We discuss the relationship between the capacity and the geometry for the range of the random walk for $d=3$. In particular, we consider how efficiently the random walk moves or what shape it forms in order to maximize its capacity. In one of our main results, we show a functional law for the capacity of the random walk. In addition, we find that there is a phase transition for the asymptotics of the capacity of the random walk when we condition the diameter of the random walk.
Junjie Dong, Rebecca A. Fischer, Lars P. Stixrude
et al.
Water has been stored in the Martian mantle since its formation, primarily in nominally anhydrous minerals. The short-lived early hydrosphere and intermittently flowing water on the Martian surface may have been supplied and replenished by magmatic degassing of water from the mantle. Estimating the water storage capacity of the solid Martian mantle places important constraints on its water inventory and helps elucidate the sources, sinks, and temporal variations of water on Mars. In this study, we applied a bootstrap aggregation method to investigate the effects of iron on water storage capacities in olivine, wadsleyite, and ringwoodite, based on high-pressure experimental data compiled from the literature, and we provide a quantitative estimate of the upper bound of the bulk water storage capacity in the FeO-rich solid Martian mantle. Along a series of areotherms at different mantle potential temperatures ($T_{p}$), we estimated a water storage capacity equal to $9.0_{-2.2} ^{+2.8}$ km Global Equivalent Layer (GEL) for the present-day Martian mantle at $T_{p}$ = 1600 K and $4.9_{-1.5}^{+1.7}$ km GEL for the initial Martian mantle at $T_{p}$ = 1900 K. The water storage capacity of the Martian mantle increases with secular cooling through time, but due to the lack of an efficient water recycling mechanism on Mars, its actual mantle water content may be significantly lower than its water storage capacity today.
This research is directed at developing renewable fuel sources, which are not only environmentally friendly, but also more importantly harvested faster and not competitive with agricultural land. For this reason, the potential oil-producing microalgae need to be explored, because it has fast growth and its cultivation development will not compete in land use with food agriculture. This study aims specifically to determine the types of microalgae producing biodiesel oil that can be isolated from the natural Wallacea in NTB waters, to determine light spectrum treatment and N elimination in microalgae culture which significantly increases the productivity and quality of the biodiesel it produces. Based on the distribution map of potential biofuel-producing microalgae types in NTB waters, samples will be collected from several NTB waters, then the target types of microalgae are isolated and cultured in two systems: a closed system (bioreactor) and an open system (raceway pool) with light spectrum variation treatment and elimination of N in microalgae culture nutrients to increase the productivity and quality of the biodiesel oil produced. Biomass was harvested every 48 hours from the bioreactor and every 4 weeks from the experimental pond. Microalgae biomass was extracted with hexane to produce primary oil. This primary oil usually still has a relatively high viscosity compared to petrodiesel, so it is then trans-esterified with methanol and an acid catalyst to increase the fire point and reduce its viscosity. Oil fractionation is also carried out to sort and determine the composition of saturated, mono-unsaturated and poly-unsaturated fatty acids which greatly determine the biodeasel quality of these microalgae. The biodiesel quality variables to be measured are density, viscosity, flash point, freezing point, solubility in water, vapor pressure, reactivity, physical appearance, odor and toxicity. The result showed that, in the community of marine microalgae from Lombok and Sumbawa Islands consist of 62 species of potential producing-oil microalgae were dominated by Bacteriastrum delicatulum, B. variance, Chaetoceros amini, C. affinis, C. liciniosum, C. lorenzianum, Gyrosigma sp., Nannochloropsis oculata, Nitzchia spp., Oscillatoria sp., Pseudonitzschia spp., and Thalassionema nitzschicoides. Types of oil-producing freshwater microalgae in Lombok Island consist of 19 species of potential producing-oil microalgae, identified with high abundance and dominance, covering Microcystis aeruginosa, M. incerta, Nostoc sp., and Pediastrum boryanum. The oil content of the three species of microalgae, namely Chaetoceros amini, Nannochloropsis oculata, and Nitzchia spp which had been cultured by trietmant were 34, 68, and 46% dry weight, respectively.
