Analytical Solution of Poisson's Equation with Application to VLSI Global Placement

Poisson's equation has been used in VLSI global placement for describing the potential field caused by a given charge density distribution. Unlike previous global placement methods that solve Poisson's equation numerically, in this paper, we provide an analytical solution of the equation to calculate the potential energy of an electrostatic system. The analytical solution is derived based on the separation of variables method and an exact density function to model the block distribution in the placement region, which is an infinite series and converges absolutely. Using the analytical solution, we give a fast computation scheme of Poisson's equation and develop an effective and efficient global placement algorithm called Pplace. Experimental results show that our Pplace achieves smaller placement wirelength than ePlace and NTUplace3. With the pervasive applications of Poisson's equation in scientific fields, in particular, our effective, efficient, and robust computation scheme for its analytical solution can provide substantial impacts on these fields

Escaping Local Optima in Global Placement

Placement is crucial in the physical design, as it greatly affects power, performance, and area metrics. Recent advancements in analytical methods, such as DREAMPlace, have demonstrated impressive performance in global placement. However, DREAMPlace has some limitations, e.g., may not guarantee legalizable placements under the same settings, leading to fragile and unpredictable results. This paper highlights the main issue as being stuck in local optima, and proposes a hybrid optimization framework to efficiently escape the local optima, by perturbing the placement result iteratively. The proposed framework achieves significant improvements compared to state-of-the-art methods on two popular benchmarks.Comment: Work-in-Progress (WIP) poster of DAC 202

Precision preparation of strings of trapped neutral atoms

We have recently demonstrated the creation of regular strings of neutral caesium atoms in a standing wave optical dipole trap using optical tweezers [Y. Miroshnychenko et al., Nature, in press (2006)]. The rearrangement is realized atom-by-atom, extracting an atom and re-inserting it at the desired position with sub-micrometer resolution. We describe our experimental setup and present detailed measurements as well as simple analytical models for the resolution of the extraction process, for the precision of the insertion, and for heating processes. We compare two different methods of insertion, one of which permits the placement of two atoms into one optical micropotential. The theoretical models largely explain our experimental results and allow us to identify the main limiting factors for the precision and efficiency of the manipulations. Strategies for future improvements are discussed.Comment: 25 pages, 18 figure

Analytical and experimental studies of an optimum multisegment phased liner noise suppression concept

Results are presented from detailed analytical studies made to define methods for obtaining improved multisegment lining performance by taking advantage of relative placement of each lining segment. Properly phased liner segments reflect and spatially redistribute the incident acoustic energy and thus provide additional attenuation. A mathematical model was developed for rectangular ducts with uniform mean flow. Segmented acoustic fields were represented by duct eigenfunction expansions, and mode-matching was used to ensure continuity of the total field. Parametric studies were performed to identify attenuation mechanisms and define preliminary liner configurations. An optimization procedure was used to determine optimum liner impedance values for a given total lining length, Mach number, and incident modal distribution. Optimal segmented liners are presented and it is shown that, provided the sound source is well-defined and flow environment is known, conventional infinite duct optimum attenuation rates can be improved. To confirm these results, an experimental program was conducted in a laboratory test facility. The measured data are presented in the form of analytical-experimental correlations. Excellent agreement between theory and experiment verifies and substantiates the analytical prediction techniques. The results indicate that phased liners may be of immediate benefit in the development of improved aircraft exhaust duct noise suppressors

Structural Assessment of Advanced Composite Tow-Steered Shells

The structural performance of two advanced composite tow-steered shells, manufactured using a fiber placement system, is assessed using both experimental and analytical methods. The fiber orientation angles vary continuously around the shell circumference from 10 degrees on the shell crown and keel, to 45 degrees on the shell sides. The two shells differ in that one shell has the full 24-tow course applied during each pass of the fiber placement system, while the second shell uses the fiber placement system s tow drop/add capability to achieve a more uniform shell wall thickness. The shells are tested in axial compression, and estimates of their prebuckling axial stiffnesses and bifurcation buckling loads are predicted using linear finite element analyses. These preliminary predictions compare well with the test results, with an average agreement of approximately 10 percent

The dynamics and control of large flexible space structures, 3. Part A: Shape and orientation control of a platform in orbit using point actuators

The dynamics, attitude, and shape control of a large thin flexible square platform in orbit are studied. Attitude and shape control are assumed to result from actuators placed perpendicular to the main surface and one edge and their effect on the rigid body and elastic modes is modelled to first order. The equations of motion are linearized about three different nominal orientations: (1) the platform following the local vertical with its major surface perpendicular to the orbital plane; (2) the platform following the local horizontal with its major surface normal to the local vertical; and (3) the platform following the local vertical with its major surface perpendicular to the orbit normal. The stability of the uncontrolled system is investigated analytically. Once controllability is established for a set of actuator locations, control law development is based on decoupling, pole placement, and linear optimal control theory. Frequencies and elastic modal shape functions are obtained using a finite element computer algorithm, two different approximate analytical methods, and the results of the three methods compared

Factors associated to clinical learning in nursing students in primary health care: An analytical cross-sectional study

Objective: to identify the students’ perception about the quality of clinical placements and asses the influence of the different tutoring processes in clinical learning. Methods: analytical crosssectional study on second and third year nursing students (n=122) about clinical learning in primary health care. The Clinical Placement Evaluation Tool and a synthetic index of attitudes and skills were computed to give scores to the clinical learning (scale 0-10). Univariate, bivariate and multivariate (multiple linear regression) analyses were performed. Results: the response rate was 91.8%. The most commonly identified tutoring process was “preceptor-professor” (45.2%). The clinical placement was assessed as “optimal” by 55.1%, relationship with team-preceptor was considered good by 80.4% of the cases and the average grade for clinical learning was 7.89. The multiple linear regression model with more explanatory capacity included the variables “Academic year” (beta coefficient = 1.042 for third-year students), “Primary Health Care Area (PHC)” (beta coefficient = 0.308 for Area B) and “Clinical placement perception” (beta coefficient = - 0.204 for a suboptimal perception). Conclusions: timeframe within the academic program, location and clinical placement perception were associated with students’ clinical learning. Students’ perceptions of setting quality were positive and a good team-preceptor relationship is a matter of relevance