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The authors hope to correct any premature conclusions about the role of the pre-Katrina Orleans Levee Board (OLB) in the failure of the outfall drainage canals in New Orleans during the 2005 hurricane – conclusions that appear to have been based on inaccurate information and/or assumptions. With regard to the 17th Street and London Avenue Canals, the authors have not uncovered any information that would suggest that the OLB behaved irresponsibly in its duties. What is evident from the project record is that the Army Corps of Engineers recommended raising the canal floodwalls for the 17th Street Canal, but recommended gated structures at the mouths of the Orleans and London Avenue Canals because the latter plan was less expensive. The OLB convinced Congress to pass legislation that required the Corps to raise the floodwalls for all three canals. Furthermore, the Corps, in a separate attempt to limit project costs, initiated a sheet pile load test (E-99 Study), but misinterpreted the results and wrongly concluded that sheet piles needed to be driven to depths of only 17 feet (1 foot = 0.3048 meters) instead of between 31 and 46 feet. That decision saved approximately US$100 million, but significantly reduced overall engineering reliability. ## Introduction On 29 August 2005, a horrified world watched an American city drown in what seemed to be a natural disaster, but is now recognized as primarily a civil engineering disaster (Christian, 2010). Levees and floodwalls in New Orleans had collapsed, some at water levels far below their design capacity. How could the US Army Corps of Engineers – the agency responsible for the performance of the hurricane surge protection – allow this to happen? An engaged world wanted to know, and quickly. In this context of haste and confusion, top officials with the Corps, and others, created a template, which they relayed consistently to the media and to stakeholder groups. While these officials did concede that the Corps was ultimately responsible for the system performance, they also stated that local New Orleans officials played a contributing role in the failure of levees and floodwalls along the city's three largest drainage canals. The storyline was that the Corps had originally proposed gated structures at the mouths of the 17th Street and London Avenue Canals (and the Orleans Avenue Canal) to prevent storm surge from entering the city, but the Corps had been blocked by the Orleans Levee Board (OLB), which forced the Corps to initiate the ‘next fallback plan’ (Schwartz, 2006). This presumption of wrongdoing by the OLB was repeated by high-level Corps officials for several years thereafter. For example, a major general with the Corps, speaking before an environmental coalition in December 2007, appeared to characterize the local citizenry as obstructionists to the Corps’ proposed plans in the past when he stated, ‘we proposed gates (for Lake Pontchartrain), and local citizens said no, fearing flooding (from) rainfall’ (Grissett, 2007). Ultimately, in this environment, an erroneous conclusion was drawn by one of the authors, namely that the Corps had been forced to build what it considered an inappropriate and inferior system of flood protection (Rogers, 2008). This conclusion was also voiced in Chapter 15 – Summary and Findings of the Independent Levee Investigation Team (ILIT) report funded by the National Science Foundation, and co-chaired by Drs Raymond Seed, Robert Bea and J. David Rogers (2006): ‘ … The USACE had tried for many years to obtain authorization to install floodgates at the north ends of the three drainage canals that could be closed to prevent storm surges from raising the water levels within the canals. That would have been the superior technical solution. Dysfunctional interaction between the local Levee Board (who were responsible for levees and floodwalls, etc.) and the local Water and Sewer Board (who were responsible for pumping water from the city via the drainage canals) prevented the installation of these gates, however, and as a result many miles of the sides of these canals had instead to be lined with levees and floodwalls …’ Years later, and after many subsequent, and often better-financed, studies have been completed, it has been found that these conclusions may have been both historically and logically flawed. But, first a little background. ## Short history of the Orleans Levee District The pre-Katrina Orleans Levee District (OLD), governed by the OLB, owned considerable assets, mainly real estate, a peculiarity that stems from its history. In the early 20th century, the OLD reclaimed a portion of Lake Pontchartrain (a 24-mile-wide lake north of New Orleans; 1 mile = 1.60934 kilometers), developed the land, and sold it to raise money to build and improve levees. The OLD also owned a marina and a small commercial airport on a man-made peninsula created from dredged material in the early 1930s. In the Flood Control Act of 1965 – legislation enacted in response to losses exceeding US$1 billion1 (including multiple levee failures) during Hurricane Betsy – Congress directed the Corps, from then forward, to be responsible for design and construction of the hurricane flood protection system enveloping New Orleans. The Corps was ordered to work in consultation with the OLD, which became the local sponsor for the ‘Lake Pontchartrain and Vicinity Hurricane Protection Project.’ When designed, the project was expected to take about 13 years to complete, but repeated reallocation and rescission proposals to shave the federal budget by the federal government in the previous two decades resulted in delaying the estimated date of project completion until 2015. However, the floodwalls along the three outfall drainage canals, the subject of this paper, were essentially complete by 2005.

Owing to the 1965 legislation, the OLD's duties regarding hurricane surge protection were now limited to collecting the 30% cost share for project design and construction, and to maintaining and operating completed flood protection structures (Mittal, 2005). However, the OLD still retained extensive assets, which by state law needed to be managed. By the early 1990s, the OLB was composed of eight paid commissioners appointed by the Governor. Four of the board members served on the Engineering Committee, which operated with advice from the Chief Staff Engineer, the Assistant Chief Staff Engineer and two staffers who were civil engineers or had engineering experience. In addition, as many as 30 civil engineering experts and consultants offered their advice to the Committee. Some of these advisors were employed by the Corps.

The New Orleans District is the largest District of the Corps of Engineers in the nation; commensurate with the number of projects, level of funding and national interest in maintaining the Mississippi floodway for commercial navigation as well as flood control (the Mississippi River drains 41% of the lower 48 states). The district employs about four times the number of personnel as compared to other regional districts.

Similarly, the local levee district was also one of the largest in the nation in terms of assets and number of personnel. Owing to its extensive land holdings, members of the OLB served on committees to oversee the airport, the marina and other real estate. Committee meetings were held monthly – generally, two weeks before each board meeting.

A post-Katrina news article observed that the OLB enjoyed ‘relatively cushy finances, pumped millions into road projects, bridges, a marina and ill-fated studies of everything from a movie studio to a fiber-optic network to a man-made island near Lake Pontchartrain's south shore’ (Donze, 2006). This would seem to describe how far-reaching the OLB was in its commercial interests, and it is clear that members of the OLB attended meetings to discuss issues not specifically related to engineering and flood protection. The airport and disputed land claims over oil producing properties consumed much of the OLB's focus in working with the state legislature, as well as litigation.

Congress's decision in 1965 to place responsibility for flood protection design and construction with the Corps affected the role of the OLB and, gradually, it became apparent that perhaps a different form of levee board governance might be more appropriate for a major marine terminal like New Orleans. Nevertheless, the issue of whether the members of the OLB Engineering Committee acted incompetently or negligently in its decisions specifically regarding the 17th Street, Orleans and London Avenue Canals deserves examination in the light of subsequently emerging data.

