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It is well known that the incompressible Euler equations in two dimensions have globally regular solutions. The inviscid surface quasi-geostrophic (SQG) equation has a Biot-Savart law that is one derivative less regular than in the Euler case, and the question of global regularity for its solutions is still open. We study here the patch dynamics in the half-plane for a family of active scalars that interpolates between these two equations, via a parameter α ϵ [0, ½] appearing in the kernels of their Biot-Savart laws. The values α = 0 and α = ½ correspond to the 2D Euler and SQG cases, respectively. We prove global in time regularity for the 2D Euler patch model, even if the patches initially touch the boundary of the half-plane. On the other hand, for any sufficiently small α > 0, we exhibit initial data that lead to a singularity in finite time. Thus, these results show a phase transition in the behavior of solutions to these equations and provide a rigorous foundation for classifying the 2D Euler equations as critical.

Cell migration through 3D extracellular matrices is critical to the normal development of tissues and organs and in disease processes, yet adequate analytical tools to characterize 3D migration are lacking. Here, we quantified the migration patterns of individual fibrosarcoma cells on 2D substrates and in 3D collagen matrices and found that 3D migration does not follow a random walk. Both 2D and 3D migration features a non-Gaussian, exponential mean cell velocity distribution, which we show is primarily a result of cell-to-cell variations. Unlike in the 2D case, 3D cell migration is anisotropic: velocity profiles display different speed and self-correlation processes in different directions, rendering the classical persistent random walk (PRW) model of cell migration inadequate. By incorporating cell heterogeneity and local anisotropy to the PRW model, we predict 3D cell motility over a wide range of matrix densities, which identifies density-independent emerging migratory properties. This analysis also reveals the unexpected robust relation between cell speed and persistence of migration over a wide range of matrix densities.

Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior among the simplest forms of life and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active nonequilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific or which generalizations of the Navier–Stokes equations are able to describe them adequately. Here, we combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence.

We provide the first mathematical proof that the connective constant of the hexagonal lattice is equal to √2 + √2. This value has been derived nonrigorously by B. Nienhuis in 1982, using Coulomb gas approach from theoretical physics. Our proof uses a parafermionic observable for the self-avoiding walk, which satisfies a half of the discrete Cauchy-Riemann relations. Establishing the other half of the relations (which conjecturally holds in the scaling limit) would also imply convergence of the self-avoiding walk to SLE(8/3).

The interest in mid-infrared technologies surrounds plenty of important optoelectronic applications ranging from optical communications, biomedical imaging to night vision cameras, and so on. Although narrow bandgap semiconductors, such as Mercury Cadmium Telluride and Indium Antimonide, and quantum superlattices based on inter-subband transitions in wide bandgap semiconductors, have been employed for mid-infrared applications, it remains a daunting challenge to search for other materials that possess suitable bandgaps in this wavelength range. Here, we demonstrate experimentally for the first time that two-dimensional (2D) atomically thin PtSe 2 has a variable bandgap in the mid-infrared via layer and defect engineering. Here, we show that bilayer PtSe 2 combined with defects modulation possesses strong light absorption in the mid-infrared region, and we realize a mid-infrared photoconductive detector operating in a broadband mid-infrared range. Our results pave the way for atomically thin 2D noble metal dichalcogenides to be employed in high-performance mid-infrared optoelectronic devices. The mid-infrared technologies are essential to various applications but suffer from limited materials with suitable bandgap. Here the authors demonstrate that two-dimensional atomically thin PtSe 2 with variable bandgaps in the mid-infrared via layer and defect engineering is highly promising for mid-infrared optoelectronics.

The diverse set of Earth system models used to conduct the CMIP5 ensemble can partly sample the uncertainties in future climate projections. However, combining those projections is complicated by the fact that models developed by different groups share ideas and code and therefore biases. The authors propose a method for combining model results into single or multivariate distributions that are more robust to the inclusion of models with a large degree of interdependency. This study uses a multivariate metric of present-day climatology to assess both model performance and similarity in two recent model intercomparisons, CMIP3 and CMIP5. Model characteristics can be interpolated and then resampled in a space defined by independent climate properties. A form of weighting can be applied by sampling more densely in the region of the space close to the projected observations, thus taking into account both model performance and interdependence. The choice of the sampling distribution’s parameters is a subjective decision that should reflect the researcher’s prior assumptions as to the acceptability of different model errors.

