Boltzmann equation and hydrodynamic equations: their equilibrium and non-equilibrium behaviour.

This short article summarizes the key features of equilibrium and non-equilibrium aspects of Boltzmann and hydrodynamic equations. Under equilibrium, the Boltzmann equation generates uncorrelated random velocity that corresponds to k2 energy spectrum for the Euler equation. The latter spectrum is produced using initial configuration with many Fourier modes of equal amplitudes but with random phases. However, for a large-scale vortex as an initial condition, earlier simulations exhibit a combination of k-5/3 (in the inertial range) and k2 (for large wavenumbers) spectra, with the range of k2 spectrum increasing with time. These simulations demonstrate an approach to equilibrium or thermalization of Euler turbulence. In addition, they also show how initial velocity field plays an important role in determining the behaviour of the Euler equation. In non-equilibrium scenario, both Boltzmann and Navier-Stokes equations produce similar flow behaviour, for example, Kolmogorov's k-5/3 spectrum in the inertial range. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Kolmogorov flow: Linear stability and energy transfers in a minimal low-dimensional model.

In this paper, we derive a four-mode model for the Kolmogorov flow by employing Galerkin truncation and the Craya-Herring basis for the decomposition of velocity field. After this, we perform a bifurcation analysis of the model. Though our low-dimensional model has fewer modes than past models, it captures the essential features of the primary bifurcation of the Kolmogorov flow. For example, it reproduces the critical Reynolds number for the supercritical pitchfork bifurcation and the flow structures of past works. We also demonstrate energy transfers from intermediate scales to large scales. We perform direct numerical simulations of the Kolmogorov flow and show that our model predictions match the numerical simulations very well.

Room Temperature Metal-Catalyzed Oxidative Acylation of Electron-Deficient Heteroarenes with Alkynes, Its Mechanism, and Application Studies.

Herein, we report an original one-step, simple, room-temperature, regioselective Minisci reaction for the acylation of electron-deficient heteroarenes with alkynes. The method has broad functional group compatibility and gives exclusively monoacylated products in good to excellent yields. The mechanistic pathway was analyzed based on a series of experiments confirming the involvement of a radical pathway. The 18O-labeling experiment suggested that water is a source of oxygen in the acylated product, and head space GC-MS experiment shows the C-C cleavage occurs via release as CO2.

Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence.

In this review we summarise the current status of the quasi-static magnetohydrodynamic turbulence. The energy spectrum is steeper than Kolmogorov's k -5/3 spectrum due to the decrease of the kinetic energy flux with wavenumber k as a result of Joule dissipation. The spectral index decreases with the increase of interaction parameter. The flow is quasi two-dimensional with strong [Formula: see text] at small k and weak [Formula: see text] at large k, where [Formula: see text] and [Formula: see text] are the perpendicular and parallel components of velocity relative to the external magnetic field. For small k, the energy flux of [Formula: see text] is negative, but for large k, the energy flux of [Formula: see text] is positive. Pressure mediates the energy transfer from [Formula: see text] to [Formula: see text].

Methyl jasmonate improves resistance in scab-susceptible Red Delicious apple by altering ROS homeostasis and enhancing phenylpropanoid biosynthesis.

Apple (Malus domestica) is an economically important rosaceous fruit crop grown at temperate climate zones. Nevertheless, its production is severely affected by scab disease caused by the ascomycetous fungus Venturia inaequalis (VI). Methyl jasmonate (MeJA) is a stress induced plant hormone, shown to induce resistance against wide range of pathogens. The current study investigated the role of MeJA in promoting scab tolerance in susceptible apple varieties through exogenous application of optimized (100 µM) MeJA concentration, followed by VI infection. According to our analysis, applying MeJA exogenously onto leaf surfaces resulted in increased membrane stability and decreased malondialdehyde levels in Red Delicious, suggesting that MeJA is capable of protecting tissues against oxidative damage through its role in restoring membrane stability. In addition, the changes in the levels of key antioxidative enzymes and reactive oxygen species (ROS) showed that exogenous MeJA maintains ROS homeostasis as well. Higher phenylalanine ammonia-lyase activity and increased accumulation of phenylpropanoids in MeJA-treated VI-infected plants indicated the MeJA reprogrammed phenylpropanoid biosynthesis pathway for scab tolerance. Our study of scab tolerance in apples induced by MeJA provides new insights into its physiological and biochemical mechanisms.