In 1965, Hurricane Betsy struck Louisiana and triggered levee breaches, which flooded parts of the Lower Ninth Ward neighborhood of New Orleans. The hurricane's storm surge along the south-westerly shores of Lake Pontchartrain also overtopped the earthen levees of all three outfall drainage canals, flooding adjacent neighborhoods and causing substantial property damage amounting to US$1.42 billion. In response, the Corps re-evaluated their design assumptions for a Category 3 storm surge along the Gulf Coast, Lake Borgne and Lake Pontchartrain, adopted in October 1967. Between 1970 and 1975, the Corps developed a plan for massive sea gates for the region east of New Orleans that would prevent storm surge from flowing through Lake Borgne and into Lake Pontchartrain through two narrow channels at the Rigolets and Chef Menteur passes. The proposed gates had embankment footprints up to 2,000-feet wide (1 foot = 0.3048 meters). Referred to as the Barrier Plan, it included a series of levees along Lake Pontchartrain and the Gulf Intracoastal Waterway (GIWW), a navigable inland waterway. The gates would have allowed water to flow back and forth between the lakes, but would have been closed in advance of a hurricane (Kysar & McGarity, 2006). A small group, led by Luke Fontana, filed a lawsuit against the Barrier Plan in 1976 over the Corps’ Environmental Impact Study (EIS). In Save our Wetlandsv Rush, the plaintiffs claimed that the Corps’ EIS did not meet the requirements of Section 102 of the National Environmental Policy Act (NEPA), a federal law enacted in 1969 (Kysar & McGarity, 2006). The court agreed with Fontana noting, among other things, that the EIS was based on obsolete data and that the Corps’ biological analysis ‘relied entirely on a single telephone conversation with a marine biologist’ (Verchick, 2010). To put this in perspective, the Corps’ final EIS, representing the entire review of a multi-year, multimillion-dollar project, consisted of only four typewritten pages. As noted by Robert Verchick, author of Facing Catastrophe (2010): ‘An EIS is a comprehensive document. Today, EISs are hundreds even thousands of pages long, but even in the 1970s, when NEPA was still being defined by the courts, federal agencies knew that courts wanted a serious effort.’ Judge Charles Schwartz issued an injunction preventing further progress on the barrier option until the Corps revised its EIS. He also wrote, however, that upon proper compliance with NEPA, ‘the injunction shall be dissolved and any hurricane plan thus properly presented will be allowed to proceed’ (Kysar & McGarity, 2006). In other words, the Judge invited the Corps to return with a more comprehensive EIS. Ultimately, however, the Corps did not return and, in 1980, concluded that an alternative option of higher levees providing hurricane protection was less costly, less damaging to the environment and more acceptable to local interests (Woolley & Shabman, 2008). Immediately after Katrina, the Corps’ abandonment of the Barrier Plan became the subject of journalists who alleged that environmentalists had blocked the Corps’ original plans for barrier structures and forced the agency to choose an alternate, and inferior, design that could not protect the city. The Barrier Plan was ‘stopped in its tracks,’ claimed a Los Angeles Times front-page news story (Vartabedian, 2005). Two law professors, Thomas McGarity and Douglas Kysar, in their article that highlighted the ‘hazards of hindsight analysis,’ put the process under the microscope. They found that subsequent to Judge Schwartz's injunction, intense public opposition arose based on concerns for the environment and fears of increased flooding for people and property outside the barrier walls. Simultaneously, costs were ballooning due to new design requirements and general delay. As observed by Verchick (2010): ‘One can say that environmental concerns contributed to the political opposition and the litigation provided the information and the time for activists to organize. But at the same time, one must acknowledge that nothing prevented the Corps from acting more quickly to perform a sufficient environmental review and get the project approved. Had it believed that superior benefits of the option justified increased costs, it could surely have moved forward.’ We have not found any documented evidence in the project record or any other indication that reveals that the Corps believed its switch from the Barrier Plan to the High Level Plan would increase the risk of flooding to New Orleans. With regard to concerns of increased risk, the authors of the Decision-Making Chronology note that the project record ‘shows that the switch to the High Level Plan involved those limited project changes that were necessary to move the project forward’ (Woolley & Shabman, 2008). By 1981, the Corps had begun working out the engineering details for implementing the High Level Plan to protect the city from storm surges that could enter the outfall drainage canals. This was necessary, because the new post-Hurricane Betsy design water levels exceeded the crest heights of most of the existing earthen levees along the outfall drainage canals and also along the Inner Harbor Navigation Canal (IHNC). The Corps initially considered five alternatives to address this threat, but eventually narrowed their alternatives to the two most cost-effective alternatives, which were (1) raising the height of the canal temporary floodwalls (‘parallel’ protection) or (2) installing gates at the canal mouths (‘frontage’ protection). The Corps presented both the Parallel and Frontage Protection plans – plans that it apparently considered equally effective – to the local sponsor before making its final recommendations. Meeting minutes from January 1988 to December 1991, critical years in the decision-making process, reveal that there were many additional meetings, entitled ‘Special Meetings,’ devoted solely to discussions of flood protection. In these meetings, the Engineering Committee asked the Corps many detailed questions about ‘storm proofing’ the outfall drainage canals. The minutes also reveal that the OLB and the Sewerage and Water Board of New Orleans (S&WB) shared concerns over the Corps’ consideration of a prototype gate plan employing self-actuating butterfly check valves, a plan that included no auxiliary pump stations like those constructed after Katrina. Both agencies viewed the gates-only plan as being incompatible with their interior drainage responsibilities and were concerned that when the gates were shut during a hurricane, the pumping stations would not be able to pump rainwater out of the city (Woolley & Shabman, 2008). The OLB and the S&WB also questioned whether the untested prototype gates would work properly during storm events. The complex gate system would require interior drainage pumping to cease at times when the city was likely to be experiencing heavy rainfall. The OLB and the S&WB also shared concerns that the butterfly gates might limit their ability to increase drainage discharge capacity in the future. Furthermore, the gates had already failed in a much publicized model test attended by OLB members at the Corps’ Waterways Experiment Station (WES) in Vicksburg (Van Heerden et al., 2006). Post-Katrina investigations correctly observed that the adoption of parallel protection for the outfall canals would significantly increase the number of miles of floodwalls and other structures exposed to storm surges, and would increase the probability that a storm surge could find a weak spot in the project perimeter. However, in the 1990s, this risk did not appear to have been recognized and/or communicated. On this issue, the Interagency Performance Evaluation Task Force (IPET), which was convened and managed by the Army Corps of Engineers after Katrina, observed: ‘ … A series of incremental decisions extending from the original ‘barrier’ plan to the ‘parallel protection’ structures ultimately constructed, systematically increased the inherent risk in the system without recognition or acknowledgment …’ This observation is corroborated by federally appointed water experts Woolley & Shabman (2008), authors of the Decision-Making Chronology for the Lake Pontchartrain & Vicinity Hurricane Protection Project. Regarding the recommendation of the parallel plan, they wrote (Woolley & Shabman, 2008): ‘There is no evidence in the project record indicating that project engineers believed that the decisions made would threaten engineering reliability.’ From today's vantage point, it appears that the local sponsors were led to believe that the ‘higher walls’ plan was technically equivalent to the ‘gates-no-pumps’ plan, but was just more expensive. As observed by the authors of Louisiana Department of Transportation and Development (DOTD) sponsored report Team Louisiana, led by coastal researcher Van Heerden et al. (2006): ‘They believed they had a right to pursue a more costly alternative if it would accomplish other purposes in addition to the hurricane protection objective. They believed the USACE, in recommending the less costly fronting protection plan, was simply establishing a limit to the portion that the federal government would be willing to pay.’ Apparently in the belief that both plans were equally effective, cost became the pre-eminent factor in the Corps’ consideration of frontage versus parallel protection. The Corps considered it a congressional mandate (and their standard of practice) to implement the least expensive alternative, assuming all of the choices to be adequately engineered. Eventually, the Corps did recommend parallel protection for the 17th Street Canal. For reasons unique to this canal, there was no significant stated difference in the cost between the two approaches due to newly authorized sheet pile construction guidelines (to be discussed later) and other factors (Lansden, 1990). Another reason noted in the project record was that the OLB and the S&WB preferred it. It is interesting to note that the 17th Street Canal was the largest and most important drainage canal in the city of New Orleans. Operating with Pumping Station No. 6 – which at that time was the most powerful pumping station in the world – the 17th Street Canal was capable of conveying 9,200 cubic feet per second (cfs) of water, more than the Orleans Avenue and London Avenue Canals combined. (The Orleans Avenue Canal, at maximum capacity, could pump 2,200 cfs and the London Avenue Canal, at maximum capacity, could pump 5,200 cfs.) However, for the much smaller capacity London and Orleans Avenue Canals, the Corps stood by its recommendation for the gates-no-pumps plan because it was significantly less expensive. The parallel protection plan was estimated in the 1980s to cost three times more than the gates plan for the London Avenue Canal (Lansden, 1990) and to cost five times more than the gates plan for the Orleans Avenue Canal (Carter, 2005). The information gleaned from the minutes of the Engineering Committee meetings – which had previously been unavailable to the authors of the ILIT report – shed considerable light on the decision-making processes that led to the adoption of the parallel plan for the 17th Street Canal. ## The OLB goes to Washington In 1988, the OLB began an aggressive push to convince the Corps to recommend parallel plans (flood walls) for all three canals. Then-OLB President, Steven Medo, hired lobbyist Bruce Feingerts to lead a legislative effort to secure the most federal aid participation possible to fund the parallel plan2. Regarding this effort, the authors of the Decision-Making Chronology, Woolley & Shabman (2008), would observe exactly 20 years later: ‘ … from the local perspective, the parallel protection plan was the best way to address both hurricane protection and interior drainage objectives and secure 70% federal funding toward those ends …’ Working with the support of the S&WB and neighborhood groups, Feingerts lobbied the Louisiana Congressional Delegation for the parallel plan for the Orleans and London Avenue Canals. The OLB made no secret of its preference for the parallel plan for all three outfall canals, and discussed the issue frequently in the various meetings convened between 1988 and 1991. Members of the Corps were nearly always present at these meetings. Thus, the Corps was aware that the OLB preferred the parallel plan for all three canals, and that the OLB was compensating Feingerts to lobby for congressional support of such a scheme in Washington DC. Feingerts detailed the local sponsor's concerns in a Briefing Paper in September of 1990. The paper addressed the OLB's concerns that ‘in the event of overtopping of the levees of these canals, many businesses and an estimated 56,000 residents of Orleans Parish would be flooded’ (Board of Commissioners of the Orleans Levee District, 1990). The OLB wanted the more expensive ‘high level plan’ over the less expensive ‘gates plan,’ because they believed it was the superior plan. Significant progress was made when Feingerts suggested to members of the Louisiana Delegation that, in conferencing, they insert a ruling or ‘language’ into an engrossed amendment of the approved version of the 1990 Water Resources Development Act (WRDA). The language redefined the Orleans and London Avenue Canals as part of the Hurricane Protection Project, which were, therefore, now a federal responsibility. The 1990 WRDA was signed by President George Bush and passed into law. The OLB had succeeded in getting the authorization for a project that they believed would keep people safe, but which would also reduce how much those same people had to contribute to the cost. Authorization for the funding and cost share soon followed. On 30 May 1991, a local affiliate of NBC TV televised a news story with anchorwoman Leslie Hill of WDSU featuring triumphant OLB members and proud legislators. ## A red herring Fifteen years later, a Los Angeles Times article would lay blame for the outfall canal floodwall failures heavily on the OLB in light of the 1990 WRDA (Braun & Vartabedian, 2005). The reporters for the Christmas Day 2005 story described ‘a deft behind-the-scenes maneuver’ by the OLB that forced the Corps to accept the higher floodwalls. The article stated that ‘Corps engineers were openly peeved in 1990 when they learned about the Orleans board's decision.’ Nonetheless, the Corps had not been caught by surprise. As previously established in this paper, the Corps had (1) already recommended the parallel plan for the 17th Street Canal, (2) was aware that the OLB preferred the same approach for the other two drainage canals, and (3) was aware that the OLB was compensating a lawyer to go to Washington DC to lobby for the parallel plan alternative. It is clear that there was some eleventh-hour maneuvering, however, this is pretty typical of how laws are passed in Washington DC. US Senator Bennett Johnston addressed this particular bit of ‘midnight magic’ in the OLB meeting minutes on 30 May 1991 (Lansden, 1991): ‘The more important things that are done, the things that touch people's lives and pocketbooks, and the things that really measure the effectiveness of what Congress does as far as people in the State of Louisiana, are done quietly, and are done by virtue of knowing what you are doing or the position of power that you are in.’ As previously noted, in their statements to the media following Katrina, Corps spokespersons, in the context of haste and confusion, laid partial responsibility for the collapse of the outfall canal floodwalls upon the OLB. However, the authors of the IPET report gave only cursory discussion to the years-long decision-making process that eventually settled upon the parallel protection plan. Its mandate was focused primarily on unraveling physical failure mechanisms rather than on the history of the decision-making processes responsible for selecting various systems of flood protection. This is what the IPET report stated regarding the decision-making process for flood protection improvements for the three outfall canals in its 7,000-page report (IPET, 2006): ‘The New Orleans District commenced examining two alternative plans for providing ‘high level’ SPH [surge protection height] protection for the outfall canals – frontage protection in the form of gated structures at the canal entrances from the lake, and parallel protection in the form of floodwalls and flood proofing of bridges. The plans and designs for the outfall canals called for gated control structures at or near the canal entrances to the lake, but the local sponsor, the OLB, indicated its preference for parallel protection. Congress settled the dispute through the 1992 Energy and Water Development Appropriations Act, which mandated construction of the parallel protection plan.’ ## Time to get to work Indeed, on page 4 of the 1992 WRDA, Congress defined the cost for the two outfall canals to be shared, namely, that the federal cost participation shall be 70% and the local cost participation 30%. The Corps now had a direct order from Congress to raise the heights of the London and Orleans Avenue Canals, the same plan that was already well on its way to being implemented along the 17th Street Canal. There were several options available to the Corps to accomplish that: taller earthen levees, T-walls, and I-walls. Earthen levees require a wide base, generally six times the height of the embankment. This alternative would not fit the existing rights of way along the edges of the outfall drainage canals, except near their mouths. Inverted T-walls are conventional reinforced concrete retaining walls, which are supported on piles driven into the crown of the levee. I-walls are simple cantilever walls constructed of steel sheet piles driven into the crown. I-walls cost about one-third as much as the pile-supported T-walls. The records show that T-walls were built into selected sections in short portions (e.g. next to bridges and gates) along the canals, but I-walls were used extensively everywhere else to reduce costs (Van Heerden et al., 2006). Faced with ever-increasing costs, the Corps of Engineers Mississippi Valley Division headquarters in Vicksburg initiated a large-scale Sheet Pile Test (the E-99 Study) in the Atchafalaya Basin, a region with soft clayey and organic soils, similar to those in New Orleans. In 1985, the Corps misinterpreted the results of the E-99 Study and concluded that (Woolley & Shabman, 2008): ‘ … when foundation soils were poor, sheet pile penetration depth beyond a certain point would not significantly increase I-wall stability under the type of short-term loading conditions believed to characterize hurricane events …’ In other words, the Corps determined that it needed to drive sheet piles down to depths of only 17 feet instead of between 31 and 46 feet, introducing a shortcoming revealed during Hurricane Katrina. At that time, the Corps believed that ‘sheet pile penetration beyond a certain depth would not improve wall stability and therefore was a wasteful expenditure.’ The misinterpretation occurred apparently because the Corps had draped a tarpaulin over the gap that formed between the bases of the deflecting sheet piles and the soil in which they were embedded, so they did not see the gap. The tarpaulin was there for safety and to stop water that would seep through the interlocks (Bea, 2008). Failure to include the gap in interpretation of the test results introduced unconservatism in the final designs based on these tests. It allowed the use of shorter sheet piles, and reduced overall flood protection reliability. Ultimately, on 23 December 1987, the Division Headquarters issued new criteria guidance to the New Orleans District on sheet-piling design based on the E-99 tests (IPET, 2006). This switch by the Corps to significantly shorter sheet piles saved approximately US$100,000,000. However, these cost savings would come at the expense of engineering reliability as the floodwalls were eventually constructed between 1993 and 1999 (IPET, 2006).

