Showing papers on "Critical radius published in 2023"

Experimental detection of quantum steerability based on the critical radius in an all-optical system

Abstract: Quantum steering is the ability that one system affects another one without delay by performing local measurements. During the past few years, the research on quantum steering has been verified in a number of experiments by the choices of measurements. But this research cannot detect all steerable states. Recently, the definition of critical radius was proposed by Nguyen et al. [Phys. Rev. Lett. 122, 240401 (2019)]. The critical radius can detect all steerable states for two-qubit states. Therefore the critical radius can be regarded as the best method for detecting the steerability of two-qubit states. However, relevant experimental research is still lacking. In this work, for comparison, we experimentally investigate three steering criteria based on the critical radius, the geometric Bell-like inequality, and the three-setting measurements steering inequality and find that the critical radius can detect the most steerable states. Furthermore, we demonstrate that the critical radius satisfies the scaling property. The results show that we only need to calculate the critical radii of some quantum states to obtain the critical radii of more scaling quantum states. Thus this property can provide the convenience for detecting the steerability of many quantum states.

Gauge theory description of Rydberg atom arrays with a tunable blockade radius

Abstract: We discuss a Rydberg atom chain with a tunable blockade radius from the gauge theoretic perspective. When the blockade radius is one lattice spacing, this system can be formulated in terms of the PXP model, and there is a $\mathbb{Z}_2$ Ising phase transition known to be equivalent to a confinement-deconfinement transition in a gauge theory, the lattice Schwinger model. Further increasing the blockade radius, one can add a next-nearest neighbor (NNN) interaction into the PXP model. We discuss the interpretation of NNN interaction in terms of the gauge theory and how finite NNN interaction alters the deconfinement behavior and propose a corresponding experimental protocol. When the blockade radius reaches two lattice spacing, the model reduces to the PPXPP model. A novel gauge theory equivalent to the PPXPP model is formulated, and the phases in the two formulations are delineated. These results are readily explored experimentally in Rydberg quantum simulators.

Radial growth rate of near-critical crystal nuclei in poly(l-lactic acid) (PLLA) in Tammann's two-stage development method.

Abstract: The specific features of crystal nucleation widely determine the morphology of the evolving crystalline material. Crystal nucleation is, as a rule, not accessible by direct observation of the nuclei, which develop with time. This limitation is caused by the small size (nanometer scale) of the critical nuclei and the stochastic nature of their formation. We describe an experimental approach to the determination of specific features of the cluster size distribution employing fast scanning calorimetry at scanning rates up to 10 000 K s-1. The surviving cluster fraction is determined by selectively melting/dissolving clusters smaller than the critical size corresponding to the highest temperature of a short spike positioned between the nucleation and the development stage in Tammann's two-stage method. This approach allows for estimating the time evolution of the radius of the largest detectable clusters in the distribution. Knowing this radius as a function of nucleation time allows for determining a radial growth rate. In the example of poly(l-lactic acid) (PLLA), the order of magnitude estimate of radial growth rates of clusters of about 2-5 nm yields values between 10-5 and 10-3 nm s-1. The radial growth rate of micrometer-sized spherulites is available from optical microscopy. The corresponding values are about three orders of magnitude higher than the values for the nanometer-sized clusters. This difference is explainable by stochastic effects, transient features, and the size dependence of the growth processes on the nanometer scale. The experimental and (order of magnitude) classical nucleation theory estimates agree well.

Critical behavior of AdS black holes surrounded by dark fluid with Chaplygin-like equation of state