Flow reversals in turbulent convection via vortex reconnections.

We employ detailed numerical simulations to probe the mechanism of flow reversals in two-dimensional turbulent convection. We show that the reversals occur via a vortex reconnection of two attracting corner rolls having the same sign of vorticity, thus leading to major restructuring of the flow. Large fluctuations in heat transport are observed during the reversal due to the flow reconfiguration. The flow configurations during the reversals have been analyzed quantitatively using large-scale modes. Using these tools, we also show why flow reversals occur for a restricted range of Rayleigh and Prandtl numbers.

Development of a validated UPLC-qTOF-MS Method for the determination of curcuminoids and their pharmacokinetic study in mice.

BACKGROUND: A specific and sensitive UPLC-qTOF-MS/MS method has been developed for the simultaneous determination of curcuminoids. These Curcuminoids comprises of curcumin, a principal curcuminoid and other two namely, demethoxycurcumin, and bisdemethoxycurcumin obtained from rhizomes of Curcuma longa an ancient Indian curry spice turmeric, family (Zingiberaceae). METHODS: These analytes were separated on a reverse phase C18 column by using a mobile phase of acetonitrile: 5% acetonitrile in water with 0.07% acetic acid (75:25 v/v), flow rate of 100 µL/min was maintained. The qTOF-MS was operated under multiple reaction monitoring (MRM) mode using electro-spray ionization (ESI) technique with positive ion polarity. The major product ions in the positive mode for curcuminoids were at m/z 369.1066, 339.1023 and 309.0214 respectively. The recovery of the analytes from mouse plasma was optimized using solid phase extraction technique. RESULTS: The total run time was 5 min and the peaks of the compounds, bisdemethoxycurcumin, demethoxycurcumin and curcumin occurred at 2.06, 2.23 and 2.40 min respectively. The calibration curves of bisdemethoxycurcumin, demethoxycurcumin and curcumin were linear over the concentration range of 2-1000 ng/mL (r2, 0.9951), 2-1000 ng/mL (r2, 0.9970) and 2-1000 ng/mL (r2, 0.9906) respectively.Intra-assay and inter-assay accuracy in terms of % bias for curcumin was in between -7.95to +6.21, and -7.03 to + 6.34; for demethoxycurcumin was -6.72 to +6.34, and -7.86 to +6.74 and for bisdesmetoxycurcumin was -8.23 to +6.37 and -8.47 to +7.81. The lower limit of quantitation for curcumin, demethoxycurcumin and bisdemethoxycurcumin was 2.0 ng/mL. Analytes were stable under various conditions (in autosampler, during freeze-thaw, at room temperature, and under deep-freeze conditions). This validated method was used during pharmacokinetic studies of curcumin in the mouse plasma. CONCLUSIONS: A specific, accurate and precise UPLC-qTOF-MS/MS method for the determination of curcumin, demethoxycurcumin and bisdemethoxycurcumin both individually and simultaneously was optimized.

Renormalization of the shell model of turbulence.

Renormalization enables a systematic scale-by-scale analysis of multiscale systems. In this paper, we employ renormalization group (RG) to the shell model of turbulence and show that the RG equation is satisfied by |u_{n}|^{2}=K_{Ko}ε^{2/3}k_{n}^{-2/3}, where Ko is the Kolmogorov constant and ν_{n}=ν_{*}sqrt[K_{Ko}]ε^{1/3}k_{n}^{-4/3}, where k_{n}andu_{n} are the wave number and velocity of shell n; ν_{*}andK_{Ko} are RG and Kolmogorov's constants; and ε is the energy dissipation rate. We find that ν_{*}≈0.5 and K_{Ko}≈1.7, consistent with earlier RG works on the Navier-Stokes equation. We verify the theoretical predictions using numerical simulations.

Bolgiano-Obukhov spectrum and mixing efficiency in stably stratified turbulence.