The authors of the Decision-Making Chronology state repeatedly that there is nothing in the available project records to suggest that the Corps was aware that its decision would jeopardize the integrity of the flood protection structures (Woolley & Shabman, 2008).

## Hurricane Katrina

On 29August 2005, the wind and storm surge associated with Hurricane Katrina arrived. At least 50 breaches occurred in the Lake Pontchartrain and Vicinity Protection Project within a few hours. The authors of the IPET (2006) observed:

‘At the 17th Street Canal, failure began with apparent displacement of a wall panel at about 0630 hr and ended with a full breach by 0900 hr. At about 0630 hr, the water level was estimated to have been 7 to 8 feet, and possibly 1 to 2 feet higher at the time of the catastrophic breach created by displacement of a levee section. No overtopping had occurred and the design water elevations had not been reached at the time of levee displacement.’

The water level at the time of failure was about five feet lower than the top of the I-wall. As the storm surge water poured through this initial breach, carrying with it sections of the concrete floodwall and earthen levee, it weakened adjacent concrete floodwall sections and the breach quickly expanded into a 450-foot wide gap. The flooding directly and indirectly killed hundreds in the adjacent neighborhood of Lakeview and caused multiple billions of dollars in property damage.

Meanwhile, the similarly catastrophic east failures and breaches on the London Avenue Canal were also initiating. As with the 17th Street Canal, water elevations several feet below the design levels caused a crack to form between the sheet piles and the foundation soils in which they were embedded on the waterside of the floodwall, and this crack or ‘gap’ allowed high pressures to be introduced directly into the foundation materials of the levee.

The London Avenue Canal was breached in two locations on either side, and both failures occurred at surge levels more than four feet below design specifications. The east breach occurred around 6 to 7 a.m. and sent tons of sand and water into the neighborhood of Mirabeau. The west breach occurred around 7 or 8 a.m. and flooded the adjacent neighborhood of Lake Vista (Anderson et al., 2007).

For the 17th Street and London Avenue Canals, the new I-walls embedded in the levees deflected when water pressure was placed against them, creating open gaps behind the sheet piles, which allowed infilling water to exert hydrostatic pressures against the full embedded length of the sheet piles within minutes of their being loaded (Anderson et al., 2007).

The Orleans Avenue Canal had similar I-walls, but these did not breach due, in part, to the presence of an unintended 100-foot-long ‘spillway,’ a section of legacy wall that was significantly lower than the adjacent newer floodwalls adjacent to Pump Station No. 7 at the south end of this canal (IPET, 2006). The unintended ‘spillway’ was located in an area where eventual floodwall (I-wall) construction would require coordinated efforts between the OLB, the S&WB, the DOTD and, possibly, the Federal Highway Administration. This had not been resolved at the time of Hurricane Katrina's arrival, so floodwaters simply poured through the open gap, which served to partially relieve water levels within the canal.

This inadvertent ‘spillway’ (gap in the I-wall) was located under a viaduct carrying Interstate-610 where the top of the existing earthen levee crest lay approximately 5–6 feet below the tops of the adjacent concrete floodwalls. Completion of the floodwall would have likely caused the brick walls of the old pump station to fail unless they had been significantly reinforced.

The presence of this spillway (gap) was a sore spot on the record of the OLB and the S&WB. Had the canal walls of the 17th Street Canal and the London Avenue Canal not been breached, this spillway could have allowed overtopping for several hours resulting in significant flooding, although not catastrophic flooding. In the end, of course, the failures of the 17th Street and London Avenue Canals made this issue moot.

With regard to the severity of Katrina's storm surge in Lake Pontchartrain, wave heights were typically similar to those assumed for the design of the structures (IPET, 2006). The Corps had designed for surge heights of about 12 feet, and the estimate of Katrina's storm surge along the drainage canal frontage was about 11 feet. Therefore, the three catastrophic breaches that occurred within the 17th Street and London Avenue drainage outfall canals represented failures of the system to meet design objectives (IPET, 2006).

