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 Sharkey’s 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$^\circ$ 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