In urban areas of Thailand, and especially in Bangkok, recent flash floods have caused severe damage and prompted a renewed focus to manage their impacts. The development of a real-time warning system could provide timely information to initiate flood management protocols, thereby reducing impacts. Therefore, we developed an innovative real-time flood forecasting system (RTFlood system) and applied it to the Ramkhamhaeng polder in Bangkok, which is particularly vulnerable to flash floods. The RTFlood system consists of three modules. The first module prepared rainfall input data for subsequent use by a hydraulic model. This module used radar rainfall data measured by the Bangkok Metropolitan Administration and developed forecasts using the TITAN (Thunderstorm Identification, Tracking, Analysis, and Nowcasting) rainfall model. The second module provided a real-time task management system that controlled all processes in the RTFlood system, i.e., input data preparation, hydraulic simulation timing, and post-processing of the output data for presentation. The third module provided a model simulation applying the input data from the first and second modules to simulate flash floods. It used a dynamic, conceptual model (PCSWMM, Personal Computer version of the Stormwater Management Model) to represent the drainage systems of the target urban area and predict the inundation areas. The RTFlood system was applied to the Ramkhamhaeng polder to evaluate the system’s accuracy for 116 recent flash floods. The result showed that 61.2% of the flash floods were successfully predicted with accuracy high enough for appropriate pre-warning. Moreover, it indicated that the RTFlood system alerted inundation potential 20 min earlier than separate flood modeling using radar and local rain stations individually. The earlier alert made it possible to decide on explicit flood controls, including pump and canal gate operations.

A quantity exists by which one can identify the approach of a dynamical system to the state of criticality, which is hard to identify otherwise. This quantity is the variance κ1 (≡〈χ2〉 − 〈χ〉2) of natural time χ, where 〈f(χ)〉 = Σ pkf(χk) and pk is the normalized energy released during the kth event of which the natural time is defined as χk = k/N and N stands for the total number of events. Then we show that κ1 becomes equal to 0.070 at the critical state for a variety of dynamical systems. This holds for criticality models such as 2D Ising and the Bak—Tang—Wiesenfeld sandpile, which is the standard example of self-organized criticality. This condition of κ1 = 0.070 holds for experimental results of critical phenomena such as growth of rice piles, seismic electric signals, and the subsequent seismicity before the associated main shock.

People automatically evaluate faces on multiple trait dimensions, and these evaluations predict important social outcomes, ranging from electoral success to sentencing decisions. Based on behavioral studies and computer modeling, we develop a 2D model of face evaluation. First, using a principal components analysis of trait judgments of emotionally neutral faces, we identify two orthogonal dimensions, valence and dominance, that are sufficient to describe face evaluation and show that these dimensions can be approximated by judgments of trustworthiness and dominance. Second, using a data-driven statistical model for face representation, we build and validate models for representing face trustworthiness and face dominance. Third, using these models, we show that, whereas valence evaluation is more sensitive to features resembling expressions signaling whether the person should be avoided or approached, dominance evaluation is more sensitive to features signaling physical strength/weakness. Fourth, we show that important social judgments, such as threat, can be reproduced as a function of the two orthogonal dimensions of valence and dominance. The findings suggest that face evaluation involves an overgeneralization of adaptive mechanisms for inferring harmful intentions and the ability to cause harm and can account for rapid, yet not necessarily accurate, judgments from faces.

Our objective in this paper is to measure the impact (valence, volume, and variance) of national online user reviews on designated market area (DMA)-level local geographic box office performance of movies. We account for three complications with analyses that use national-level aggregate box office data: (i) aggregation across heterogeneous markets (spatial aggregation), (ii) serial correlation as a result of sequential release of movies (endogenous rollout), and (iii) serial correlation as a result of other unobserved components that could affect inferences regarding the impact of user reviews. We use daily box office ticket sales data for 148 movies released in the United States during a 16-month period (out of the 874 movies released) along with user review data from the Yahoo! Movies website. The analysis also controls for other possible box office drivers. Our identification strategy rests on our ability to identify plausible instruments for user ratings by exploiting the sequential release of movies across markets-because user reviews can only come from markets where the movie has previously been released, exogenous variables from previous markets would be appropriate instruments in subsequent markets. In contrast with previous studies that have found that the main driver of box office performance is the volume of reviews, we find that it is the valence that seems to matter and not the volume. Furthermore, ignoring the endogenous rollout decision does not seem to have a big impact on the results from our DMA-level analysis. When we carry out our analysis with aggregated national data, we obtain the same results as those from previous studies, i.e., that volume matters but not the valence. Using various market-level controls in the national data model, we attempt to identify the source of this difference. By conducting our empirical analysis at the DMA level and accounting for prerelease advertising, we can classify DMAs based on their responsiveness to firm-initiated marketing effort (advertising) and consumer-generated marketing (online word of mouth). A unique feature of our study is that it allows marketing managers to assess a DMA's responsiveness along these two dimensions. The substantive insights can help studios and distributors evaluate their future product rollout strategies. Although our empirical analysis is conducted using motion picture industry data, our approach to addressing the endogeneity of reviews is generalizable to other industry settings where products are sequentially rolled out.