The breach of the 17th Street Canal and the two breaches of the London Avenue Canal caused at least US$27 billion combined in direct residential, commercial, and public property damage in the city's main basin (Anderson et al., 2007). ## Monday morning quarterbacking After the 2005 hurricane, critics of the pre-Katrina OLB contend that the agency should have questioned the ability of the Corps to competently construct the parallel plan for the three outfall canals. However, one must keep in mind that the Corps was the federal agency that had previously built thousands of miles of levees along the Ohio, Missouri and Mississippi Rivers capable of withstanding surge heights of up to 20 feet for 30 days or more. Why would the OLB believe the Corps could not build levees along a few miles of drainage canals capable of withstanding surge heights of about nine feet for a period of a few hours? As observed by Van Heerden et al. (2006): ‘ … These were modern structures designed to protect a high-value, heavily populated urban area by what was thought to be the world's premier civil engineering organization …’ According to the authors of the Team Louisiana report, some Corps spokespersons appear to have used an ‘I told you so’ logic to defend the federal agency for the catastrophic failure of the outfall drainage canals (Van Heerden et al., 2006). Nonetheless, at the heart of the argument of why the local agencies should share in the blame was the assumption that the gates-no-pumps plan would have kept the city safe and dry. There were 50 breaches in the flood protection project on 29 August 2005 (US Army Corps of Engineers, 2012). Any attempt to pass the buck to the OLB regarding the failed outfall drainage canal walls is founded in an unexamined presupposition that the Corps’ preferred gates-no-pumps plan would have protected the city from flooding. It is instructive to note that after Katrina, the Corps installed floodgates with enormous auxiliary pump stations (Eisler, 2009) funded as an emergency measure of Congress at a cost to the American taxpayers of hundreds of millions of dollars (Garzino, 2009). Furthermore, all repairs of breached I-walls were repaired with the more conservative T-walls. But no matter what plan was selected in the early 1990s, as professional engineers, the Corps had a duty to design and construct its Congressionally-mandated flood protection in a professional and competent manner. As noted by Van Heerden et al. (2006): ‘ … the principles of foundation design, which rests primarily on the interpretation of subsurface information derived from suitably detailed boring programs, and from long experience with the response of soils and structures to the forces developed under critical conditions were well understood by practicing civil engineers of the late 1980s and early 1990s …’ The authors of the Team Louisiana report also suggest that perhaps the Corps may have felt absolved, to some degree, from some responsibility to assure the effectiveness of the hurricane protection for the three drainage canals when the local sponsors so vigorously pursued their parallel protection plan (Van Heerden et al., 2006). As was the Corps’ congressional mandate, it would appear that the Corps was vigorously searching for ways to reduce costs for the more expensive parallel plans. The authors of this paper find it particularly ironic that the Corps initiated a series of sheet pile wall load tests, but misinterpreted the results, drawing conclusions that severely limited the ability of the 17th Street and London Avenue drainage canal walls to perform as assumed. The field tests were precisely what was needed to validate the design assumptions, but these were not subjected to peer review by anyone outside of the Corps because the services of WES's permanent geotechnical consulting board had been terminated in 1978 as another federal cost-saving measure (Fatherree, 2006). The authors of the IPET report observed that the E-99 Study in 1985 – and the subsequent failure of the outfall canals in 2005 – points out a dilemma. They wrote: ‘While new pieces of knowledge were available over time that were relevant to the ultimate performance of the I-walls on the outfall canals, the pieces were not put together to solve the puzzle of the failure mechanism that occurred. The Corps’ own testing of sheet-pile stability (E-99) in the mid-1980s was not directed at the behavior of I-walls, but with hindsight, some of the behavior observed was indicative of the deflection of a structure that designers essentially assume to be rigid’ (IPET, 2006). These same authors also wrote about a distinct loss in energy and resources expended in the search for new knowledge in design criteria, particularly in the domain of hurricane and flood protection, specifically in the geotechnical fields that are at the heart of the levee and floodwall performance issues in Katrina. For a solution, they suggest a ‘push’ and a ‘pull’ (IPET, 2006). ‘Awareness and capability are gained best when there is both technology push (research creating new knowledge and capabilities) and requirements pull (designers/constructors seeking and pulling information from the research and professional communities). The solution is not more research or more outreach alone, it is the ability of the design/construction and research communities to work together in an environment enabling collaboration and experimentation with new knowledge and approaches to old and new problems.’ After the city of New Orleans was dewatered and its residents began their journey toward rebuilding, there were two takeaways firmly cemented into the minds of Americans, pinning blame on local residents for their misfortune. The most misleading ‘accepted truth,’ which has been discussed here in depth, was that the Corps had been thwarted by a politically connected local levee board. There was also a second takeaway sound bite firmly planted in the minds of many Americans. After Katrina, news stories reported that ‘annual levee inspections in Orleans Parish tended to be quick drive-by affairs ending with lunch for 40–60 people costing the state as much as$900’ (Marshall, 2005). This is true, but the reports went on to suggest that the inspections might have contributed to the catastrophic flooding and that the OLD might be partly responsible (Russell, 2005). Neither suggestion was ultimately borne out by the facts.

The authors suggest that there may be confusion relating to the word ‘inspection.’ Pre-Katrina, the Corps was required to administer annual levee inspections of maintenance of federally built flood protection in Orleans Parish. Termed ‘Inspections of Completed Works,’ these were designed to ensure that the OLD was complying with its federally mandated levee maintenance (Engineer Regulations, 1996). The responsibility of the OLD was mainly cutting the grass on levee embankments, removing unwanted vegetation and debris, and visually judging the surface manifestations of under seepage. The OLD also performed informal year-round ‘inspections’ including, but not limited to, inspecting for ruts, depressions, and erosion of their earthen levees.

Legal responsibility for the annual Inspection of Completed Works belongs to the Corps. For clarity, the Corps' inspections should be thought of as independent, once-per-year ‘quality audits’ of the OLD's year-round maintenance activities. Furthermore, as observed in the Decision-Making Chronology (Woolley & Shabman, 2008):

‘ … The annual inspections of levees and floodwalls involve visual verifications of local sponsors’ compliance with required maintenance; they do not, however, include the types of engineering assessments that would be needed to verify structure stability and performance …’

We have found no documented evidence that improper maintenance on the part of the OLD played a role in the failure of the 17th Street and London Avenue Canals. The authors of the Decision-Making Chronology did not include any detailed discussion of the inspections in the body of their paper. Instead, they were relegated to, and placed into, text boxes, indicating their minimal significance.

## Post-Katrina legislation

Before Katrina, five different levee districts operated as separate local sponsors for the federally built flood protection in the Greater New Orleans area. Soon after the levees broke in 2005, the presumption – made in haste in a complex environment – was that the commissioners of the OLB were not paying enough attention to flood protection and were therefore partly responsible for the flood disaster. So Congress, with relative speed, ordered the creation of a single state agency to be the local sponsor and, in response, the State of Louisiana created the Coastal Protection and Restoration Authority, in 2006.

Concurrently, there was a separate local effort to pass legislation to create a new board that would replace the five separate levee boards. The legislation was intended to (1) remove distractions, (2) replace parochial flood control with regional flood control, and (3) require commissioners to have professional expertise including hydrology, construction engineering and civil engineering (Donze, 2006).

While a direct causal link between the actions of the pre-Katrina OLB and the breaching of the outfall drainage canals has not been established, few would disagree that a new form of levee board governance might be necessary and beneficial for a major marine terminal like Greater New Orleans. Ultimately, two levee board ‘authorities’ were created, each of which had jurisdiction on opposite sides of the Mississippi River.

The historic levee board legislation put Louisiana on the frontier of good governance, as it was the first state in the nation to legislate such requirements. Soon after, California followed suit and voted for a package of flood bills that required professional backgrounds of its flood protection board members similar to Louisiana (Russo, 2007).

## Post-Katrina litigation

Numerous class-action lawsuits were filed against the Corps after Katrina, and these were consolidated by US District Court Judge Stanwood R. Duval, Jr. into two separate cases. The Mississippi River Gulf Outlet (MR-GO) case alleged that the Corps was negligent in its maintenance of a 76-mile shipping channel constructed by the agency in the mid-20th century. The suit alleged that its design allowed salt-water intrusion that damaged buffering cypress forests and wetlands, which historically had protected the New Orleans region from storm surge (Freudenburg et al., 2009).

In September 2009, federal District Judge Stanwood Duval approved a US$5 million settlement of a federal class-action lawsuit against the OLD. It is instructive to note, however, that in a case such as this where the settlement money comes from insurance resulting from policies the OLD held on the levees, a settlement should not be considered evidence of wrongdoing. Insurance companies have a risk of being found in bad faith for refusing a bona fide settlement offer within or at policy limits (Rawls & Hudson, 2006). Explained more simply, if an insurer refuses to pay a proposed settlement, they could potentially become liable for the full amount of any future settlement or a judgment even if it exceeds their policy limits. The total damages claimed by the plaintiffs for the levee and floodwall failures were many billions of dollars. In this case, the insurer had the choice to pay US$5 million or possibly become bankrupt. The settlement reflects a legal strategy on the part of both defendants and plaintiffs.

In November 2009, Judge Duval ruled that the Corps’ mismanagement of maintenance at the MR-GO was directly responsible for flood damage in St. Bernard Parish and the Lower 9th Ward neighborhood after Katrina (Schleifstein, 2009). The US 5th Circuit Court of Appeals ruled in March 2012 that Judge Duval was correct in his groundbreaking decision; however, the panel reversed its own decision six months later (Schleifstein, 2012). The Corps was immune from damages because of a provision governing suits against the federal government that protects an agency when it makes a discretionary decision.

The second case, commonly called the LEVEE case, included areas that flooded due to the outfall canal floodwall failures and also the IHNC failures. In January 2008, Judge Duval placed responsibility for the floodwall collapses of the 17th Street and London Avenue Canals on the Corps (Nossiter, 2008). However, the Corps could not be found financially liable due to sovereign immunity established by the Flood Control Act of 1928. Judge Duval wrote (Katrina Canal Breaches Consolidated Litigation, 2008):

‘The cruel irony here is that the Corps cast a blind eye, either as a result of executive directives or bureaucratic parsimony, to flooding caused by drainage needs and until otherwise directed by Congress, solely focused on flooding caused by storm surge. Nonetheless, damage caused by either type of flooding is ultimately borne by the same public fisc. Such egregious myopia is a caricature of bureaucratic inefficiency.’