H2O Innovation Inc is expanding its manufacturing plant in Ham-Nord (Quebec), Canada to respond to the sustained growth of its Maple business line and the anticipated increase in water treatment project sales.
This paper considers a binary channel with deletions. We derive two close form upper bound on the capacity of binary deletion channel. The first upper bound is based on computing the capacity of an auxiliary channel and we show how the capacity of auxiliary channel is the upper bound of the binary deletion channel. Our main idea for the second bound is based on computing the mutual information between the sent bits and the received bits in binary deletion channel. We approximate the exact mutual information and we give a close form expression. All bounds utilize first-order Markov process for the channel input. The second proposed upper bound improves the best upper bound [6,11] up to 0.1.
We study the private information retrieval (PIR) problem under arbitrary collusion pattern for replicated databases. We find its capacity, which is the same as the capacity of the original PIR problem with the number of databases $N$ replaced by a number $S^*$. The number $S^*$ is the optimal solution to a linear programming problem that is a function of the collusion pattern. Hence, the collusion pattern affects the capacity of the PIR problem only through the number $S^*$.
In this paper, we consider capacity degradations stemming from potential hardware impairments (HWI) of newly proposed Large Intelligent Surface (LIS) systems. Without HWI, the utility of surface-area (the first-order derivative of the capacity with respect to surface-area) is shown to be proportional to the inverse of it. With HWI, the capacity as well as the utility of surface-area are both degraded, due to a higher effective noise level caused by the HWI. After first modeling the HWI in a general form, we derive the effective noise density and the decrement of utility in closed-forms. With those the impacts of increasing the surface-area can be clearly seen. One interesting but also natural outcome is that both the capacity and utility can be decreased when increasing the surface-area in the cases with severe HWI. The turning points where the capacity and the utility start to decrease with HWI can be evaluated from the derived formulas for them. Further, we also consider distributed implementations of a LIS system by splitting it into multiple small LIS-Units, where the impacts of HWI can be significantly suppressed due to a smaller surface-area of each unit.
Microgrids, as small-scale islandable power systems, are considered as viable promotors of renewable energy resources. In particular, microgrids can efficiently integrate solar photovoltaic (PV) as the deployment of this customer-deployed technology is growing in distribution grids. However, there is a limit on how much PV can be hosted by a microgrid. High penetration of PVs can potentially put the microgrid at operational risks including but not limited to over and under voltages, excessive line losses, overloading of transformers and feeders, and protection failure. To avoid such potential negative impacts, the concept of hosting capacity is introduced and used. The hosting capacity is defined as the total capacity of DERs that can be integrated into a given feeder/microgrid without exceeding operational restrictions and/or requiring system upgrades. Hosting capacity studies are primarily done based on steadystate analyses. However, in case of microgrids and when transitioning between grid-connected and islanded modes, dynamic operation becomes more restrictive than steady-state operation and thus is worthy of detailed investigation to provide a better understanding of the amount of DER that the microgrid can host. This paper examines this problem and provides extensive simulations on a practical test system to show its importance and merits.
We prove that, for $κ\le 4$, backward chordal SLE$_κ$ admits backward chordal SLE$_κ(-4,-4)$ decomposition for the capacity parametrization. This means that, for any bounded measurable subset $U\subset Q_4:={\mathbb R}_+\times{\mathbb R}_-$, if we integrate the laws of extended backward chordal SLE$_κ(-4,-4)$ with different pairs of force points $(x,y)$ against some suitable density function $G(x,y)$ restricted to $U$, then we get a measure, which is absolutely continuous with respect to the law of backward chordal SLE$_κ$, and the Radon-Nikodym derivative is a constant depending on $κ$ times the capacity time that the generated welding curve $t\mapsto (d_t,c_t)$ spends in $U$, where $d_t>0>c_t$ are the pair of points that are swallowed by the process at time $t$. For the forward SLE curve, a similar analysis has been done for SLE in the natural parametrization ([1] $κ\leq 4$, [10] $κ<8$), and for the capacity parametrization ([10] $κ< \infty$).