Abstract: Supposing the existence of Dark Fluid with a Chaplygin-like equation of state $p=-B/\rho$ (CDF) as a cosmic background, we obtain a static spherically-symmetric black hole (BH) solution to the Einstein gravitational equations. We study the $P-V$ critical behavior of AdS BH surrounded by the CDF in the extended phase space where the cosmological constant appears as pressure, and our results show the existence of the Van der Waals like small/large BH phase transition. Also, it is found that such a BH displays a first-order low/high-$\Phi$ BH phase transition and admits the same criticality with van der Waals liquid/gas system in the non-extended phase space, where the normalization factor $q$ is considered as a thermodynamic variable, while the cosmological constant being fixed. In both $P-V$ and the newly proposed $q-\Phi$ phase spaces, we calculate the BH equations of state and then numerically study the corresponding critical quantities. Moreover, the critical exponents are derived and the results show the universal class of the scaling behavior of thermodynamic quantities near criticality. Finally, we study the shadow thermodynamics of AdS BHs surrounded by the CDF. We find that, there exists a positive correlation between the shadow radius and the event horizon radius in our case. By analyzing the temperature and heat capacity curves under the shadow context, we discover that the shadow radius can replace the event horizon radius to demonstrate the BH phase transition process, and the changes of the shadow radius can serve as order parameters for the small/large BH phase transition, indicating that the shadow radius could give us a glimpse into the BH phase structure from the observational point of view.

The Formation and Stability of Nanosphere Composites

Abstract: The nucleation of spherical particles forms an interesting study on new nano composites. If smaller, disperse particles are desired, tuning of parameters becomes necessary. According to classical teachings, a critical radius exists for “homogenous” nucleation. This thermodynamic approach needs to be reconciled with the heat transfer balances dictated by rate parameters and boundary conditions, which are absent in the former approach The reconciliation of the two can be attempted by examining the moving boundary problem and its solution which depends on the phase transformation parameters, the heat transfer coefficients and the “under cooling” or thermal driving force dependent on the boundary and initial conditions. Without going into abstract mathematical arguments, a stable moving interface can be expressed as a function of time and radius and hence the two approaches can be connected where the radial growth is expressed as a power of time—a quasi steady state solution is obtainable.

Key to an extension or shortening of focal length in the enhancement of autofocusing ability of a circular Airyprime beam caused by a linear chirp factor.

Abstract: Researchers are puzzled whether the enhancement of the abruptly autofocusing ability caused by a linear chirp factor is accompanied by the shortening or the extension of the focal length. In this Letter, a circular Airyprime beam is chosen as the research object to reveal this mystery. Extension or shortening of the focal length in the enhancement of the abruptly autofocusing ability depends on the exponential decay factor a and the dimensionless radius of the primary ring. When a is small enough, there exists a critical value for the dimensionless radius. If the dimensionless radius is greater than the critical value, the focal length is shortened in the enhancement of the abruptly autofocusing ability. If the dimensionless radius is less than the critical value, the focal length is extended in the enhancement of the abruptly autofocusing ability. As a increases, the critical value for the dimensionless radius decreases until it reaches zero. The physical mechanism of extension or shortening of the focal length in the enhancement of the abruptly autofocusing ability is elucidated.

Study on the Coalescence-Induced Jumping of Droplets with Different Radii on Superhydrophobic Surface

Abstract: The phenomenon of droplet coalescence and jumping has received increasing attention due to its potential applications in the fields of condensation heat transfer and surface self-cleaning. Basic research on the process and mechanism of coalescence-induced droplet jumping has been carried out, and some universal laws have been established. However, it is found that the focus of these studies is based on two identical droplets, and the coalescence-induced jumping with different radii is rarely investigated, which is commonly encountered in nature. Therefore, it is essential to proceed with the research of coalescence and jumping of droplets with unequal radii. In this paper, molecular dynamics (MD) simulations are performed to reveal the effects of radius ratio and radius of small droplets on jumping velocity. The results show that as the increasing of radius ratio with an unchanged small droplet radius of 8.1 nm, the jumping velocity increases then decreases, which indicates there is an optimal radius ratio to maximize the jumping velocity. Additionally, it is found that if the small droplet radius is changed, the critical radius ratio for characterizing whether the coalesced droplet jumping increases with increasing the small droplet radius. Furthermore, according to energy conservation, the conversion efficiency of energy is discussed. The results show that when the radius ratio is greater than 1.3 with three different small droplet radii, the energy conversion efficiency rapidly decreases to below 1.0%; and the critical radius ratios are consistent with the result obtained from the velocity analysis. This work broadens the understanding of the more general phenomenon of coalescence-induced droplet jumping and can better guide industrial applications.