In this paper, using a shell model, we simulate highly turbulent stably stratified flow for weak to moderate stratification at unitary Prandtl number. We investigate the energy spectra and fluxes of velocity and density fields. We observe that for moderate stratification, in the inertial range, the kinetic energy spectrum E_{u}(k) and the potential energy spectrum E_{b}(k) show dual scaling-Bolgiano-Obukhov scaling [E_{u}(k)∼k^{-11/5} and E_{b}(k)∼k^{-7/5}] for kk_{B}. In addition, we find that the mixing efficiency η_{mix} varies as η_{mix}∼Ri for weak stratification, whereas η_{mix}∼Ri^{1/3} for moderate stratification, where Ri is the Richardson number.

Nonlinear energy dissipation and transfers in coarsening systems.

During coarsening, small structures disappear, leaving behind only large ones. Here we study the spectral energy transfers in Model A, where the order parameter ϕ evolves via nonconserved dynamics. We show that the nonlinear interactions dissipate fluctuations and facilitate energy transfers among the Fourier modes so that only ϕ(k=0), where k is the wave number, survives at the end and approaches the asymptotic value +1 or -1. We contrast the coarsening evolution for the initial conditions with 〈ϕ(x,t=0)〉=0 and with uniformly positive or negative ϕ(x,t=0).

Overview on century progress in research on mosaic disease of apple (Malus domestica Borkh) incited by apple mosaic virus/apple necrotic mosaic virus.

Apple mosaic is widely distributed disease throughout the apple growing regions leading to the major adverse effects both qualitatively and quantitatively. Earlier the apple mosaic virus-ApMV was regarded as the only causal agent of the disease, but recently a novel virus apple necrotic mosaic virus-ApNMV have been reported as the causal pathogen from various apple growing countries. Accurate diagnosis of disease and detection of ApMV and ApNMV are of utmost importance, because without this ability we can neither understand nor control this disease. Both the viruses are mostly controlled through quarantine, isolation, sanitation and certification programs depending on sensitive and specific detection methods available. Here we review the 100-year progress in research on apple mosaic disease, which includes history, yield losses, causal agents, their genome organization, replication, traditional to recent detection methods, transmission, distribution and host range of associated viruses and management of the disease.

Ayurveda-based phytochemical composition attenuates lung inflammation and precipitates pharmacokinetic interaction with favipiravir: an in vivo investigation using disease-state of acute lung injury.

Acute respiratory distress syndrome (ARDS) is a critical form of acute lung injury (ALI). Here, we investigated the effect of a defined combination of ten pure phytochemicals in equal proportions of weight (NPM) from plants, recommended by Ayurveda for any protective action against lipopolysaccharide (LPS)-induced ALI. Results indicate that NPM markedly improved protein and neutrophil contents, myeloperoxidase and hydroxyproline levels, oxidative stress markers (glutathione and malonaldehyde), inflammatory cytokines, and genes (IL-6, TNF-α, TGF-ß, and NF-κB/IκBα) in BALF/lung tissue. The histopathological examination of the lung revealed the shielding effect of NPM against ALI. NPM exhibited a protective effect on the lung by reducing oxidative stress and inhibiting inflammation. A substantial drop in favipiravir's oral exposure was observed in ALI-state compared to normal-state, but oral exposure upon NPM treatment in ALI-state followed similar behaviour of favipiravir alike normal-state without NPM treatment. Overall, results offer potential insight into Ayurvedic recommendations for immunity boosting during ALI situations.

Equilibrium states of Burgers and Korteweg-de Vries equations.

We simulate Korteweg-de Vries (KdV) and dissipationless Burgers equations using δ-correlated random noise as an initial condition. We observe that the energy fluxes of the two equations remain zero throughout, thus, indicating their equilibrium nature. We characterize the equilibrium states using Gaussian probability distribution for the real space field, and using Boltzmann distribution for the modal energy. We show that the single soliton of the KdV equation too exhibits zero energy flux, hence, it is in equilibrium. We argue that the energy flux is a good measure for ascertaining whether a system is in equilibrium or not.

Dynamics of zero-Prandtl number convection near onset.

We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Bénard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (2009)]. We also observed a set of periodic and chaotic wavy rolls in DNS and in the model similar to those observed in experiments and numerical simulations. The time period of the wavy rolls is closely related to the eigenvalues of the stability matrix of the Hopf bifurcation points at the onset of convection. This time period is in good agreement with the experimental results for low-Prandtl number fluids. The chaotic attractor of the wavy roll solutions is born through a quasiperiodic and phase-locking route to chaos.

Universal Epidemic Curve for COVID-19 and Its Usage for Forecasting.

