Waves in active matter: The transition from ballistic to diffusive behavior

We highlight the unique wavelike character observed in the relaxation dynamics of active systems via a Smoluchowski based theoretical framework and Brownian dynamic simulations. Persistent swimming motion results in wavelike dynamics until the advective swim displacements become sufficiently uncorrelated, at which point the motion becomes a random walk process characterized by a swim diffusivity, D^(swim) = U²₀τ_R/[d(d−1)], dependent on the speed of swimming U₀, reorientation time τ_R, and reorientation dimension d. This change in behavior is described by a telegraph equation, which governs the transition from ballistic wavelike motion to long-time diffusive motion. We study the relaxation of active Brownian particles from an instantaneous source, and provide an explanation for the nonmonotonicity observed in the intermediate scattering function. Using our simple kinetic model we provide the density distribution for the diffusion of active particles released from a line source as a function of time, position, and the ratio of the activity to thermal energy. We extend our analysis to include the effects of an external field on particle spreading to further understand how reorientation events in the active force vector affect relaxation. The strength of the applied external field is shown to be inversely proportional to the decay of the wavelike structure. Our theoretical description for the evolution of the number density agrees with Brownian dynamic simulation data

The "isothermal" compressibility of active matter

We demonstrate that the mechanically defined “isothermal” compressibility behaves as a thermodynamic-like response function for suspensions of active Brownian particles. The compressibility computed from the active pressure—a combination of the collision and unique swim pressures—is capable of predicting the critical point for motility induced phase separation, as expected from the mechanical stability criterion. We relate this mechanical definition to the static structure factor via an active form of the thermodynamic compressibility equation and find the two to be equivalent, as would be the case for equilibrium systems. This equivalence indicates that compressibility behaves like a thermodynamic response function, even when activity is large. Finally, we discuss the importance of the phase interface when defining an active chemical potential. Previous definitions of the active chemical potential are shown to be accurate above the critical point but breakdown in the coexistence region. Inclusion of the swim pressure in the mechanical compressibility definition suggests that the interface is essential for determining phase behavior

The "isothermal" compressibility of active matter

We demonstrate that the mechanically-defined "isothermal" compressibility behaves as a thermodynamic-like response function for suspensions of active Brownian particles. The compressibility computed from the active pressure - a combination of the collision and unique swim pressures - is capable of predicting the critical point for motility induced phase separation, as expected from the mechanical stability criterion. We relate this mechanical definition to the static structure factor via an active form of the thermodynamic compressibility equation and find the two to be equivalent, as would be the case for equilibrium systems. This equivalence indicates that compressibility behaves like a thermodynamic response function, even when activity is large. Finally, we discuss the importance of the phase interface when defining an active chemical potential. Previous definitions of the active chemical potential are shown to be accurate above the critical point but breakdown in the coexistence region. Inclusion of the swim pressure in the mechanical compressibility definition suggests that the interface is essential for determining phase behavior

The collective quantization of three-flavored Skyrmions revisited

A self-consistent large $N_c$ approach is developed for the collective quantization of SU(3) flavor hedgehog solitons, such as the Skyrmion. The key to this analysis is the determination of all of the zero modes associated with small fluctuations around the hedgehog. These are used in the conventional way to construct collective coordinates. This approach differs from previous work in that it does not implicitly assume that each static zero mode is associated with a dynamical zero mode. It is demonstrated explicitly in the context of the Skyrmion that there are fewer dynamical zero modes than static ones due to the Witten-Wess-Zumino term in the action. Group-theoretic methods are employed to identify the physical states resulting from canonical quantization of the collectively rotating soliton. The collective states fall into representations of SU(3) flavor labeled by $(p,q)$ and are given by $(2J, \frac{Nc}{2} -J)$ where $J={1/2},{3/2},...$ is the spin of the collective state. States with strangeness $S > 0$ do not arise as collective states from this procedure; thus the $\theta^{+}$ (pentaquark) resonance does not arise as a collective excitation in models of this type.Comment: 12 pages; uses package "youngtab