Critical behavior of AdS black holes surrounded by dark fluid with Chaplygin-like equation of state

Abstract: Supposing the existence of Dark Fluid with a Chaplygin-like equation of state $p=-B/\rho$ (CDF) as a cosmic background, we obtain a static spherically-symmetric black hole (BH) solution to the Einstein gravitational equations. We study the $P-V$ critical behavior of AdS BH surrounded by the CDF in the extended phase space where the cosmological constant appears as pressure, and our results show the existence of the Van der Waals like small/large BH phase transition. Also, it is found that such a BH displays a first-order low/high-$\Phi$ BH phase transition and admits the same criticality with van der Waals liquid/gas system in the non-extended phase space, where the normalization factor $q$ is considered as a thermodynamic variable, while the cosmological constant being fixed. In both $P-V$ and the newly proposed $q-\Phi$ phase spaces, we calculate the BH equations of state and then numerically study the corresponding critical quantities. Moreover, the critical exponents are derived and the results show the universal class of the scaling behavior of thermodynamic quantities near criticality. Finally, we study the shadow thermodynamics of AdS BHs surrounded by the CDF. We find that, there exists a positive correlation between the shadow radius and the event horizon radius in our case. By analyzing the temperature and heat capacity curves under the shadow context, we discover that the shadow radius can replace the event horizon radius to demonstrate the BH phase transition process, and the changes of the shadow radius can serve as order parameters for the small/large BH phase transition, indicating that the shadow radius could give us a glimpse into the BH phase structure from the observational point of view.

Characterizing the radius of influence during pumping tests using the absolute critical drawdown criterion: Cases of integer flow dimensions

Abstract: Determining the radius of influence r0 of wells during pumping tests is critical for the characterization of aquifers and the management of groundwater. However, because a convenient analytical interpretative framework is lacking, this is a very difficult task during routine investigations. Practicing hydrogeologists have resorted to using semi-empirical equations developed by certain authors. Most studies aiming to characterize the radius of influence are based on radial flow models. In this study, we propose to investigate, from an analytical standpoint, the radius of influence equation for integer flow dimensions (n=1,2,3), using both Barker’s generalized radial flow model and Theis’ radial flow model. The current approach may thus be considered valid for those hydrogeological contexts (fractured or granular aquifer media) that produce the specified flow dimension. The radius of influence is defined as the maximum distance from the pumping well at which the drawdown reaches its critical value of detectability: the absolute critical drawdown criterion sc. The radius of influence is a theoretical, non-intrinsic and variable parameter that reflects the ability of drawdown recording systems to measure very small variations. Our investigations show that the radius of influence equation can be generalized as follows: r0=Ctγ where the coefficients C and γ depend not only on the flow dimension parameter n, but also on the criterion sc, the pumping flow rate Q, the hydraulic conductivity K and the aquifer thickness b. The specificities of the radius of influence equation for each flow dimension are also discussed. Finally, results obtained from this analytical approach are verified against numerical simulations.

Homogenization in perforated domains at the critical scale

Abstract: We describe the asymptotic behaviour of the minimal heterogeneous $d$-capacity of a small set, which we assume to be a ball for simplicity, in a fixed bounded open set $\Omega\subseteq \mathbb{R}^d$, with $d\geq2$. Two parameters are involved: $\varepsilon$, the radius of the ball, and $\delta$, the length scale of the heterogeneity of the medium. We prove that this capacity behaves as $C|\log \varepsilon|^{d-1}$, where $C=C(\lambda)$ is an explicit constant depending on the parameter $\lambda:=\lim_{\varepsilon\to0}|\log \delta|/|\log\varepsilon|$. Applying this result, we determine the $\Gamma$-limit of oscillating integral functionals subjected to Dirichlet boundary conditions on periodically perforated domains. In this instance, our first result is used to study the behaviour of the functionals near the perforations which are exactly balls of radius $\varepsilon$. We prove that, as in the homogeneous case, these lead to an additional term that involves $C(\lambda)$.