skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: The dipolar field of rotating bodies in two dimensions
The fluid velocity far from a translating body in two-dimensional irrotational flow is generally dipolar. This is a classical result. Here we ask when the dipolar component vanishes. Lamb (1945, § 126) provides symmetry conditions on the virtual mass tensor for this to be the case. We show that these conditions are not necessary and obtain the sufficient and necessary condition in terms of the shape of the body using conformal maps. Some explicit examples are constructed based on this condition.  more » « less
Award ID(s):
0133978
PAR ID:
10300494
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Fluid Mechanics
Volume:
607
ISSN:
0022-1120
Page Range / eLocation ID:
109 to 118
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, ASME Letters in Dynamic Systems and Control)
    null (Ed.)
    Abstract This paper presents an investigation of zeros in the SISO dynamics of an undamped three degrees-of-freedom (3DOF) linear time invariant (LTI) flexible system. Of particular interest are non-minimum phase zeros, which severely impact closed-loop performance. This study uses modal decomposition and zero loci to reveal all types of zeros—marginal minimum phase (MMP), real minimum phase (RMP), real non-minimum phase (RNMP), complex minimum phase (CMP), and complex non-minimum phase (CNMP)—that can exist in the system under various parametric conditions. It is shown that if CNMP zeros occur in the dynamics of an undamped LTI flexible system, they will always occur in a quartet of CMP-CNMP zeros. Consequently, the simplest undamped LTI flexible system that can exhibit CNMP zeros in its dynamics is a 3DOF system. Motivated by practical examples of flexible systems that exhibit CNMP zeros, the undamped 3DOF system considered in this paper comprised one rigid-body mode and two flexible modes. For this system, the following conclusions are mathematically established: (1) This system exhibits all possible types of zeros, (2) The precise conditions on modal frequencies and modal residues associated with every possible zero provide a mathematical formulation of the necessary and sufficient conditions for the existence of each type of zero, and (3) Alternating signs of modal residues is a necessary condition for the presence of CNMP zeros in the dynamics of this system. Conversely, avoiding alternating signs of modal residues is a sufficient condition to guarantee the absence of CNMP zeros in this system. 
    more » « less
  2. ; ; (, Proceedings of the ASME Dynamic Systems and Control Conference)
    null (Ed.)
    This paper presents an investigation of zeros in the SISO dynamics of an undamped three-DoF LTI flexible system. Of particular interest are non-minimum phase zeros, which severely impact closed-loop performance. This study uses modal decomposition and zero loci to reveal all types of zeros – marginal minimum phase (MMP), real minimum phase (RMP), real non-minimum phase (RNMP), complex minimum phase (CMP) and complex non-minimum phase (CNMP) – that can exist in the system under various parametric conditions. It is shown that if CNMP zeros occur in the dynamics of an undamped LTI flexible system, they will always occur in a quartet of CMP-CNMP zeros. And, that the simplest undamped LTI flexible system that can exhibit CNMP zeros in its dynamics is a three-DoF system. Motivated by practical examples of flexible systems that exhibit CNMP zeros, the undamped three-DoF system considered in this paper comprises of one rigid-body mode and two flexible modes. For this system, the following conclusions are mathematically established: (1) This system exhibits all possible types of zeros. (2) The precise conditions on modal frequencies and modal residues associated with every possible zero provide a mathematical formulation of the necessary and sufficient conditions for the existence of each type of zero. (3) Alternating signs of modal residues is a necessary condition for the presence of CNMP zeros in the dynamics of this system. Conversely, avoiding alternating signs of modal residues is a sufficient condition to guarantee the absence of CNMP zeros in this system. 
    more » « less
  3. ; ; (, Soft Matter)
    Presented herein is the first report on dipolar Janus liposomes–liposomes that contain opposite surface charges decorating the two hemispheres of the same colloidal body. Such heterogeneous organization of surface charge is achieved through cholesterol-modulated lipid phase separation, which sorts anionic/cationic lipids into coexisting liquid-ordered/liquid-disordered domains. We present optimized experimental conditions to produce these liposomes in high yields, based on the gel-assisted hydration of ternary lipid systems consisting of cholesterol, 1,2-dipalmitoyl- sn-glycero -3-phosphocholine, and 1,2-dioleoyl- sn-glycero -3-phosphocholine. The size/charge distribution and domain configuration of these liposomes are characterized in detail by confocal fluorescence microscopy, nanosphere binding and zeta potential measurements. Using confocal fluorescence microscopy, we also follow the electrokinetic motion as well as the electrostatic self-assembly of these new dipolar Janus particles. 
    more » « less
  4. ; ; ; ; ; (, PRX Quantum)
    We develop double microwave shielding, which has recently enabled evaporative cooling to the first Bose-Einstein condensate of polar molecules [Bigagli , Nature , 289 (2024)]. Two microwave fields of different frequency and polarization are employed to effectively shield polar molecules from inelastic collisions and three-body recombination. Here, we describe in detail the theory of double microwave shielding. We demonstrate that double microwave shielding effectively suppresses two- and three-body losses. Simultaneously, dipolar interactions and the scattering length can be flexibly tuned, enabling comprehensive control over interactions in ultracold gases of polar molecules. We show that this approach works universally for a wide range of molecules. This opens the door to studying many-body physics with strongly interacting dipolar quantum matter. 
    more » « less
  5. ; ; ; ; ; ; (, Nature)
    Ensembles of particles governed by quantum mechanical laws exhibit fascinating emergent behavior. Atomic quantum gases, liquid helium, and electrons in quantum materials all show distinct properties due to their composition and interactions. Quantum degenerate samples of bosonic dipolar molecules promise the realization of novel phases of matter with tunable dipolar interactions and new avenues for quantum simulation and quantum computation. However, rapid losses, even when reduced through collisional shielding techniques, have so far prevented cooling to a Bose-Einstein condensate (BEC). In this work, we report on the realization of a BEC of dipolar molecules. By strongly suppressing two- and three-body losses via enhanced collisional shielding, we evaporatively cool sodium-cesium (NaCs) molecules to quantum degeneracy. The BEC reveals itself via a bimodal distribution and a phase-space-density exceeding one. BECs with a condensate fraction of 60(10) % and a temperature of 6(2) nK are created and found to be stable with a lifetime close to 2 seconds. This work opens the door to the exploration of dipolar quantum matter in regimes that have been inaccessible so far, promising the creation of exotic dipolar droplets, self-organized crystal phases, and dipolar spin liquids in optical lattices. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email