We construct a universal epidemic curve for COVID-19 using the epidemic curves of eight nations that have reached saturation for the first phase and then fit an eight-degree polynomial that passes through the universal curve. We take India's epidemic curve up to January 1, 2021 and match it with the universal curve by minimizing square-root error between the model prediction and actual value. The constructed curve has been used to forecast epidemic evolution up to February 25, 2021. The predictions of our model and those of supermodel for India (Agrawal et al. in Indian J Med Res, 2020; Vidyasagar et al. in https://www.iith.ac.in/~m_vidyasagar/arXiv/Super-Model.pdf, 2020) are reasonably close to each other considering the uncertainties in data fitting.

Nutritional and Phytochemical Traits of Apricots (Prunus Armeniaca L.) for Application in Nutraceutical and Health Industry.

Apricot (Prunus armeniaca L.) is a nutritious fruit, rich in bioactive compounds, known for their health benefits. The present study attempts to evaluate nutritional (sugars, organic acids, minerals) and nutraceutical traits (total phenolics, flavonoids, carotenoids, antioxidant activity) of six commercial apricot genotypes grown in India. Antioxidant activity was determined using three in-vitro assays, namely CUPRAC (cupric reducing antioxidant capacity), FRAP (ferric reducing antioxidant power) and DPPH (1,1-diphenyl-2-picryl-hydrazyl). Significant (p < 0.05) differences were observed in the genotypes concerning nutritional and nutraceutical traits. Sucrose accounted for more than 60% of total sugars in most genotypes, followed by glucose and fructose. Citric acid accounted for more than 50% of the total organic acids present, followed by malic and succinic acids. Apricot is a good source of potassium (1430.07 to 2202.69 mg/100 g dwb) and iron (2.69 to 6.97 mg/100 g dwb) owing to its mineral composition. Total carotenoids content ranged from 0.44 to 3.55 mg/100 g, with ß-carotene accounting for 33-84% of the total content. The results strongly suggest that genotypes 'CITH-A-1' and 'CITH-A-2', which have high dry matter and carotenoids content, are well suited for drying. 'Roxana' and 'CITH-A-3' are great for fresh consumption, while 'Shakarpara' and 'Gold Cot' are excellent for juice processing.

COVID-19 Pandemic: Power Law Spread and Flattening of the Curve.

In this paper, we analyze the real-time infection data of COVID-19 epidemic for nine nations. Our analysis is up to May 04, 2020. South Korea, China, Italy, France, Spain, and Germany have either flattened or close to flattening their epidemic curves. USA and Japan have transitioned to a linear regime, while India is still in a power-law phase. We argue that the transition from an exponential regime to a succession of power-law regimes is a good indicator for flattening of the epidemic curve. We also argue that lockdowns, long-term community transmission, and the transmission by asymptomatic carriers traveling long distances may be inducing the power-law growth of the epidemic.

Energy transfers in shell models for magnetohydrodynamics turbulence.

A systematic procedure to derive shell models for magnetohydrodynamic turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross helicity, and the magnetic helicity, as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest-neighbor shells, this procedure reproduces well-known models but suggests a reinterpretation of the energy fluxes.

Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence.

In this paper, using Pao's conjecture [Y.-H. Pao, Phys. Fluids 8, 1063 (1965)10.1063/1.1761356], we derive expressions for the spectra and fluxes of kinetic energy and enstrophy for two-dimensional (2D) forced turbulence that extend beyond the inertial range. In these expressions, the fluxes and the spectra contain additional factors of the exponential form. To validate these model predictions, we perform numerical simulations of 2D turbulence with external force applied at wavenumber band (k_{f},k_{f}+1) in the intermediate range. The numerical results match with the model predictions, except for the energy and enstrophy fluxes for k

Dynamo transition in low-dimensional models.

Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and current helicity. The velocity modes are forced in both these models. These low-dimensional models exhibit a dynamo transition at a critical forcing amplitude that depends on the Prandtl number. In the nonhelical model, dynamo exists only for magnetic Prandtl number beyond 1, while the helical model exhibits dynamo for all magnetic Prandtl number. Although the model is far from reproducing all the possible features of dynamo mechanisms, its simplicity allows a very detailed study and the observed dynamo transition is shown to bear similarities with recent numerical and experimental results.