Judge Duval dismissed the case, which has not been appealed.

## Conclusions

Any investigative study ought to be considered preliminary until better researched and documented data are introduced. Clarification of vetted facts is important because previous conclusions regarding the local New Orleans officials’ roles in the flooding disaster of 2005, made in the context of haste, have been oft-repeated in books and articles, and may even have been injurious to the flood survivors.

There can be no doubt that individuals on the pre-Katrina OLB spent time and locally generated funds on ancillary issues that were not directly related to flood safety. Owing to its history of land acquisition to finance levee building, the OLB had extensive assets, which under state law needed to be managed, and by 2005, the need for a different form of levee board governance was emerging. Also, as demonstrated by the unintended spillway at the transition between the Orleans Avenue Canal and Pump Station No. 7, there were periods of less- than- functional interaction between the OLB, the S&WB and other state agencies in the years immediately preceding Hurricane Katrina.

Nonetheless, with regard to the 17th Street and the London Avenue Canals, we have not uncovered any information that would suggest that the members of the OLB who served on the Engineering Committee or the OLD staff engineers behaved irresponsibly or in a manner that did not place the interests of the city residents at the forefront. Neither have we have found any data with regard to the 17th Street and the London Avenue Canals suggesting that the OLD failed to perform its congressionally mandated duties, which were to collect the 30% cost share for project design and construction, and to maintain and operate completed structures.

What is evident from the project record is that the Corps recommended parallel protection for the 17th Street Canal, but recommended frontage protection for the Orleans and London Avenue Canals because the plan for the latter two canals was less expensive, in keeping with its congressional mandate to employ measures with the most favorable cost–benefit ratios. The OLB lobbied its congressional delegation, which succeeded in convincing Congress to pass legislation that required the Corps to provide parallel protection for all three canals, not just the 17th Street Canal.

What is also evident is that the Corps, in a separate attempt to limit project costs, initiated a sheet pile load test (E-99 Study) in the Atchafalaya Basin of Louisiana, but misinterpreted the results and concluded that sheet piles needed to be driven to depths of only 17 feet instead of between 31 and 46 feet. That decision saved approximately US\$100 million, but significantly reduced the reliability of the floodwalls during Hurricane Katrina.

With regard to both the Corps’ recommendation to build the parallel plan for the 17th Street Canal, and to reduce the depths of the sheet piling in the I-walls, there is no evidence that either the Corps or the OLB believed that risk would be significantly increased.

And so here, we hope to correct any premature conclusions that appear to have been based on inaccurate information and/or assumptions about the role of the pre-Katrina OLB in the failure of the outfall drainage canals in New Orleans. The conclusions presented here are based upon a subsequently emerging volume of consistent, comprehensive and compelling data gleaned from interviews with the actual participants and from the transcripts of public meetings that were previously unavailable.

## Acknowledgments

We would like to acknowledge our appreciation of Sandy Rosenthal for her research, which was often tedious, in the preparation of this paper.

1

Throughout the paper, the term ‘billion’ represents 109.

2

The roll of the OLB meeting minutes of 20 April 1988, page 1, shows that Feingerts was present.

## References

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Braun
S.
Vartabedian
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Carter
N. T.
(
2005
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Protecting New Orleans: from Hurricane Barriers to Floodwalls (CRS Report No. RL 33188)
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Christian
J. T.
(
2010
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.
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,
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USA
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Donze
F.
(
2006
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,
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.
Eisler
P.
(
2009
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.
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(
1996
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Regulation Number 1130-2-530
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Flood Control Operations and Maintenance Policies
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United States Army Corps of Engineers
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Washington, DC
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B. H.
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Erikson
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F.
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.
Schleifstein
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,
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.


text:
Integer type:  int32  int64  nag_int  show int32  show int32  show int64  show int64  show nag_int  show nag_int

Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_pde_1d_parab_euler_osher (d03pv)

Purpose

nag_pde_1d_parab_euler_osher (d03pv) calculates a numerical flux function using Osher's Approximate Riemann Solver for the Euler equations in conservative form. It is designed primarily for use with the upwind discretization schemes nag_pde_1d_parab_convdiff (d03pf), nag_pde_1d_parab_convdiff_dae (d03pl) or nag_pde_1d_parab_convdiff_remesh (d03ps), but may also be applicable to other conservative upwind schemes requiring numerical flux functions.

Syntax

[flux, ifail] = d03pv(uleft, uright, gamma, path)
[flux, ifail] = nag_pde_1d_parab_euler_osher(uleft, uright, gamma, path)

Description

nag_pde_1d_parab_euler_osher (d03pv) calculates a numerical flux function at a single spatial point using Osher's Approximate Riemann Solver (see Hemker and Spekreijse (1986) and Pennington and Berzins (1994)) for the Euler equations (for a perfect gas) in conservative form. You must supply the left and right solution values at the point where the numerical flux is required, i.e., the initial left and right states of the Riemann problem defined below. In the functions nag_pde_1d_parab_convdiff (d03pf), nag_pde_1d_parab_convdiff_dae (d03pl) and nag_pde_1d_parab_convdiff_remesh (d03ps), the left and right solution values are derived automatically from the solution values at adjacent spatial points and supplied to the function argument numflx from which you may call nag_pde_1d_parab_euler_osher (d03pv).
The Euler equations for a perfect gas in conservative form are:
 $∂U ∂t + ∂F ∂x =0,$ (1)
with
 (2)
where $\rho$ is the density, $m$ is the momentum, $e$ is the specific total energy, and $\gamma$ is the (constant) ratio of specific heats. The pressure $p$ is given by
 $p=γ-1 e-ρu22 ,$ (3)
where $u=m/\rho$ is the velocity.
The function calculates the Osher approximation to the numerical flux function $F\left({U}_{L},{U}_{R}\right)=F\left({U}^{*}\left({U}_{L},{U}_{R}\right)\right)$, where $U={U}_{L}$ and $U={U}_{R}$ are the left and right solution values, and ${U}^{*}\left({U}_{L},{U}_{R}\right)$ is the intermediate state $\omega \left(0\right)$ arising from the similarity solution $U\left(y,t\right)=\omega \left(y/t\right)$ of the Riemann problem defined by
 $∂U ∂t + ∂F ∂y =0,$ (4)
with $U$ and $F$ as in (2), and initial piecewise constant values $U={U}_{L}$ for $y<0$ and $U={U}_{R}$ for $y>0$. The spatial domain is $-\infty , where $y=0$ is the point at which the numerical flux is required. Osher's solver carries out an integration along a path in the phase space of $U$ consisting of subpaths which are piecewise parallel to the eigenvectors of the Jacobian of the PDE system. There are two variants of the Osher solver termed O (original) and P (physical), which differ in the order in which the subpaths are taken. The P-variant is generally more efficient, but in some rare cases may fail (see Hemker and Spekreijse (1986) for details). The argument path specifies which variant is to be used. The algorithm for Osher's solver for the Euler equations is given in detail in the Appendix of Pennington and Berzins (1994).

References

Hemker P W and Spekreijse S P (1986) Multiple grid and Osher's scheme for the efficient solution of the steady Euler equations Applied Numerical Mathematics 2 475–493
Pennington S V and Berzins M (1994) New NAG Library software for first-order partial differential equations ACM Trans. Math. Softw. 20 63–99
Quirk J J (1994) A contribution to the great Riemann solver debate Internat. J. Numer. Methods Fluids 18 555–574

Parameters

Compulsory Input Parameters

1:     $\mathrm{uleft}\left(3\right)$ – double array
${\mathbf{uleft}}\left(\mathit{i}\right)$ must contain the left value of the component ${U}_{\mathit{i}}$, for $\mathit{i}=1,2,3$. That is, ${\mathbf{uleft}}\left(1\right)$ must contain the left value of $\rho$, ${\mathbf{uleft}}\left(2\right)$ must contain the left value of $m$ and ${\mathbf{uleft}}\left(3\right)$ must contain the left value of $e$.
Constraints:
• ${\mathbf{uleft}}\left(1\right)\ge 0.0$;
• Left pressure, $\mathit{pl}\ge 0.0$, where $\mathit{pl}$ is calculated using (3).
2:     $\mathrm{uright}\left(3\right)$ – double array
${\mathbf{uright}}\left(\mathit{i}\right)$ must contain the right value of the component ${U}_{\mathit{i}}$, for $\mathit{i}=1,2,3$. That is, ${\mathbf{uright}}\left(1\right)$ must contain the right value of $\rho$, ${\mathbf{uright}}\left(2\right)$ must contain the right value of $m$ and ${\mathbf{uright}}\left(3\right)$ must contain the right value of $e$.
Constraints:
• ${\mathbf{uright}}\left(1\right)\ge 0.0$;
• Right pressure, $\mathit{pr}\ge 0.0$, where $\mathit{pr}$ is calculated using (3).
3:     $\mathrm{gamma}$ – double scalar
The ratio of specific heats, $\gamma$.
Constraint: ${\mathbf{gamma}}>0.0$.
4:     $\mathrm{path}$ – string (length ≥ 1)
The variant of the Osher scheme.
${\mathbf{path}}=\text{'O'}$
Original.
${\mathbf{path}}=\text{'P'}$
Physical.
Constraint: ${\mathbf{path}}=\text{'O'}$ or $\text{'P'}$.

