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We consider a class of one-dimensional nonlinear Schrödinger equations of the form $$ \begin{align*} & (i\partial_{t}+\Delta)u = [1+a]|u|^{2} u. \end{align*}$$For suitable localized functions $a$, such equations admit a small-data modified scattering theory, which incorporates the standard logarithmic phase correction. In this work, we prove that the small-data modified scattering behavior uniquely determines the inhomogeneity $a$.

 

Network emulation allows unmodified code execution on lightweight containers to enable accurate and scalable networked application testing. However, such testbeds cannot guarantee fidelity under high workloads, especially when many processes concurrently request resources (e.g., CPU, disk I/O, GPU, and network bandwidth) that are more than the underlying physical machine can offer. A virtual time system enables the emulated hosts to maintain their own notion of virtual time. A container can stop advancing its time when not running (e.g., in an idle or suspended state). The existing virtual time systems focus on precise time management for CPU-intensive applications but are not designed to handle other operations, such as disk I/O, network I/O, and GPU computation. In this paper, we develop a lightweight virtual time system that integrates precise I/O time for container-based network emulation. We model and analyze the temporal error during I/O operations and develop a barrier-based time compensation mechanism in the Linux kernel. We also design and implement Dynamic Load Monitor (DLM) to mitigate the temporal error during I/O resource contention. VT-IO enables accurate virtual time advancement with precise I/O time measurement and compensation. The experimental results demonstrate a significant improvement in temporal error with the introduction of DLM. The temporal error is reduced from 7.889 seconds to 0.074 seconds when utilizing the DLM in the virtual time system. Remarkably, this improvement is achieved with an overall overhead of only 1.36% of the total execution time. 

P4’s data-plane programmability allows for highly customizable and programmable packet processing, enabling rapid innovation in network applications, such as virtualization, security, load balancing, and traffic engineering. Researchers extensively use Mininet, a popular network emulator, integrated with BMv2, for fast and flexible prototyping of these P4-based applications, but due to its lower performance in terms of throughput and latency compared to a production-grade software switch like Open vSwitch, it is crucial to have an accurate and scalable emulation testbed. In this paper, we develop a lightweight virtual time system and integrate it into Mininet with BMv2 to enhance fidelity and scalability. By scaling the time of interactions between containers and the underlying physical machine by a time dilation factor (TDF), we can trade time with system resources, making the emulated P4 network appear to be faster from the viewpoint of the switch/host processes in the container. Our experimental results show that the testbed can accurately emulate much larger networks with high loads, scaled by a factor of TDF with extremely low system overhead. 

We present a unique virtual testbed that combines a data-plane programmable network emulator and a power distribution system simulator to evaluate smart grid security and resilience applications. The testbed employs a virtual time system for effective simulation synchronization and fidelity enhancement. We showcase the advantages of the simulation testbed through an anomaly detection case study. 

We present a new, to the best of our knowledge, experimental method for assessing sub-micron level subsurface damage (SSD) on optical glass. The method correlates surface characteristics such as the fracture toughness and Young’s modulus via nanoindentation with the penetration depth into the tested surfaces at different overall penetration depths, as revealed by magnetorheological finishing spotting techniques. Our results on ground surfaces suggest that low surface roughness does not necessarily imply the absence of SSD. We also compared SSD on surfaces processed by deterministic microgrinding and femtosecond (fs) laser polishing. The fs-laser polished surfaces revealed no detectable SSD, thus establishing the feasibility of fs-laser polishing for precision optical manufacturing.