance to the nonlinear Schrödinger equation,

$\mathrm{i}{?}_{t}u+\mathrm{\Delta }u+|u{|}^{p?1}u=0,t\in \mathbb{R},x\in {\mathbb{R}}^d,$

in mass-subcritical cases $1<p<1+\frac{4}{d}$ and mass-supercritical cases $1+\frac{4}{d}<p<\frac{d+2}{d?2}$, i.e. solutions $u(t)$ satisfying

${6u(t)?{\mathrm{e}}^{\mathrm{i}\gamma (t)}\sum _{k=1}^{2}Q(??x_k(t))6}_{H^1}\to 0$

and

$|x_1(t)?x_2(t)|～2\log ?t,\text{as}t\to +\infty ,$

where Q is the ground state. The logarithmic distance is related to strong interactions between solitary waves.In the integrable case ($d=1$ and $p=3$), the existence of such solutions is known by inverse scattering (E. Olmedilla, Multiple pole solutions of the nonlinear Schrödinger equation, Physica D 25 (1987) 330–346; T. Zakharov, A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP 34 (1972) 62–69). The mass-critical case $p=1+\frac{4}{d}$ exhibits a specific behavior related to blow-up, previously studied in Y. Martel, P. Raphaël (Strongly interacting blow up bubbles for the mass critical NLS, Ann. Sci. Éc. Norm. Supér. 51 (2018) 701–737).     

On periodic subsolutions to steady second-order systems and applications

Bostan and Namah (Remarks on bounded solutions of steady Hamilton–Jacobi equations, C. R. Acad. Sci. Paris, Ser. I 347(15–16) (2009) 873–878) proved that constant functions are the only bounded solutions to $H(Du)=H(0)$ when H is superlinear and strictly convex. In this short note, we present a proof other than that of Bostan and Namah for equations that can be easily applied to some types of possibly degenerate parabolic systems. Our proof applies for periodic subsolutions instead of bounded solutions like that of Bostan and Namah; however, we need periodic subsolutions, which is quite restrictive. We do not consider Hopf–Lax's formula in our proof, so we can relax some restrictions on H. We also present an application to the large-time behavior of solutions to degenerate parabolic systems.     

Polyethylene glycol-assisted sol-gel synthesis of magnetic CoFe2O4 powder as photo-Fenton catalysts in the presence of oxalic acid

Journal of Sol-Gel Science and Technology - The aim of the study was to prepare magnetic photo-Fenton catalysts based on CoFe2O4 by polyethylene glycol-assisted sol-gel method for the degradation...     

A nanocomposite prepared from FeOOH and N-doped carbon nanosheets as a peroxidase mimic,and its application to enzymatic sensing of glucose in human urine

A method is described for the synthesis of a nanocomposite containing FeOOH and N-doped carbon nanosheets. The nanocomposite was synthesized by a hydrothermal method using a Fe₃O₄/chitosan nanocomposite as the precursor. The nanocomposite displays peroxidase-like activity and catalyzes the oxidation of 3,3′,5,5′-tetramethylbenzidine (TMB) by H₂O₂. This results in the formation of a blue colored product with an absorption maximum at 652 nm in the UV-vis spectra. Based on these findings, colorimetric assays were worked out for both hydrogen peroxide and glucose. The H₂O₂ assay works in the 5 to 19 μM concentration range, and the limit of detection is 5 nM. The glucose assay works in the 8 μM to 0.8 mM concentration range and has a 0.2 μM detection limit. The method was successfully applied to the determination of glucose in human urine.

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Graphical abstract Schematic of the hydrothermal synthesis of a FeOOH/N-doped carbon nanocomposite. It was used to replace peroxidase enzyme for the catalytic oxidation of 3,3′,5,5′-tetramethylbenzidine (TMB) in a visual colorimetric test for glucose in human urine.

     

Carbon-coated LiFePO4–carbon nanotube electrodes for high-rate Li-ion battery

Journal of Solid State Electrochemistry - Olivine LiFePO4 (LFP) is a promising cathode material for high-rated lithium-ion batteries. However, olivine faced a severe disadvantage of low...     

Crystal structure of cis-[Ru(bpy)2{PMe(o-tol)2}Cl+][ClO−4]: Steric effects in some PMen(o-tol)3−n (n = 1-3) derivatives of ruthenium(II)

The complex cis-[Ru(bpy)₂{PMe(o-tol)₂}Cl⁺][ClO^– ₄] crystallizes in space group P2₁/c witha = 9.375(2) Å, b = 22.019(7) Å, c = 16.153(4) Å, = 90.83(2)°, V = 3333.9(16) ų and D(calc'd) = 1.547 g/cm³ for Z = 4. The Ru-PMe(o-tol)₂ bond length of 2.357(3) Å is significantly longer than distances of Ru-PMe₂(o-tol) = 2.324(2) Å and Ru-PMe₃ = 2.310(2) Å in analogous complexes. The corresponding Ru-P(o-tol)₃ complex has eluded synthesis, probably due to steric hindrance.     