Yucheng Liu, Parastoo Sadeghi, Fatemeh Arbabjolfaei
et al.
The distributed index coding problem is studied, whereby multiple messages are stored at different servers to be broadcast to receivers with side information. First, the existing composite coding scheme is enhanced for the centralized (single-server) index coding problem, which is then merged with fractional partitioning of servers to yield a new coding scheme for distributed index coding. New outer bounds on the capacity region are also established. For 213 out of 218 non-isomorphic distributed index coding problems with four messages the achievable sum-rate of the proposed distributed composite coding scheme matches the outer bound, thus establishing the sum-capacity for these problems.
We consider an energy harvesting multiple access channel (MAC) where the transmitters are powered by an exogenous stochastic energy harvesting process and equipped with finite batteries. We characterize the capacity region of this channel as n-letter mutual information rate and develop inner and outer bounds that differ by a constant gap. An interesting conclusion that emerges from our results is that the sum-capacity approaches that of a standard AWGN MAC (with only an average constraint on the transmitted power), as the number of users in the MAC becomes large.
Heterogeneous wireless networks (HetNets) provide a means to increase network capacity by introducing small cells and adopting a layered architecture. HetNets allocate resources flexibly through time sharing and cell range expansion/contraction allowing a wide range of possible schedulers. In this paper we define the capacity of a HetNet down link in terms of the maximum number of downloads per second which can be achieved for a given offered traffic density. Given this definition we show that the capacity is determined via the solution to a continuous linear program (LP). If the solution is smaller than 1 then there is a scheduler such that the number of mobiles in the network has ergodic properties with finite mean waiting time. If the solution is greater than 1 then no such scheduler exists. The above results continue to hold if a more general class of schedulers is considered.
We consider an AWGN channel with a transmitter powered by an energy harvesting source. The node is equipped with a finite energy buffer. Such a system can be modelled as a channel with side information (about energy in the energy buffer) causally known at the transmitter. The receiver may or may not have the side information. We prove that Markov energy management policies are sufficient to achieve the capacity of the system and provide a single letter characterization for the capacity. The computation of the capacity is expensive. Therefore, we discuss an achievable scheme that is easy to compute. This achievable rate converges to the infinite buffer capacity as the buffer length increases.
Y. Ozan Basciftci, Onur Gungor, C. Emre Koksal
et al.
We consider a block fading wiretap channel, where a transmitter attempts to send messages securely to a receiver in the presence of a hybrid half-duplex adversary, which arbitrarily decides to either jam or eavesdrop the transmitter-to- receiver channel. We provide bounds to the secrecy capacity for various possibilities on receiver feedback and show special cases where the bounds are tight. We show that, without any feedback from the receiver, the secrecy capacity is zero if the transmitter-to-adversary channel stochastically dominates the effective transmitter-to-receiver channel. However, the secrecy capacity is non-zero even when the receiver is allowed to feed back only one bit at the end of each block. Our novel achievable strategy improves the rates proposed in the literature for the non-hybrid adversarial model. We also analyze the effect of multiple adversaries and delay constraints on the secrecy capacity. We show that our novel time sharing approach leads to positive secrecy rates even under strict delay constraints.
The sum capacity of a class of discrete memoryless interference channels is determined. This class of channels is defined analogous to the Gaussian Z-interference channel with weak interference; as a result, the sum capacity is achieved by letting the transceiver pair subject to the interference communicates at a rate such that its message can be decoded at the unintended receiver using single user detection. Moreover, this class of discrete memoryless interference channels is equivalent in capacity region to certain discrete degraded interference channels. This allows the construction of a capacity outer-bound using the capacity region of associated degraded broadcast channels. The same technique is then used to determine the sum capacity of the discrete memoryless interference channel with mixed interference. The above results allow one to determine sum capacities or capacity regions of several new discrete memoryless interference channels.