None.

Output Parameters

1:     $\mathrm{flux}\left(3\right)$ – double array
${\mathbf{flux}}\left(\mathit{i}\right)$ contains the numerical flux component ${\stackrel{^}{F}}_{\mathit{i}}$, for $\mathit{i}=1,2,3$.
2:     $\mathrm{ifail}$int64int32nag_int scalar
${\mathbf{ifail}}={\mathbf{0}}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:
${\mathbf{ifail}}=1$
 On entry, ${\mathbf{gamma}}\le 0.0$, or ${\mathbf{path}}\ne \text{'O'}$ or $\text{'P'}$.
${\mathbf{ifail}}=2$
 On entry, the left and/or right density or pressure value is less than $0.0$.
${\mathbf{ifail}}=-99$
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.

Accuracy

nag_pde_1d_parab_euler_osher (d03pv) performs an exact calculation of the Osher numerical flux function, and so the result will be accurate to machine precision.

nag_pde_1d_parab_euler_osher (d03pv) must only be used to calculate the numerical flux for the Euler equations in exactly the form given by (2), with ${\mathbf{uleft}}\left(\mathit{i}\right)$ and ${\mathbf{uright}}\left(\mathit{i}\right)$ containing the left and right values of $\rho ,m$ and $e$, for $\mathit{i}=1,2,3$, respectively. It should be noted that Osher's scheme, in common with all Riemann solvers, may be unsuitable for some problems (see Quirk (1994) for examples). The time taken depends on the input argument path and on the left and right solution values, since inclusion of each subpath depends on the signs of the eigenvalues. In general this cannot be determined in advance.

Example

See Example in nag_pde_1d_parab_convdiff_dae (d03pl).
```function d03pv_example

fprintf('d03pv example results\n\n');

uleft  = [1  0  2.5];
uright = [2  1  0.5];
gamma  = 1.9;
path = 'P';
[flux, ifail] = d03pv(uleft, uright, gamma, path);

fprintf(' Given uleft = [%7.1f %7.1f %7.1f]\n',uleft);
fprintf('  and uright = [%7.1f %7.1f %7.1f]\n',uright);
fprintf('  with gamma =  %7.4f and path = ''%s''\n',gamma,path);
fprintf('\n        flux = [%7.4f %7.4f %7.4f]\n',flux);

```
```d03pv example results

Given uleft = [    1.0     0.0     2.5]
and uright = [    2.0     1.0     0.5]
with gamma =   1.9000 and path = 'P'

flux = [ 0.5540  1.3956  1.9266]
```

format: plain


text:
# Flavor symmetry for strong phases and determination of $β s, ΔΓ$ in $B s o J-ψφ$ - High Energy Physics - Phenomenology

Flavor symmetry for strong phases and determination of $β s, ΔΓ$ in $B s o J-ψφ$ - High Energy Physics - Phenomenology - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: Studies of angular and time distributions and CP-violating observables in$B s\to J-\psi \phi$ decays yield a space of parameters which can beconsiderably reduced if relative strong phases among different amplitudes arespecified. We show that the relations between $B s \to J-\psi \phi$ and $B^0\to J-\psi K^{*0}$ amplitudes given by flavor symmetry actually U3 ratherthan SU3 are likely to be quite reliable, and hence the use of strong phasesfrom $B^0 \to J-\psi K^{*0}$ in the analysis of $B s \to J-\psi\phi$ isjustified. We point out the potential advantage of using helicity angles overtransversity angles, and comment on a way to measure a sizable CP-violatingphase independent of strong phases.

Autor: Michael Gronau, Jonathan L. Rosner

Fuente: https://arxiv.org/


text:
# RSS Feed for personal personal

personal

## Convert Docx to LaTeX!

• March 24, 2011 18:34

Just stumbled across an interesting link that has info on converting a Microsoft Docx file into a latex file! Harri Kiiskinen over at http://pastcounts.wordpress.com/ wrote up an XSL stylesheet that can match elements in Microsofts OOXML format and print out the latex formatting.

The actual information on doing this all is located here: http://pastcounts.wordpress.com/2011/03/22/using-xsl-to-convert-docx-to-latex/

First, you need to break open the .docx file. It basically is a simple zipped archive, so an ‘unzip testdoc.docx’ should do the trick; you’ll end up with several files and sub-directories, of which only the directory called ‘word’ is necessary for this test.

Second, here’s the XSL transformation to save in a file:
 <?xml version="1.0"?> <xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform" xmlns:w="http://schemas.openxmlformats.org/wordprocessingml/2006/main">

 <xsl:template match="/w:document"> \documentclass{article} <xsl:apply-templates/> </xsl:template> <xsl:template match="w:body"> \begin{document} <xsl:apply-templates/> \end{document} </xsl:template> <xsl:template match="w:p"> <xsl:apply-templates/><xsl:if test="position()!=last()"><xsl:text> </xsl:text></xsl:if> </xsl:template> <xsl:template match="w:r"> <xsl:if test="w:footnoteReference"><xsl:text>\footnote{</xsl:text> <xsl:call-template name="footnote"> <xsl:with-param name="fid"><xsl:value-of select="//@w:id"/></xsl:with-param> </xsl:call-template> <xsl:text>}</xsl:text> </xsl:if> <xsl:if test="w:rPr/w:b"><xsl:text>\textbf{</xsl:text></xsl:if> <xsl:call-template name="pastb"/> <xsl:if test="w:rPr/w:b"><xsl:text>}</xsl:text></xsl:if> </xsl:template> <xsl:template name="pastb"> <xsl:if test="w:rPr/w:i"><xsl:text>\textit{</xsl:text></xsl:if> <xsl:call-template name="pasti"/> <xsl:if test="w:rPr/w:i"><xsl:text>}</xsl:text></xsl:if> </xsl:template> <xsl:template name="pasti"> <xsl:apply-templates select="w:t"/> </xsl:template> <xsl:template name="footnote"> <xsl:param name="fid"/> <xsl:apply-templates select="document('footnotes.xml')/w:footnotes/w:footnote[@w:id=$fid]"/> </xsl:template> <xsl:template match="//w:footnote"> <xsl:apply-templates select="w:p"/> </xsl:template>  </xsl:stylesheet>  You can save that in a file called docxtolatex.xsl in the ‘word’ directory. Then, in that directory, run ‘xsltproc docxtolatex.xsl document.xml’, and you’ll have your screen full of the document, in LaTeX markup. You’ll notice, that this XSLT only converts bold, italics and footnotes. But then again, that’s what I often only need to convert… So yea..I’ll definitely use this to convert some word docs I have that I’ve been wanting to push into latex format. I also think I might do some additional research into tweaking this XSL so that *.docx files could potentially be converted to LaTeX, in their entirety! Also — in order to successfully post a copy of the XSL stylesheet above, I found myself needing a script to safely escape all the xml entities….if you’re interested, here’s that script I just slapped together for doing this:  #!/usr/bin/env php <?php$handle = @fopen($argv[1], "r"); if ($handle) { while (($buffer = fgets($handle, 4096)) !== false) { echo htmlentities($buffer); } if (!feof($handle)) { echo "Error: unexpected fgets() fail\n"; } fclose(\$handle); } ?>

Simply copy the above script into a php file, make it executable, and then run it with an input file as an argument and it’ll spit out whatever XML input you give it the encoded version of the markup.

• March 13, 2011 15:26

Seeing as I haven’t written in awhile…I figured I’d at least drop a link to my xmonad.hs file that I’ve put together for my own setup. For those of you who don’t know what XMonad is, it’s a tiling window manager. You should check it out!

I’ve been meaning to write a more meaningful post on how put together my current XMonad setup and what not. Perhaps in the near future!

## Busy busy busy and new sites!

• December 13, 2010 11:52

Well…I don’t have a lot of time to pour into this post unfortunately, but I have just enough time to mention that I’m still plowing through my capstone proposal so I can finally start working on my final project for my masters degree.

You can get a glance at my work on the proposal here –> http://capstone.geoffreyanderson.net/

As for the other site, I finally got my partner to start designing a better portfolio site for her work. We set up a basic sub-domain for her here –> http://cullenillustration.geoffreyanderson.net/

Check out her stuff, pretty good art!

## I miss halloween hockey

• October 29, 2010 18:46

For this reason…

RIT Hockey on Halloween!

## Welcome back to RIT!

• September 8, 2010 09:47

Well, RIT’s officially alive and classes are back on track and going full swing.  I decided that there’s plenty of time in a day for me to do various kinds of work: working on my capstone, finishing my last online class, TA’ing Fundamentals of DBMS Architecture (and seeing the coursework I’ve created get used!), working on the databases for various other classes, and sitting in on a class or two!

Phew, it all seems like so much, yet I’m still finding that I’ve got an awful lot of free time (y’know…since I don’t have 16 hours worth of real classes..).  Suffice to say, I’m excited for all the things I’ll get to work on this year, and especially getting to spend a lot more time with my partner now that we’ve moved in together at the new apartments across from campus!

