Zonal-meridional decomposition and the Hamiltonian description of planetary fluid dynamics

The basic properties of planetary flows are studied within the framework of the noncanonical Hamiltonian approach formulated by Morrison. A zonal-symmetric decomposition is applied in order to characterize the contributions of the different dynamical terms. Steady states and the Lorenz energy and angular momentum cycles are also written within the Lie-Poisson bracket formalism.     

Nascent Proteomics: Chemical Tools for Monitoring Newly Synthesized Proteins

Cellular proteins are dynamically regulated in response to environmental stimuli. Conventional proteomics compares the entire proteome in different cellular states to identify differentially expressed proteins, which suffers from limited sensitivity for analyzing acute and subtle changes. To address this challenge, nascent proteomics has been developed, which selectively analyzes the newly synthesized proteins, thus offering a more sensitive and timely insight into the dynamic changes of the proteome. In this Minireview, we discuss recent advancements in nascent proteomics, with an emphasis on methodological developments. Also, we delve into the current challenges and provide an outlook on the future prospects of this exciting field.     

Hamiltonian fluid reductions of electromagnetic drift-kinetic equations for an arbitrary number of moments

We present an infinite family of Hamiltonian electromagnetic fluid models for plasmas, derived from drift-kinetic equations. An infinite hierarchy of fluid equations is obtained from a Hamiltonian drift-kinetic system by taking moments of a generalized distribution function and using Hermite polynomials as weight functions of the velocity coordinate along the magnetic guide field. Each fluid model is then obtained by truncating the hierarchy to a finite number N+1$N+1$ of equations by means of a closure relation. We show that, for any positive N$N$, a linear closure relation between the moment of order N+1$N+1$ and the moment of order N$N$ guarantees that the resulting fluid model possesses a Hamiltonian structure, thus respecting the Hamiltonian character of the parent drift-kinetic model. An orthogonal transformation is identified which maps the fluid moments to a new set of dynamical variables in terms of which the Poisson brackets of the fluid models become a direct sum and which unveils remarkable dynamical properties of the models in the two-dimensional (2D) limit. Indeed, when imposing translational symmetry with respect to the direction of the magnetic guide field, all models belonging to the infinite family can be reformulated as systems of advection equations for Lagrangian invariants transported by incompressible generalized velocities. These are reminiscent of the advection properties of the parent drift-kinetic model in the 2D limit and are related to the Casimirs of the Poisson brackets of the fluid models. The Hamiltonian structure of the generic fluid model belonging to the infinite family is illustrated treating a specific example of a fluid model retaining five moments in the electron dynamics and two in the ion dynamics. We also clarify the connection existing between the fluid models of this infinite family and some fluid models already present in the literature.     

Gauge-free Hamiltonian structure of the spin Maxwell-Vlasov equations

We derive the gauge-free Hamiltonian structure of an extended kinetic theory, for which the intrinsic spin of the particles is taken into account. Such a semi-classical theory can be of interest for describing, e.g., strongly magnetized plasma systems. We find that it is possible to construct a generalized noncanonical Poisson bracket on the extended phase space, and discuss the implications of our findings, including stability of monotonic equilibria.     

A compressible Hamiltonian electromagnetic gyrofluid model

A Lie-Poisson bracket is presented for a four-field gyrofluid model with magnetic field curvature and compressible ions, thereby showing the model to be Hamiltonian. The corresponding Casimir invariants are presented, and shown to be associated to four Lagrangian invariants advected by distinct velocity fields. This differs from a cold ion limit, in which the Lie-Poisson bracket transforms into the sum of direct and semidirect products, leading to only three Lagrangian invariants.     

New additions to the arsenal of biocatalysts for noncanonical amino acid synthesis

Noncanonical amino acids (ncAAs) merge the conformational behavior and native interactions of proteinogenic amino acids with nonnative chemical motifs and have proven invaluable in developing modern therapeutics. This blending of native and nonnative characteristics has resulted in essential drugs like nirmatrelvir, which comprises three ncAAs and is used to treat COVID-19. Enzymes are appearing prominently in recent syntheses of ncAAs, where they demonstrate impressive control over the stereocenters and functional groups found therein. Here we review recent efforts to expand the biocatalyst arsenal for synthesizing ncAAs with natural enzymes. We also discuss how new-to-nature enzymes can contribute to this effort by catalyzing reactions inspired by the vast repertoire of chemical catalysis and acting on substrates that would otherwise not be used in synthesizing ncAAs. Abiotic enzyme-catalyzed reactions exploit the selectivity afforded by a macromolecular catalyst to access molecules not available to natural enzymes and perhaps not even chemical catalysis.     

Oscillation of second-order nonlinear noncanonical differential equations with deviating argument

The purpose of this paper is to study the second-order nonlinear noncanonical differential equation ${\left(r\left(t\right)y^{\prime }\left(t\right)\right)}^{\prime }+p\left(t\right)f\left(y\left(\tau \left(t\right)\right)\right)=0$under the condition ${\int }_{}^{\infty }\frac{1}{r\left(t\right)}\mathrm{d}t<\infty$. Contrary to most existing results, oscillation of the studied equation is attained via only one condition. We consider both delay and advanced differential equations. A particular example of Euler type equation is provided in order to illustrate the significance of our main results.     

Hamiltonian-Dirac simulated annealing: Application to the calculation of vortex states

A simulated annealing method for calculating stationary states for models that describe continuous media is proposed. The method is based on the noncanonical Poisson bracket formulation of media, which is used to construct Dirac brackets with desired constraints, and symmetric brackets that cause relaxation with the desired constraints. The method is applied to two-dimensional vortex dynamics and a variety of numerical examples is given, including the calculation of monopole and dipole vortex states.     

Oscillation of 2nd-order Nonlinear Noncanonical Difference Equations with Deviating Argument

The purpose of this paper is to establish some new criteria for the oscillation of the second-order nonlinear noncanonical difference equations of the form \[ \Delta \left( a\left( n\right) \Delta x\left( n\right) \right) +q(n)x^{\beta }\left( g(n)\right) =0,\text{ \ \ }n\geq n_{0} \] under the assumption \[ \sum_{s=n}^{\infty }\frac{1}{a\left( s\right) }<\infty \text{.} \] Corresponding difference equations of both retarded and advanced type are studied. A particular example of Euler type equation is provided in order to illustrate the significance of our main results.