Carbene-catalyzed atroposelective synthesis of axially chiral styrenes

Axially chiral styrenes bearing a chiral axis between a sterically non-congested acyclic alkene and an aryl ring are difficult to prepare due to low rotational barrier of the axis. Disclosed here is an N-heterocyclic carbene (NHC) catalytic asymmetric solution to this problem. Our reaction involves ynals, sulfinic acids, and phenols as the substrates with an NHC as the catalyst. Key steps involve selective 1,4-addition of sulfinic anion to acetylenic acylazolium intermediate and sequential E-selective protonation to set up the chiral axis. Our reaction affords axially chiral styrenes bearing a chiral axis as the product with up to > 99:1 e.r., > 20:1 E/Z selectivity, and excellent yields. The sulfone and carboxylic ester moieties in our styrene products are common moieties in bioactive molecules and asymmetric catalysis.

Carbene-Catalyzed Atroposelective Synthesis of Axially Chiral Styrenes Bearing Acyclic Alkenes

Axially chiral styrenes bearing a chiral axis between a sterically non-congested acyclic alkene and an aryl ring are difficult to prepare due to low rotational barrier of the axis. Disclosed here is an N-heterocyclic carbene (NHC) catalytic asymmetric solution to this problem. Our reaction involves ynals, sulfinic acids, and phenols as the substrates with an NHC as the catalyst. Key steps involve selective 1,4-addition of sulfinic anion to acetylenic acylazolium intermediate and sequential E-selective protonation to set up the chiral axis. Our reaction affords axially chiral styrenes bearing a chiral axis as the product with up to >99:1 e.r., >20:1 E/Z selectivity, and excellent yields. The sulfone and carboxylic ester moieties in our styrene products are common moieties in bioactive molecules and asymmetric catalysis.

Spontaneous mirror-symmetry breaking coupled to top-bottom chirality transfer: from porphyrin self-assembly to scalemic Diels–Alder adducts

This report shows how the net supramolecular chirality that emerged by spontaneous mirror-symmetry breaking (SMSB) at the mesoscale level can be transferred towards asymmetric solution chemistry.

Oscillating path between self-similarities in liquid pinch-off

Many differential equations involved in natural sciences show singular behaviors; i.e., quantities in the model diverge as the solution goes to zero. Nonetheless, the evolution of the singularity can be captured with self-similar solutions, several of which may exist for a given system. How to characterize the transition from one self-similar regime to another remains an open question. By studying the classic example of the pinch-off of a viscous liquid thread, we show experimentally that the geometry of the system and external perturbations play an essential role in the transition from a symmetric to an asymmetric solution. Moreover, this transient regime undergoes unexpected log-scale oscillations that delay dramatically the onset of the final self-similar solution. This result sheds light on the strong impact external constraints can have on predictions established to explain the formation of satellite droplets or on the rheological tests applied on a fluid, for example.

Shock-Sensitivity in Shell-Like Structures: With Simulations of Spherical Shell Buckling

Under increasing compression, an unbuckled shell is in a metastable state which becomes increasingly precarious as the buckling load is approached. So to induce premature buckling, a lateral disturbance will have to overcome a decreasing energy barrier which reaches zero at buckling. Two archetypal problems that exhibit a severe form of this behavior are the axially-compressed cylindrical shell and the externally pressurized spherical shell. Focusing on the cylinder, a nondestructive technique was recently proposed to estimate the “shock-sensitivity” of a laboratory specimen using a lateral probe to measure the nonlinear load-deflection characteristic. If a symmetry-breaking bifurcation is encountered on the path, computer simulations showed how this can be suppressed by a controlled secondary probe. Here, we extend our understanding by assessing in general terms how a single control can capture remote saddle solutions: in particular, how a symmetric probe could locate an asymmetric solution. Then, more specifically, we analyze the spherical shell with point and ring probes, to test the procedure under challenging conditions to assess its range of applicability. Rather than a bifurcation, the spherical shell offers the challenge of a destabilizing fold (limit point) under the rigid control of the probe.

Electrohydrodynamic rotation of drops at large electric Reynolds numbers

When subject to sufficiently strong electric fields, particles and drops suspended in a weakly conducting liquid exhibit spontaneous rotary motion. This so-called Quincke rotation is a fascinating example of nonlinear symmetry-breaking phenomena. To illuminate the rotation of liquid drops we here analyse the asymptotic limit of large electric Reynolds numbers, $\mathit{Re}\gg 1$, within the framework of a two-dimensional Taylor–Melcher electrohydrodynamic model. A non-trivial dominant balance in this singular limit results in both the fluid velocity and surface-charge density scaling as $\mathit{Re}^{-1/2}$. The flow is governed by a self-contained nonlinear boundary-value problem that does not admit a continuous fore–aft symmetric solution, thus necessitating drop rotation. Furthermore, thermodynamic arguments reveal that a fore–aft asymmetric solution exists only when charge relaxation within the suspending liquid is faster than that in the drop. The flow problem possesses both mirror-image (with respect to the direction of the external field) and flow-reversal symmetries; it is transformed into a universal one, independent of the ratios of electric conductivities and dielectric permittivities in the respective drop phase and suspending liquid phase. The rescaled angular velocity is found to depend weakly upon the viscosity ratio. The corresponding numerical solutions of the exact equations indeed collapse at large $\mathit{Re}$ upon the asymptotically calculated universal solution.

Linear and nonlinear parity-time-symmetric oligomers: a dynamical systems analysis

In the present work, we focus on the cases of two-site (dimer) and three-site (trimer) configurations, i.e. oligomers, respecting the parity-time ( ) symmetry, i.e. with a spatially odd gain–loss profile. We examine different types of solutions of such configurations with linear and nonlinear gain/loss profiles. Solutions beyond the linear -symmetry critical point as well as solutions with asymmetric linearization eigenvalues are found in both the nonlinear dimer and trimer. The latter feature is absent in linear -symmetric trimers, while both of them are absent in linear -symmetric dimers. Furthermore, nonlinear gain/loss terms enable the existence of both symmetric and asymmetric solution profiles (and of bifurcations between them), while only symmetric solutions are present in the linear -symmetric dimers and trimers. The linear stability analysis around the obtained solutions is discussed and their dynamical evolution is explored by means of direct numerical simulations. Finally, a brief discussion is also given of recent progress in the context of -symmetric quadrimers.

Asymmetric travelling waves in a square duct

Two types of asymmetric solutions are found numerically in square-duct flow. They emerge through a symmetry-breaking bifurcation from the mirror-symmetric solutions discovered by Okino et al. (J. Fluid Mech., vol. 657, 2010, pp. 413–429). One of them is characterized by a pair of streamwise vortices and a low-speed streak localized near one of the sidewalls and retains the shift-and-reflect symmetry. The bifurcation nature as well as the flow structure of the solution show striking resemblance to those of the asymmetric solution in pipe flow found by Pringle & Kerswell (Phys. Rev. Lett., vol. 99, 2007, A074502), despite the geometrical difference between their cross-sections. The solution seems to be embedded in the edge state of square-duct flow identified by Biau & Bottaro (Phil. Trans. R. Soc. Lond. A, vol. 367, 2009, pp. 529–544). The other solution deviates slightly from the mirror-symmetric solution from which it bifurcates: the shift-and-rotate symmetry is retained but the mirror symmetry is broken.