So, to break down everything I’m working on this school term (and year):

• Need to (start and) finish my capstone proposal for a potential course in Business Intelligence that could be offered in the IST department at RIT
• Want an ‘A’ in Data Architecture and Management — I should probably get started on the paper we have due next week
• I need to create some more in-class exercises for the Database course I’m TA’ing so our students can get a better grasp of the material.  This is also because the course format changed to a “studio style” class (students meet 3x a week for 2 hours) from it’s old lecture format (1.5 hour lecture 2x a week and a 2 hour lab 1x a week).  I also need to get the new coursework to our database tutors for this year.
• I need to rebuild the virtual machine for our Information Assurance course at some point and also tweak the database for our Database Performance and Tuning class.
• Try and keep up with the homework assignments for Native Mobile Application Development (since I’m “sitting in” and not auditing/registered for the class)

Beyond that, I’ll try to snap some pictures of the changes happening around campus to share!


text:
# On cycles in intersection graphs of rings

Document Type: Research Paper

Authors

Abstract

Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$-claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. We show that such graphs are indeed pancyclic.

Keywords

Main Subjects

### References

A. Akbari, R. Nikandish and M. J. Nikmehr, Some results on the intersection graphs of ideals of rings, J. Algebra Appl. 12 (2013), no. 4, 13 pages.

J. Bos_ak, The graphs of semigroups, Theory of Graphs and Application, 119--125, Publ. House Czechoslovak Acad. Sci., Prague, 1964.

I. Chakrabarty, S. Ghosh, T. K. Mukherjee and M. K. Sen, Intersection graphs of ideals of rings, Discrete Math. 309 (2009), no. 17, 5381--5392.

B. Cs_ak_eany and G. Poll_ak, The graph of subgroups of a finite group, Czechoslovak Math. J. 19 (1969) 241--247.

M. Herzog, P. Longobardi and M. Maj, On a graph related to the maximal subgroups of a group, Bull. Aust. Math. Soc. 81 (2010), no. 2, 317--328.

S. H. Jafari and N. Jafari Rad, Domination in the intersection graphs of rings and modules, Ital. J. Pure Appl. Math. 28 (2011) 19--22.

S. H. Jafari and N. Jafari Rad, Planarity of intersection graphs of ideals of rings, Int. Electron. J. Algebra 8 (2010) 161--166.

B. R. Macdonald, Finite Rings with Identity, Marcel Dekker, Inc., New York, 1974.

T. A. McKee and F. R. McMorris, Topic in Intersection Graph Theory, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1999.

R. Shen, Intersection graphs of subgroups of finite groups, Czech. Math. J. 60(135) (2010), no. 4, 945--950.

B. Zelinka, Intersection graphs of finite abelian groups, Czechoslovak Math. J. 25 (1975) 171--174.

### History

• Receive Date: 05 November 2013
• Revise Date: 14 February 2015
• Accept Date: 15 February 2015


text:
# Standardized coefs in regression with a categorical predictor: there's something wrong

From what I understood, standardized coefficients can be used as indices of effect size (with the possibility of using rules of thumb such as Cohen's 1988). I also understood that standardized coefs are expressed in terms of standard deviation, which makes them relatively close to a Cohen's d.

I also understood that one way of obtaining standardized coefs is to standardize the data beforehand. Another is to use the std.coef function from the MuMIn package.

These two methods are equivalent when using a linear predictor:

library(tidyverse)
library(MuMIn) # For stds coefs

df <- iris %>%
select(Sepal.Length, Sepal.Width) %>%
scale() %>%
as.data.frame() %>%
mutate(Species = iris$Species) fit <- lm(Sepal.Length ~ Sepal.Width, data=df) round(coef(fit), 2) round(MuMIn::std.coef(fit, partial.sd = TRUE), 2)  In both cases, the coefficient is -0.12. I interpret it as follows: for each increase of 1 standard deviation of Sepal.Width, Sepal.Length diminishes of 0.12 of its SD. And yet, these two methods give different results with a categorical predictor: fit <- lm(Sepal.Length ~ Species, data=df) round(coef(fit), 2) round(MuMIn::std.coef(fit, partial.sd = TRUE), 2)  Which gives, for the effect of versicolor as compared to setosa (the intercept), 1.12 and 0.46. Which should I believe to be able to say "the difference between versicolor and setosa is ... of Sepal.Length's SD"? Thanks a lot • The standard deviation relies on the mean. What do you think the mean species means? The mode I can understand but the mean? If the mean is meaningless then so is the standard deviation. Jul 11 '18 at 17:14 ## 1 Answer First, recall that categorical variables are silently recoded into dummies in lm function. MuMIn package standardizes these dummy variables (which is straightforward since they contain only 0's and 1's). On the other hand, you did not standardize them when creating your df object. This is why you get two different results. To find difference between setosa and versicolor in units of Sepal Length SD, you need to standardize only Sepal Length, which is exactly what you did in your df object. • You're right, I found that standardizing the dummies gives the same coefs as those obtained with MuMin dummies <- scale(contrasts(df$Species)[df\$Species,]) fit <- lm(Sepal.Length ~ dummies, data = df). But then, for using rules of thumb for effect size interpretation (for example roughly follow the Cohen's d grid), should I use the fully standardized, or just the "dependent" variable standardized results? Thanks a lot! Jul 12 '18 at 7:07
• I believe you should use just the "dependent" variable standardized results. Because Cohen's d quantifies difference between groups with respect to pooled standard deviation. So you sholud keep gruoping variable (dummies in this case) on it's original scale. Jul 12 '18 at 7:29


text:
Jonathan wrote in [#9](https://forum.azimuthproject.org/discussion/comment/20134/#Comment_20134)
>[David wrote](https://forum.azimuthproject.org/discussion/comment/20132/#Comment_20132):
>> Answer to **Puzzle 194**: \$$S\multimap T=\bigvee \lbrace A : \; S \otimes A \le T \rbrace=\bigvee \lbrace A : \; S \cup A \subseteq T\rbrace\$$, so this is the set with the most elements such that its union with \$$S\$$ is \$$T\$$. This set is \$$S^c\cap T\$$ (where \$$S^c\$$ denotes the set complement operation), since the addition of any more elements of \$$X\$$ would make its union with \$$S\$$ a proper superset of \$$T\$$.

>Couldn't it be \$$S \cup (S^c \cap T)\$$ as well, since union is idempotent? If \$$S \cup A \subseteq T\$$ is true, then \$$S \cup (S \cup A) \subseteq T\$$ is also, and vice versa.

>EDIT: And this just simplifies to \$$S \cup T\$$.

Yes, you're right, but it is not true that \$$S\cup T\subseteq T\$$ (unless \$$S\subseteq T\$$). In fact, even if we try with \$$S\multimap T=\emptyset\$$, we would have to have \$$S\subseteq T\$$ in order for \$$S\cup\emptyset\subseteq T\$$ to hold. So, I was wrong, this monoidal poset is not closed since \$$S\multimap T\$$ does not exist, in general.


text:
# Solving differential equation without finding integrating factor

I have been trying to solve this equation

$$\left( 8y+10x \right) \mathrm{d}x+\left( 5y+7x \right) \mathrm{d}y=0\\$$

by finding integrating factor, though is there more rational way to do it?

• Hint: Let $$y = v x \implies y' = v + v' x$$ Now substitute and solve. – Moo May 28 '17 at 22:36
• Thank you, that should do it! – Jack Nickolson May 28 '17 at 22:39

Turning Moo's comment into an answer. In general if we have something of the form $$\frac{\mathrm{d}y}{\mathrm{d}x} = -\frac{8y + 10x}{5y + 7x} = -\frac{8\frac{y}{x} + 10}{5\frac{y}{x} + 7}$$ i.e $y' = f(y/x)$ then it is a good idea to try the substitution $y=vx \implies y' = v + v'x$ to get $$v + x\frac{\mathrm{d}v}{\mathrm{d}x}=-\frac{8v+10}{5v +7}\implies x\frac{\mathrm{d}v}{\mathrm{d}x} = -\left(\frac{8v+10}{5v+7} +\frac{5v^2+7v}{5v+7}\right)=-\frac{5(v+2)(v+1)}{5v+7}$$ which is a separable equation $$\int\frac{5v+7}{5(v+2)(v+1)}\, \mathrm{d}v=-\log x + c \implies \log(v+1)^2(v+2)^3=-5 \log x + c$$ via partial fractions giving $$(v+1)^2(v+2)^3=\frac{A}{x^5} \implies (y+x)^2(y+2x)^3 = A.$$


text:
Fundamental of Mathematics

Algebra Level 4

If $$P(x)$$ is a cubic polynomial with leading coefficient 2 such that $$P(1)=2 , P(2)=8 , P(3)=18$$, find $$P(4)$$.

×


text:
Generating an atomic stoichiometric matrix

| categories: | tags: | View Comments

In computing thermodynamic properties with species, it is sometimes required to get a matrix that specifies number of each type of atom in each species. For example, we can create this by hand as follows:

 H2O CO2 H2 CO H 2 0 2 0 C 0 1 0 1 O 1 2 0 1

Here we aim to generate this table from code. Why? 1. We can readily add species to it if we do it right. 2. We are less likely to make mistakes in generation of the table, and if we do, it will be faster to regenerate the table.

