On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion

We study the small mass limit (or: the Smoluchowski–Kramers limit) of a class of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic bath spectral density with a Lorentz–Drude cutoff, we derive the Heisenberg–Langevin equations for the particle’s observables using a quantum stochastic calculus approach. We set the mass of the particle to equal \(m = m_{0} \epsilon \), the reduced Planck constant to equal \(\hbar = \epsilon \) and the cutoff frequency to equal \(\varLambda = E_{\varLambda }/\epsilon \), where \(m_0\) and \(E_{\varLambda }\) are positive constants, so that the particle’s de Broglie wavelength and the largest energy scale of the bath are fixed as \(\epsilon \rightarrow 0\). We study the limit as \(\epsilon \rightarrow 0\) of the rescaled model and derive a limiting equation for the (slow) particle’s position variable. We find that the limiting equation contains several drift correction terms, the quantum noise-induced drifts, including terms of purely quantum nature, with no classical counterparts.     

Replica Bounds by Combinatorial Interpolation for Diluted Spin Systems

In two papers Franz et al. proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution (Franz and Leone in J Stat Phys 111(3–4):535–564, 2003) and a general distribution (Franz et al. in J Phys A 36(43), 10967, 2003). Panchenko and Talagrand (Probab Theo Relat Fields 130(3):319–336, 2004) simplified the proof and generalized the result of Franz and Leone (J Stat Phys 111(3–4):535–564, 2003) for the Poisson case. We provide a new proof for the general degree distribution case and as a corollary, we obtain new bounds for the size of the largest independent set (also known as hard core model) in a large random regular graph. Our proof uses a combinatorial interpolation based on biased random walks (Salez in Combin Probab Comput 25(03):436–447, 2016) and allows to bypass the arguments in Franz et al. (J Phys A 36(43):10967, 2003) based on the study of the Sherrington–Kirkpatrick (SK) model.     

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

We study a spatial birth-and-death process on the phase space of locally finite configurations \({\varGamma }^+ \times {\varGamma }^-\) over \({\mathbb {R}}^d\). Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator \(L^+(\gamma ^-) + \frac{1}{\varepsilon }L^-\), \(\varepsilon > 0\). Here \(L^-\) describes the environment process on \({\varGamma }^-\) and \(L^+(\gamma ^-)\) describes the system process on \({\varGamma }^+\), where \(\gamma ^-\) indicates that the corresponding birth-and-death rates depend on another locally finite configuration \(\gamma ^- \in {\varGamma }^-\). We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states \(\mu _t^{\varepsilon }\) on \({\varGamma }^+ \times {\varGamma }^-\). Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let \(\mu _{\mathrm {inv}}\) be the invariant measure for the environment process on \({\varGamma }^-\). In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of \(\mu _t^{\varepsilon }\) onto \({\varGamma }^+\) converges weakly to an evolution of states on \({\varGamma }^+\) associated with the averaged Markov birth-and-death operator \({\overline{L}} = \int _{{\varGamma }^-}L^+(\gamma ^-)d \mu _{\mathrm {inv}}(\gamma ^-)\).     

Motion of a Rigid Body in a Special Lorentz Gas: Loss of Memory Effect

Linear motion of a rigid body in a special kind of Lorentz gas is mathematically analyzed. The rigid body moves against gas drag according to Newton’s equation. The gas model is a special Lorentz gas consisting of gas molecules and background obstacles, which was introduced in Tsuji and Aoki (J Stat Phys 146:620–645, 2012). The specular boundary condition is imposed on the resulting kinetic equation. This study complements the numerical study by Tsuji and Aoki cited above—although the setting in this paper is slightly different from theirs, qualitatively the same asymptotic behavior is proved: The velocity V(t) of the rigid body decays exponentially if the obstacles undergo thermal motion; if the obstacles are motionless, then the velocity V(t) decays algebraically with a rate \(t^{-\,5}\) independent of the spatial dimension. This demonstrates the idea that interaction of the molecules with the background obstacles destroys the memory effect due to recollision.     