Hydrogen bond networks determine emergent mechanical and thermodynamic properties across a protein family

Background

Gram-negative bacteria use periplasmic-binding proteins (bPBP) to transport nutrients through the periplasm. Despite immense diversity within the recognized substrates, all members of the family share a common fold that includes two domains that are separated by a conserved hinge. The hinge allows the protein to cycle between open (apo) and closed (ligated) conformations. Conformational changes within the proteins depend on a complex interplay of mechanical and thermodynamic response, which is manifested as an increase in thermal stability and decrease of flexibility upon ligand binding.

Results

We use a distance constraint model (DCM) to quantify the give and take between thermodynamic stability and mechanical flexibility across the bPBP family. Quantitative stability/flexibility relationships (QSFR) are readily evaluated because the DCM links mechanical and thermodynamic properties. We have previously demonstrated that QSFR is moderately conserved across a mesophilic/thermophilic RNase H pair, whereas the observed variance indicated that different enthalpy-entropy mechanisms allow similar mechanical response at their respective melting temperatures. Our predictions of heat capacity and free energy show marked diversity across the bPBP family. While backbone flexibility metrics are mostly conserved, cooperativity correlation (long-range couplings) also demonstrate considerable amount of variation. Upon ligand removal, heat capacity, melting point, and mechanical rigidity are, as expected, lowered. Nevertheless, significant differences are found in molecular cooperativity correlations that can be explained by the detailed nature of the hydrogen bond network.

Conclusion

Non-trivial mechanical and thermodynamic variation across the family is explained by differences within the underlying H-bond networks. The mechanism is simple; variation within the H-bond networks result in altered mechanical linkage properties that directly affect intrinsic flexibility. Moreover, varying numbers of H-bonds and their strengths control the likelihood for energetic fluctuations as H-bonds break and reform, thus directly affecting thermodynamic properties. Consequently, these results demonstrate how unexpected large differences, especially within cooperativity correlation, emerge from subtle differences within the underlying H-bond network. This inference is consistent with well-known results that show allosteric response within a family generally varies significantly. Identifying the hydrogen bond network as a critical determining factor for these large variances may lead to new methods that can predict such effects.     

Spin-glass behaviour in the coordination polymer [Co(C3H3N2)2]n

The magnetic behaviour of the coordination polymer [Co(C(3)H(3)N(2))(2)](n) has been investigated by magnetization and specific heat measurements. Low-field magnetic susceptibility shows the presence of two maxima at approximately 8 and 4 K (T(f)), which reflect short-range low-dimensional antiferromagnetic behaviour and the existence of a spin-glass-like state, respectively. The latter state was observed by magnetic irreversibility in both the zero-field cooled and field-cooled data, and was also confirmed by specific heat measurements. The magnetic specific heat (C(mag)) shows a lack of any long-range ordered peaks. Instead, a broad maximum near T(f) was observed in the C(mag)(T)/T-curve. Below T(f), the C(mag)(T) data follow the relation: C(mag)(T)/T = gamma + AT. We suggest that the competition of the antiferromagnetic (AF) intra-chain and the ferromagnetic (F) inter-chain interactions in a low-dimensional arrangement of magnetic Co(2+) ions can produce the spin-glass behaviour in the sample. The susceptibility data was analyzed in terms of a spin S = 3/2 Heisenberg linear-chain model with a small exchange energy and is consistent with the presence of both F and AF interactions. The splitting of the crystal field energy levels of the Co(2+) ions causes a Schottky-type specific heat anomaly of around 60 K.     

Thermal decomposition of methyl butanoate: ab initio study of a biodiesel fuel surrogate

In this paper, we report a detailed analysis of the breakdown kinetic mechanism for methyl butanoate (MB) using theoretical approaches. Electronic structures and structure-related molecular properties of reactants, intermediates, products, and transition states were explored at the BH&HLYP/cc-pVTZ level of theory. Rate constants for the unimolecular and bimolecular reactions in the temperature range of 300-2500 K were calculated using Rice-Ramsperger-Kassel-Marcus and transition state theories, respectively. Thirteen pathways were identified leading to the formation of small compounds such as CH(3), C(2)H(3), CO, CO(2), and H(2)CO. For the initial formation of MB radicals, H, CH(3), and OH were considered as reactive radicals participating in hydrogen abstraction reactions. Kinetic simulation results for a high temperature pyrolysis environment show that MB radicals are mainly produced through hydrogen abstraction reactions by H atoms. In addition, the C(O)OCH(3) = CO + CH(3)O reaction is found to be the main source of CO formation. The newly computed kinetic sub-model for MB breakdown is recommended as a core component to study the combustion of oxygenated species.     

An expedient synthesis of the fibril binding compound FSB via sequential Pd-catalyzed coupling reactions

The styryl benzene derivative (E, E)-1-fluoro-2,5-bis(3-hydroxycarbonyl-4-hydroxy)styrylbenzene (FSB), well-known for its binding to beta-amyloid peptide fibrils, was synthesized in an efficient manner exploiting two sequential palladium(0)-catalyzed coupling reactions in a 34% overall yield. This is a substantial improvement to the previously reported synthesis of FSB in 1.1%.