Crop phenology is fundamental for understanding crop growth and development, and increasingly influences many agricultural management practices. Water deficits are one environmental factor that can ...influence crop phenology through shortening or lengthening the developmental phase, yet the phenological responses to water deficits have rarely been quantified. The objective of this article is to describe the science and general evaluation of a decision support technology software tool, PhenologyMMS (Modular Modeling Software) V1.2. PhenologyMMS was developed to simulate the phenological response of different crops to varying levels of soil water. The program is intended to be simple to use, requires minimal information for calibration, and can be easily incorporated into other crop simulation models. New and revised developmental sequences of the shoot apex correlated with phenological events and the response to soil water availability are provided for proso millet (Panicum milaceum L.), hay/foxtail millet Setaria italica (L.) P. Beauv., sunflower (Helianthus annuus L.), and sorghum (Sorghum bicolor L.). Model evaluation consisted of testing algorithms using "generic" default phenology parameters for a crop (i.e., no calibration for specific cultivars was used) for a variety of field experiments to predict developmental events such as seedling emergence, floral initiation, flowering, and physiological maturity. Additionally, an application of the program predicting mean dates of winter wheat (Triticum aestivum L.) phenology across the Central Great Plains based on historical weather records is presented. Results demonstrated that PhenologyMMS has general applicability for predicting crop phenology and offers a simple and easy to use approach to predict and understand how phenology responds to varying water deficits. PhenologyMMS software may be downloaded from http://www.ars.usda.gov/services (select "Software") or http://arsagsoftware.ars.usda.gov.
A material's acoustic properties depend critically upon porosity. Doping a soft material with gas-filled microballoons permits a controlled variation of the porosity through a scalable fabrication ...process while generating well-tailored spherical cavities that are impermeable to liquids. However, evidence is lacking of how the nanometer-scale polymeric shell contributes to the overall effective material properties in the regime where the wavelength is comparable to the sample thickness. Here, we measure ultrasound transmission through a microballoon-doped soft material as a function of microballoon and impurity concentration, sample thickness, and frequency. The measured longitudinal wave speeds are an order of magnitude larger than those in similar systems where no shell is present, while the transverse wave speed is found to linearly increase with microballoon concentration, also in contrast to systems with no shell. Furthermore, we find the results are independent of the soft material's elastic moduli as well as a lesser contribution of the microballoon shell on material attenuation. The results are validated with a multiple scattering model and suggest the shell contributes significantly to the material's bulk acoustic properties despite its thickness being 4 orders of magnitude smaller than the acoustic wavelength. Our results demonstrate how a nanometer-scale interface between a gas cavity and a soft polymer can be used in the submicrometer design of acoustic materials, and are important for observations of such phenomena as strong interference effects in soft matter.
We describe the development of an experiment to measure the weak value of the transverse momentum operator (local momentum 1) of cold atoms passing through a matter- wave interferometer. The results ...will be used to reconstruct the atom's average trajectories. We describe our progress towards this goal using laser cooled argon atoms.
Let m and n be positive integers with n⩾2 and 1⩽m⩽n−1. We study rearrangement-invariant quasinorms ϱR and ϱD on functions f:(0, 1)→R such that to each bounded domain Ω in Rn, with Lebesgue measure ...|Ω|, there corresponds C=C(|Ω|)>0 for which one has the Sobolev imbedding inequality ϱR(u*(|Ω|t))⩽CϱD(|∇mu|*(|Ω|t)), u∈Cm0(Ω), involving the nonincreasing rearrangements of u and a certain mth order gradient of u. When m=1 we deal, in fact, with a closely related imbedding inequality of Talenti, in which ϱD need not be rearrangement-invariant, ϱR(u*(|Ω|t))⩽CϱD((d/dt)∫{x∈Rn:|u(x)|>u*(|Ω|t)}|(∇u)(x)|dx), u∈C10(Ω). In both cases we are especially interested in when the quasinorms are optimal, in the sense that ϱR cannot be replaced by an essentially larger quasinorm and ϱD cannot be replaced by an essentially smaller one. Our results yield best possible refinements of such (limiting) Sobolev inequalities as those of Trudinger, Strichartz, Hansson, Brézis, and Wainger.
Let
I
=
a
,
b
⊂
R
, let
1
<
p
⩽
q
<
∞
, let
u and
v be positive functions with
u
∈
L
p
′
(
I
)
,
v
∈
L
q
(
I
)
and let
T
:
L
p
(
I
)
→
L
q
(
I
)
be the Hardy-type operator given by
(
T
f
)
(
x
)
=
...v
(
x
)
∫
a
x
f
(
t
)
u
(
t
)
d
t
,
x
∈
I
.
We show that the Bernstein numbers
b
n
of
T satisfy
lim
n
→
∞
n
b
n
=
c
p
q
(
∫
I
(
u
v
)
r
d
t
)
1
/
r
,
1
/
r
=
1
/
p
′
+
1
/
q
,
where
c
p
q
is an explicit constant depending only on
p and
q.
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