We measure the thermophoresis of polysterene beads over a wide range of temperature gradients and find a pronounced nonlinear phoretic characteristic. The transition to the nonlinear behavior is ...marked by a drastic slowing down of thermophoretic motion and is characterized by a Péclet number of order unity as corroborated for different particle sizes and salt concentrations. The data follow a single master curve covering the entire nonlinear regime for all system parameters upon proper rescaling of the temperature gradients with the Péclet number. For low thermal gradients, the thermal drift velocity follows a theoretical linear model relying on the local-equilibrium assumption, while linear theoretical approaches based on hydrodynamic stresses, ignoring fluctuations, predict significantly slower thermophoretic motion for steeper thermal gradients. Our findings suggest that thermophoresis is fluctuation dominated for small gradients and crosses over to a drift-dominated regime for larger Péclet numbers in striking contrast to electrophoresis.
Quantum probes are atomic sized devices mapping information of their environment to quantum-mechanical states. By improving measurements and at the same time minimizing perturbation of the ...environment, they form a central asset for quantum technologies. We realize spin-based quantum probes by immersing individual Cs atoms into an ultracold Rb bath. Controlling inelastic spin-exchange processes between the probe and bath allows us to map motional and thermal information onto quantum-spin states. We show that the steady-state spin population is well suited for absolute thermometry, reducing temperature measurements to detection of quantum-spin distributions. Moreover, we find that the information gain per inelastic collision can be maximized by accessing the nonequilibrium spin dynamic. Keeping the motional degree of freedom thermalized, individual spin-exchange collisions yield information about the gas quantum by quantum. We find that the sensitivity of this nonequilibrium quantum probing effectively beats the steady-state Cramér-Rao limit by almost an order of magnitude, while reducing the perturbation of the bath to only three quanta of angular momentum. Our work paves the way for local probing of quantum systems at the Heisenberg limit, and moreover, for optimizing measurement strategies via control of nonequilibrium dynamics.
We report on the experimental investigation of individual Cs atoms impinging on a dilute cloud of ultracold Rb atoms with variable density. We study the relaxation of the initial nonthermal state and ...detect the effect of single collisions which has so far eluded observation. We show that, after few collisions, the measured spatial distribution of the tracer atoms is correctly described by a Langevin equation with a velocity-dependent friction coefficient, over a large range of Knudsen numbers. Our results extend the simple and effective Langevin treatment to the realm of light particles in dilute gases. The experimental technique developed opens up the microscopic exploration of a novel regime of diffusion at the level of individual collisions.
PRINCIPAL FACTORS AND LATTICE MINIMA IN CUBIC FIELDS AOUISSI, Siham; AZIZI, Abdelmalek; ISMAILI, Moulay Chrif ...
Kyushu Journal of Mathematics,
2022, 2022-00-00, 20220101, Letnik:
76, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Let k = ℚ(3√d, ζ3), where d > 1 is a cube-free positive integer, k0 = ℚ(ζ3) be the cyclotomic field containing a primitive cube root of unity ζ3, and G ＝ Gal(k / k0). The possible prime ...factorizations of d in our main result in previous work (Theorem 1.1 in Aouissi et al, Preprint, arXiv:1808.04678v2) give rise to new phenomena concerning the chain Θ = (θi)i∈ℤ of lattice minima in the underlying pure cubic subfield L = ℚ(3√d) of k. The aims of the present work are to give criteria for the occurrence of generators of primitive ambiguous principal ideals (ν) ∈ PkG / Pk0 among the lattice minima Θ = (θi)i∈ℤ of the underlying pure cubic field L = ℚ(3√d), and to explain the exceptional behavior of the chain Θ for certain radicands d with impact on determining the principal factorization type of L and k by means of Voronoi's algorithm.
Let (kμ)μ=14 be a quartet of cyclic cubic number fields sharing a common conductor c=pqr divisible by exactly three prime(power)s, p,q,r. For those components of the quartet whose 3-class group ...Cl3(kμ)≃(Z/3Z)2 is elementary bicyclic, the automorphism group M=Gal(F32(kμ)/kμ) of the maximal metabelian unramified 3-extension of kμ is determined by conditions for cubic residue symbols between p,q,r and for ambiguous principal ideals in subfields of the common absolute 3-genus field k* of all kμ. With the aid of the relation rank d2(M), it is decided whether M coincides with the Galois group G=Gal(F3∞(kμ)/kμ) of the maximal unramified pro-3-extension of kμ.
We calculate the thermophoretic drift of a charged single colloidal particle with hydrodynamically slipping surface immersed in an electrolyte solution in response to a small temperature gradient. ...Here we rely on a linearized hydrodynamic approach for the fluid flow and the motion of the electrolyte ions while keeping the full nonlinearity of the Poisson-Boltzmann equation of the unperturbed system to account for possible large surface charging. The partial differential equations are transformed into a coupled set of ordinary differential equations in linear response. Numerical solutions are elaborated for parameter regimes of small and large Debye shielding and different hydrodynamic boundary conditions encoded in a varying slip length. Our results are in good agreement with predictions from recent theoretical work and successfully describe experimental observations on thermophoresis of DNA. We also compare our numerical results with experimental data on polystyrene beads.
For an infinite family of monogenic trinomials
P
(
X
)
=
X
3
±
3
r
b
X
-
b
∈
Z
X
, arithmetical invariants of the cubic number field
L
=
Q
(
θ
)
, generated by a zero
θ
of
P
(
X
)
, and of its ...Galois closure
N
=
L
(
d
L
)
are determined. The conductor
f
of the cyclic cubic relative extension
N
/
K
, where
K
=
Q
(
d
L
)
denotes the unique quadratic subfield of
N
, is proved to be of the form
3
e
b
with
e
∈
{
1
,
2
}
, which admits statements concerning primitive ambiguous principal ideals, lattice minima, and independent units in
L
. The number
m
of non-isomorphic cubic fields
L
1
,
…
,
L
m
sharing a common discriminant
d
L
i
=
d
L
with
L
is determined.
Tbet+CD11c+ B cells, also known as age-associated B cells (ABCs), are pivotal contributors to humoral immunity following infection and in autoimmunity, yet their in vivo generation is incompletely ...understood. We used a mouse model of systemic acute lymphocytic choriomeningitis virus infection to examine the developmental requirements of ABCs that emerged in the spleen and liver. IL-21 signaling through STAT3 was indispensable for ABC development. In contrast, IFN-γ signaling through STAT1 was required for B cell activation and proliferation. Mice that underwent splenectomy or were deficient in lymphotoxin α generated hepatic ABCs despite the lack of secondary lymphoid organ contributions, suggesting that the liver supported de novo generation of these cells separately from their development in lymphoid organs. Thus, IFN-γ and IL-21 signaling have distinct, stage-specific roles in ABC differentiation, while the tissue microenvironment provides additional cues necessary for their development.
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