Unique Identification of Lee-Wick Gauge Bosons at Linear Colliders

Grinstein, O'Connell and Wise have recently presented an extension of the Standard Model (SM), based on the ideas of Lee and Wick (LW), which demonstrates an interesting way to remove the quadratically divergent contributions to the Higgs mass induced by radiative corrections. This model predicts the existence of negative-norm copies of the usual SM fields at the TeV scale with ghost-like propagators and negative decay widths, but with otherwise SM-like couplings. In earlier work, it was demonstrated that the LW states in the gauge boson sector of these models, though easy to observe, cannot be uniquely identified as such at the LHC. In this paper, we address the issue of whether or not this problem can be resolved at an $e^+e^-$ collider with a suitable center of mass energy range. We find that measurements of the cross section and the left-right polarization asymmetry associated with Bhabha scattering can lead to a unique identification of the neutral electroweak gauge bosons of the Lee-Wick type.Comment: 16 pages, 6 figures; discussion and references adde

Asymmetric WIMP dark matter

In existing dark matter models with global symmetries the relic abundance of dark matter is either equal to that of anti-dark matter (thermal WIMP), or vastly larger, with essentially no remaining anti-dark matter (asymmetric dark matter). By exploring the consequences of a primordial asymmetry on the coupled dark matter and anti-dark matter Boltzmann equations we find large regions of parameter space that interpolate between these two extremes. Interestingly, this new asymmetric WIMP framework can accommodate a wide range of dark matter masses and annihilation cross sections. The present-day dark matter population is typically asymmetric, but only weakly so, such that indirect signals of dark matter annihilation are not completely suppressed. We apply our results to existing models, noting that upcoming direct detection experiments will constrain a large region of the relevant parameter space.Comment: 32 pages, 6 figures, updated references, updated XENON100 bounds, typo in figure caption correcte

Field-scale mapping of evaporative stress indicators of crop yield: An application over Mead, NE, USA

The Evaporative Stress Index (ESI) quantifies temporal anomalies in a normalized evapotranspiration (ET) metric describing the ratio of actual-to-reference ET (fRET) as derived from satellite remote sensing. At regional scales (3–10 km pixel resolution), the ESI has demonstrated the capacity to capture developing crop stress and impacts on regional yield variability in water-limited agricultural regions. However, its performance in some regions where the vegetation cycle is intensively managed appears to be degraded due to spatial and temporal limitations in the standard ESI products. In this study, we investigated potential improvements to ESI by generating maps of ET, fRET, and fRET anomalies at high spatiotemporal resolution (30-m pixels, daily time steps) using a multi-sensor data fusion method, enabling separation of landcover types with different phenologies and resilience to drought. The study was conducted for the period 2010–2014 covering a region around Mead, Nebraska that includes both rainfed and irrigated crops. Correlations between ESI and measurements of maize yield were investigated at both the field and county level to assess the potential of ESI as a yield forecasting tool. To examine the role of crop phenology in yield-ESI correlations, annual input fRET time series were aligned by both calendar day and by biophysically relevant dates (e.g. days since planting or emergence). At the resolution of the operational U.S. ESI product (4 km), adjusting fRET alignment to a regionally reported emergence date prior to anomaly computation improves r2 correlations with county-level yield estimates from 0.28 to 0.80. At 30-m resolution, where pure maize pixels can be isolated from other crops and landcover types, county-level yield correlations improved from 0.47 to 0.93 when aligning fRET by emergence date rather than calendar date. Peak correlations occurred 68 days after emergence, corresponding to the silking stage for maize when grain development is particularly sensitive to soil moisture deficiencies. The results of this study demonstrate the utility of remotely sensed ET in conveying spatially and temporally explicit water stress information to yield prediction and crop simulation models

Noether Symmetry Approach in "Cosmic Triad" Vector Field Scenario

To realize the accelerations in the early and late periods of our universe, we need to specify potentials for the dominant fields. In this paper, by using the Noether symmetry approach, we try to find suitable potentials in the "cosmic triad" vector field scenario. Because the equation of state parameter of dark energy has been constrained in the range of $-1.21\leq \omega\leq -0.89$ by observations, we derive the Noether conditions for the vector field in quintessence, phantom and quintom models, respectively. In the first two cases, constant potential solutions have been obtained. What is more, a fast decaying point-like solution with power-law potential is also found for the vector field in quintessence model. For the quintom case, we find an interesting constraint $\tilde{C}V_{p}'=-CV_{q}'$ on the field potentials, where $C$ and $\tilde{C}$ are constants related to the Noether symmetry.Comment: 15 pages, no figures, accepted by Classical and Quantum Gravity