Invisibility cloaking via non-smooth transformation optics and ray tracing

We present examples of theoretically-predicted invisibility cloaks with shapes other than spheres and cylinders, including cones and ellipsoids, as well as shapes spliced from parts of these simpler shapes. In addition, we present an example explicitly displaying the non-uniqueness of invisibility cloaks of the same shape. We depict rays propagating through these example cloaks using ray tracing for geometric optics.     

Conformational probe: static quenching is reduced upon acid triggered ring flip of a myo-inositol derivative

The aromatic rings in 4-O-dabsyl-6-O-dansyl-myo-inositol-1,3,5-orthoformate (6) participate in electron transfer causing static quenching as detected by the absence of fluorescence. Upon addition of acid, the orthoformate lock is cleaved, with subsequent conformational change of the myo-inositol ring from penta-axial to the more stable penta-equatorial chair, which causes some increase in fluorescence due to spatial separation of fluorophore and a quencher and reduction in static quenching. In the case of 4,6-O-bisdansyl-myo-inositol-1,3,5-orthoformate (3), the acid-induced removal of the orthoformate lock leads to substantial change of fluorescence following spatial separation of two dansyl groups.     

Synthetic Utility of Epoxides for Chiral Functionalization of Isoxazoles

The lithio-anion of isoxazole 2 was found to ring open propylene oxide in good yields with complete regioselectivity. Vinylic and benzylic epoxides were utilized as key examples of electrophiles and found to produce a mixture of regioisomeric adducts. Additionally, the use of chiral epoxides was explored, and absolute configuration was determined by X-ray crystallography to prove that nucleophilic attack at the benzylic carbon of (R)-styrene oxide proceeds with 100% inversion at the benzylic carbon to afford the (S)-alcohol (4b).     

Photochemically-Driven CO2 Release Using a Metastable-State Photoacid for Energy Efficient Direct Air Capture

One of the grand challenges underlying current direct air capture (DAC) technologies relates to the intensive energy cost for sorbent regeneration and CO₂ release, making the massive scale (GtCO₂/year) deployment required to have a positive impact on climate change economically unfeasible. This challenge underscores the critical need to develop new DAC processes with substantially reduced regeneration energies. Here, we report a photochemically-driven approach for CO₂ release by exploiting the unique properties of an indazole metastable-state photoacid (mPAH). Our measurements on simulated and amino acid-based DAC systems revealed the potential of mPAH to be used for CO₂ release cycles by regulating pH changes and associated isomers driven by light. Upon irradiating with moderate intensity light, a ≈55 % and ≈68 % to ≈78 % conversion of total inorganic carbon to CO₂ was found for the simulated and amino acid-based DAC systems, respectively. Our results confirm the feasibility of on-demand CO₂ release under ambient conditions using light instead of heat, thereby providing an energy efficient pathway for the regeneration of DAC sorbents.     

Polarization and image rotation induced by a rotating dielectric rod: an optical angular momentum interpretation

When light is transmitted along the axis of a rotating glass rod, the polarization of the light is rotated through a small angle [Proc. R. Soc. London, Ser. A349, 423 (1976)]. Under the same conditions, we predict a rotation of the transmitted image by exactly the same angle. The treatment of the two effects in terms of light's spin and orbital angular momentum suggests that they share a common origin.     

Oxazinanones as chiral auxiliaries: synthesis and evaluation in enolate alkylations and aldol reactions

Homochiral beta-amino esters (prepared on multigram scale by lithium amide conjugate addition) are readily transformed into oxazinanones. N-acyl derivatives of oxazinanones undergo stereoselective enolate alkylation reactions, with higher stereoselectivities observed for the enolate alkylation of (R)-N-propanoyl-4-iso-propyl-6,6-dimethyl-oxazinan-2-one than the corresponding Evans oxazolidin-2-one. A C(4)-iso-propyl stereodirecting group within the oxazinanone conveys higher stereoselectivity than the analogous C(4)-phenyl substituent. gem-Dimethyl substitution at C(6) within the oxazinanone framework facilitates exclusive exocyclic cleavage upon hydrolysis to furnish alpha-substituted carboxylic acid derivatives and the parent oxazinanone in good yield. Asymmetric aldol reactions of a range of aromatic and aliphatic aldehydes with the chlorotitanium enolate of (R)-N-propanoyl-4-iso-propyl-6,6-dimethyl-oxazinan-2-one proceed with excellent diastereoselectivity. Hydrolysis of the aldol products affords homochiral alpha-methyl-beta-hydroxy-carboxylic acids.     

The design of efficient and selective routes to pyridyl analogues of 3-oxo-3,4-dihydro-2H-1,4-(benzothiazine or benzoxazine)-6-carbaldehydes

This Letter describes the synthesis of challenging pyridyl analogues of 3-oxo-3,4-dihydro-2H-1,4-(benzothiazine or benzoxazine)-6-carbaldehydes. The six different routes described are high yielding, contain no major purification issues and have been used to give gram quantities of each aldehyde.     

Growth conditions for entire functions with only bounded Fatou components

Let f be a transcendental entire function of order less than 1/2. Denote the maximum and minimum modulus of f by M(r, f) = max{|f(z)|: |z| = r} and m(r, f) = min{|f(z)|: |z| = r}. We obtain a minimum modulus condition satisfied by many f of order zero that implies all Fatou components are bounded. A special case of our result is that if

Influence of atmospheric turbulence on states of light carrying orbital angular momentum

We have experimentally studied the degradation of mode purity for light beams carrying orbital angular momentum (OAM) propagating through simulated atmospheric turbulence. The turbulence is modeled as a randomly varying phase aberration, which obeys statistics postulated by Kolmogorov turbulence theory. We introduce this simulated turbulence through the use of a phase-only spatial light modulator. Once the turbulence is introduced, the degradation in mode quality results in crosstalk between OAM modes. We study this crosstalk in OAM for 11 modes, showing that turbulence uniformly degrades the purity of all the modes within this range, irrespective of mode number.     

Faster first-order primal-dual methods for linear programming using restarts and sharpness

Mathematical Programming - First-order primal-dual methods are appealing for their low memory overhead, fast iterations, and effective parallelization. However, they are often slow at finding high...