13,689 research outputs found
Ancient solutions in Lagrangian mean curvature flow
Ancient solutions of Lagrangian mean curvature flow in C^n naturally arise as
Type II blow-ups. In this extended note we give structural and classification
results for such ancient solutions in terms of their blow-down and, motivated
by the Thomas-Yau Conjecture, focus on the almost calibrated case. In
particular, we classify Type II blow-ups of almost calibrated Lagrangian mean
curvature flow when the blow-down is a pair of transverse planes or, when n=2,
a multiplicity two plane. We also show that the Harvey-Lawson Clifford torus
cone in C^3 cannot arise as the blow-down of an almost calibrated Type II
blow-up.Comment: 30 pages, v2: minor typos corrected, accepted in Ann. Sc. Norm.
Super. Pisa Cl. Sc
Strange Carers
The present comment focuses on the distinction between attachment as bond formation and expectations of availability and responsiveness (security) within attachment relationships. We enumerate key components of bonding and functions of carer secure base support. Our analysis has implications for design and suggests that robots are unlikely to serve effectively as sole carers. Even with robots as part-time carers, attachment-like bonds would likely focus on human carers. Similarly, although infants and children would certainly build expectations regarding the availability and responsiveness of robot carers, the quality of human care would probably be the determining influence on later development and competence. Notwithstanding their limitations of robots as attachment figures they have considerable potential to extend parental care and enrich infant exploration. The Sharkeyâs paper and further consideration of robots as carers for infants, children, older adults, an
A BIOTIC CONTROL PERSPECTIVE ON NITRATE CONTAMINATION OF GROUNDWATER FROM AGRICULTURAL PRODUCTION
Agronomists consider the continuity and nutrient capturing properties of cover crops as important determinants of nutrient cycling in agricultural systems. Managing for these biotic control functions can help limit nutrient loss and groundwater contamination between main crop harvests. This simulation study highlights the potential role of cover crop management in a welfare economics framework. The objective is to find the optimal combination of nutrient input to the main crop, the extent of off-season cover crops, and crop functional diversity to maximize the sum of benefits from agricultural production and groundwater protection.Crop Production/Industries,
Tailoring many-body entanglement through local control
We construct optimal time-local control pulses based on a multipartite
entanglement measure as target functional. The underlying control Hamiltonians
are derived in a purely algebraic fashion, and the resulting pulses drive a
composite quantum system rapidly into that highly entangled state which can be
created most efficiently for a given interaction mechanism, and which bears
entanglement that is robust against decoherence. Moreover, it is shown that the
control scheme is insensitive to experimental imperfections in first order.Comment: 12 pages, 11 figure
Integrating out the Dirac sea in the Walecka model
We derive a purely fermionic no-sea effective theory, featuring
positive-energy states only for the Walecka model. In contrast to the so-called
mean-field theory approach with the no-sea approximation, where the Dirac sea
is simply omitted from the outset, we turn to the relativistic Hartree
approximation and explicitly construct a no-sea effective theory from the
underlying quantum field theory. Several results obtained within these two
approaches are confronted with each other. This sheds new light on the
reliability of the mean-field theory with the no-sea approximation as well as
the role of the Dirac sea. Restricting to 1+1 dimensions, we obtain new
analytical insights into nonuniform nuclear matter.Comment: 15 pages, 8 figures, several points clarified, Fig.7 replaced,
references adde
Full phase diagram of isolated skyrmions in a ferromagnet
Magnetic skyrmions are topological quasi particles of great interest for data
storage applications because of their small size, high stability, and ease of
manipulation via electric current. Theoretically, however, skyrmions are poorly
understood since existing theories are not applicable to small skyrmion sizes
and finite material thicknesses. Here, we present a complete theoretical
framework to determine the energy of any skyrmion in any material, assuming
only a circular symmetric 360 domain wall profile and a homogeneous
magnetization profile in the out-of-plane direction. Our model precisely agrees
with existing experimental data and micromagnetic simulations. Surprisingly, we
can prove that there is no topological protection of skyrmions. We discover and
confirm new phases, such as bi-stability, a phenomenon unknown in magnetism so
far. The outstanding computational performance and precision of our model allow
us to obtain the complete phase diagram of static skyrmions and to tackle the
inverse problem of finding materials corresponding to given skyrmion
properties, a milestone of skyrmion engineering
Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model
The long-time behavior of transport coefficients in a model for spatially
heterogeneous media in two and three dimensions is investigated by Molecular
Dynamics simulations. The behavior of the velocity auto-correlation function is
rationalized in terms of a competition of the critical relaxation due to the
underlying percolation transition and the hydrodynamic power-law anomalies. In
two dimensions and in the absence of a diffusive mode, another power law
anomaly due to trapping is found with an exponent -3 instead of -2. Further,
the logarithmic divergence of the Burnett coefficient is corroborated in the
dilute limit; at finite density, however, it is dominated by stronger
divergences.Comment: Full-length paragraph added that exemplifies the relevance for dense
fluids and makes a connection to recently observed, novel long-time tails in
a hard-sphere flui
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