An integrated structure- and pharmacophore-based MMP-12 virtual screening

MMP-12 belongs to a large family of proteases called matrix metalloproteinases (MMPs) that degrades elastin. The main pathologic role of MMP-12 overexpression was suggested to be associated with pathogenesis mechanism of inflammatory respiratory diseases and atherosclerosis. An integrated ligand- and structure-based virtual screening was employed in hope of finding inhibitors with new scaffolds and selectivity for MMP-12. Seven compounds among 18 experimentally tested compounds had a measurable effect on the inhibition of MMP-12 enzyme. Our results demonstrated the applicability of the developed pharmacophore model and selected crystal structure (PDB code: 3F17) to discover new MMP-12 inhibitors. The receptor structure was selected based on cross-docking results. Here, we report the discovery of new class of MMP-12 inhibitors that could be used for lead optimization. For the inhibition of MMP-12, the significance of its interactions with the catalytic residues Glu219 and Ala182 was emphasized through the inspection of the docking poses.     

Microwave-assisted green synthesis of 4,5-dihydro-1<Emphasis Type="Italic">H</Emphasis>-pyrazole-1-carbothioamides in water

Rapid, efficient, simple and green procedure for the synthesis of 4,5-dihydro-1H-pyrazole-1-carbothioamides via the multicomponent reaction of aryl aldehydes, acetophenones and thiosemicarbazide in water in the presence of tetrabutylammonium hydroxide under microwave irradiation is reported.     

Free-standing WS<Subscript>2</Subscript><Emphasis Type="Strikethrough">-</Emphasis>MWCNTs hybrid paper integrated with polyaniline for high-performance flexible supercapacitor

As two-dimensional layered nanomaterials, the tungsten disulfide (WS₂) nanosheets can be used as building blocks of paper-like electrodes for high-performance FSs. However, poor conductivity and mechanical property of WS₂ nanosheets (NSs) paper greatly hinders their capacitance and/or rate performance. To solve these problems, we fabricated the WS₂-multiwalled carbon nanotubes (MWCNTs)/polyaniline (PANI) composite papers based on liquid exfoliation and electrochemical deposition for high-performance flexible supercapacitors. The WS₂-MWCNTs/PANI with conductive PANI chains linked WS₂ NSs and MWCNTs takes the advantages of high-electronic double-layer capacitance originated from the internal surface areas of MWCNTs and effective pseudocapacitance generated by exfoliated WS₂ NSs and PANI. Electrochemical studies showed that the gravimetric-specific capacitance of WS₂-MWCNTs/PANI can reach ~760.1 F/g at a current density of 1 A/g. A symmetric flexible solid-state supercapacitor was also assembled and studied. The WS₂-MWCNTs/PANI-assembled FS device also has an excellent area specific capacitance of 1158.7 mF/cm² at a current density of 0.5 mA/cm² together with a high-capacity retention of ~82.5% after 2000 cycles.     

Tuning Pt–Cu nanostructures by bromide ions and their superior electrocatalytic activities for methanol oxidation reaction

Dendritic Pt–Cu nanoparticles were synthesized by a facile one-step method with the help of surfactant Brij58 at room temperature, and we also studied the effects of different Pt–Cu ratios on the morphology and size of nanoparticles. In addition, we further tuned the morphology of the Pt–Cu nanostructures by introducing bromide ions, eventually leading to the appearance of some tripod-like structures. Compared with dendritic Pt–Cu and commercial Pt black, these tripod-like Pt–Cu nanostructures exhibited higher electrocatalytic activity and CO tolerance for catalyzing methanol oxidation.

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Microwave photonics reconfigurable mixer based on polarization modulator

A reconfigurable and stable mixer is proposed and demonstrated in this paper. It mainly consists of a dual-driven Mach–Zehnder modulator and a polarization modulator with several polarization controllers (PC) and polarizers (Pol). According to the theoretical analysis, different functions (such as single ended mixer, balanced mixer, I/Q mixer and image rejection mixer) can be realized by adjusting the PCs and Pols. The simulation results verify the possibility of multi-functions that realized by the reconfigurable mixer. In addition, another research on how the non-ideal parameters affect the image rejection ratio (ISR) and conversion efficiency of the mixer is also carried. The results show that both of them perform better as the extinction ratio gets higher. However, they are incurring a sharp decrease if the DC bias points deviate from the settled values. In the meantime, the results also indicate that the higher modulation indices lead to a better ISR. A 57.12 dB ISR can be achieved with conversion efficiency of ? 9.53 dB.