We will start with a list of strings that represent the chemical formula of each species. We will need to parse the strings to find the elements, and number of them. We will use a fairly naive regular expression to parse a chemical formula. Basically, we match a capital letter + an optional lowercase letter, followed by an optional number. Here is a fictitous example to illustrate. Note, this will not work with formulas that have parentheses, or charges.

import re
m = re.findall('([A-Z][a-z]?)(\d?)' , 'ArC2H6Cu56Pd47Co')
print m

[('Ar', ''), ('C', '2'), ('H', '6'), ('Cu', '5'), ('Pd', '4'), ('Co', '')]

Now, we need to loop over the species, and collect all the elements in them. We will just make a list of all of the elments, and then get the set.

import re

# save for future use
cf = re.compile('([A-Z][a-z]?)(\d?)')

species = ['H2O', 'CO2', 'H2', 'CO2']

all_elements = []

for s in species:
for el, count in re.findall(cf, s):
all_elements += [el]

print set(all_elements)

set(['H', 'C', 'O'])

Finally, we can create the table. We need to loop through each element, and then through each species

import re

# save for future use
cf = re.compile('([A-Z][a-z]?)(\d?)')

species = ['H2O', 'CO2', 'H2', 'CO2']

all_elements = []

for s in species:
for el, count in re.findall(cf, s):
all_elements += [el]

atoms = set(all_elements)

# we put a placeholder in the first row
counts = [[""] + species]
for e in atoms:
# store the element in the first column
count = [e]
for s in species:
d = dict(re.findall(cf, s))
n = d.get(e, 0)
if n == '': n = 1
count += [int(n)]
counts += [count]

# this directly returns the array to org-mode
return counts

 H2O CO2 H2 CO2 H 2 0 2 0 C 0 1 0 1 O 1 2 0 2

For this simple example it seems like a lot of code. If there were 200 species though, it would be the same code! Only the list of species would be longer. It might be possible to avoid the two sets of looping, if you could represent the stoichiometric matrix as a sparse matrix, i.e. only store non-zero elements. The final comment I have is related to the parsing of the chemical formulas. Here we can only parse simple formulas. To do better than this would require a pretty sophisticated parser, probably built on the grammar of chemical formulas. The example here implements the code above using pyparsing, and could probably be extended to include more complex formulas such as (CH3)3CH.


text:
# Collision question -- 2 balls colliding elastically

1. May 4, 2015

### SteveS

1. The problem statement, all variables and given/known data
A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown. If the first ball moves away with angle 30° to the original path, determine
1. the speed of the first ball after the collision.
2. the speed and direction of the second ball after the collision.
** I realize there is another thread for this question, but I hadn't seen any activity on it for a month after asking a question so I'm posting again.

2. Relevant equations

m1v1 + m2v2 = m1v1' + m2v2'

1/2m1(v1)^2 + 1/2 m2(v2)^2 = 1/2m1(v1')^2 + 1/2m2(v2')^2

3. The attempt at a solution

Ok. I have 3 unknowns in this equation. The v1', v2' and the angle of the second ball. For this I need 3 equations

For the X component I have:

V1 = v1' * Cos 30 + v2' * Cos θ

For the Y component I have:

v1' * Sin 30 = -v2' * Sin θ

Using the Conservation of energy I have:

V1^2 = v1'^2 + v2'^2

From here, I'm not sure where to proceed. I have tried some substitutions but I get into really long ugly math that turns circular and I never get anywhere. Any help would be appreciated. I know I need to use the trig relation of
Cos^2 θ + Sin^2 θ = 1, but i've not been able to get to any point where I can apply it.

2. May 4, 2015

### haruspex

You can certainly use cos2+sin2=1 to eliminate theta. First, you need to get cos theta = (an expression not involving theta) and likewise for sin theta. Even if it does get a bit messy, please post your work as far as you get. It's the only way we can see where you are getting stuck.
You can avoid some of the mess by using Newton's Experimental Law, about ratios of velocities in the direction of impact, but in the context of the current problem it might not be much easier.

3. May 6, 2015

### SteveS

Honestly I've got four pages of scribbles and I'm really turned around. I'm not sure what to do anymore. The last thing I did was

I rearranged the x component equation to v1' = va - v2' * Cos θ / Cos 30

I then substituted this into the energy equation which i got down to Cos 30 = Cos θ

is this right? Are the angles the same? I'm really not sure where to go from here.

I can rearrange the y component equation so that v2' = - v1' Sin 30 / Sin θ but putting this into an equation leads me to a no where. I'm really not sure what to do.

4. May 6, 2015

### PeroK

There's a neat shortcut to eliminating one of the angles by using the vector nature of momentum and the law of cosines. It amounts to the same as squaring things and using $cos^2 + sin^2 = 1$.

Using the law of cosines, you get:

$v_2^2 = u_1^2 + v_1^2 - 2uv_1cos(30)$

That plus your conservation of energy should get you on the right track.

(I used $u$ for the initial velocity, as it made the latex easier!)

5. May 6, 2015

### SteveS

In my previous post I mentioned I was aware of the relation cos^2 θ + sin ^2 θ = 1... What i'm not sure is how you got to that equation you posted.

6. May 6, 2015

### PeroK

Draw a vector diagram (triangle) involving the three velocity vectors involved and apply the law of cosines. Normally you would use the momentum vectors $mv$ but the masses cancel in this case - as you know.

7. May 6, 2015

### SteveS

I have done so already which is what leads to the three equations that I laid out at the beginning.

8. May 6, 2015

### PeroK

Yes, but using the law of cosines is a significant shortcut to eliminating the unknown angle.

9. May 6, 2015

### SteveS

I'm sorry i don't mean to be rude , but tell me something i've not already said.... I know. I don't know how to use it. I can't ever get to a point where I can actually use the relation. In my circular calculations for the last three days I haven't been able to reduce anything to the point where I can get any sort of an answer. Really frustrated and I have half a mind to simply not do this question as I've already wasted 4 days trying to figure it out.

10. May 6, 2015

### PeroK

You've got:

$v_2^2 = u_1^2 + v_1^2 - 2uv_1cos(30)$

and

$u_1^2 = v_1^2 + v_2^2$

That gives you $v_1$ in terms of $u$. The rest should follow.

11. May 6, 2015

### SteveS

The equation

u1^2 = v1^2 + v2^2 is the conservation of energy equation I already posted. The other equation you posted I do not know how to derive and the rest does not follow. Never mind I'm done with this crap. Pretty frustrated.

12. May 6, 2015

### chriskary

The equation
u1^2 = v1^2 + v2^2 is the conservation of energy equation and Pithagoreio inverse theorem says v1 is vertical to v2...

13. May 6, 2015

### SteveS

I'm not sure what that means or how that even helps. me. never mind no need for more replies. I can't waste any more time on this question.

14. May 6, 2015

### haruspex

You don't understand how hard it is to help people who won't take the trouble to post all their working.
The equation you don't recognise is the cosine law, an essential tool in your toolbox. if you don't know it, learn it.

To finish the discussion on using cos^2 θ + sin ^2 θ = 1, which leads to the same equation:
You posted:
V1 = v1' * Cos 30 + v2' * Cos θ
v1' * Sin 30 = -v2' * Sin θ
From those we get ( v2')^2 = ( v2' * Cos θ)^2 + (v2' * Sin θ)^2 = (V1 - v1' * Cos 30)^2 + (v1' * Sin 30)^2 = (V1)^2 + (v1')^2 - 2 V1 v1'Cos 30

15. May 6, 2015

### chriskary

#### Attached Files:

• ###### 20150507_003802.jpg
File size:
91.3 KB
Views:
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16. May 6, 2015

### SteveS

Ok. Sorry to those who have been trying to help me. I'm an accountant who graduated from university the first time about 12 years ago. I'm now a microbiology major and haven't had to use trig in a very very long time, but I have to take this one physics class in order to graduate. I took a walk around the block and came up with this solution that worked. I tried it before and must have made an error so that it didn't work. Here is what I did:

I took the x component equation I initially started with and rearranged it to isolate the θ on the right. This gave me:

v1-v1' * Cos 30 = v2' Cos θ

I then rearranged the y component equation to also isolate θ on the right. This gave me:

v1' * Sin 30 = v2' Sin θ

I then squared each of these equations and added them together. This then gave me use of the previously mentioned relation and simplified down to:

v1^2 + v1'^2 -2v1v1'*Cos 30 = v2'^2 .... I recognize now the equation previously posted from the cosine law.

I then rearranged the conservation of energy equation I previously had to isolate v2' on the right. I then subtracted this energy equation from the previously derived equation that eliminated θ.

This left me with an equation of:

v1' = v1 * Cos 30
v1' = 2.60 ( rounded answer)

feeding this back into the kinetic energy equation,

v2' = sqrt ( (9) - (2.60)^2)
v2' = 1.5 m/s

I can then use one of the component equations such as the x component equation and plug in the numbers to find θ:

Cos θ = v1 - v1' Cos 30 / v2' = (3) - (2.6)*Cos 30 / 1.5

θ = 60°

So the speed of mass 1 after the initial collision is 2.6 m/s and the speed of mass 2 after the initial collision is 1.5 m/s @ 60° below the horizontal x plane.

I think I've got it now.


text:
# Don't electrons have discrete energy levels in semiconductors?

I am having a hard time understanding the relation between the fermi distribution of electrons in a semiconductor, and the fact the electron energy states are discrete.

The fermi distribution is supposed to give us the probability of an energy level being occupied by electrons. It looks like this:

yet electrons are supposed to have discrete energy states, and no electron is supposed to be in the band gap:

I must be missing something here, how is it that electrons have a fairly high probability of being in the band gap ?

There are two important contributions: First the density of states, which tells you the states, which can potentially be occupied. Then there is the Fermi-Dirac distribution, which tells you, which energies are occupied. The Fermi-Dirac distribution does not include allowed and forbidden states. You must fold it with the density of states, which is then called combined density of states. This function then tells you the distribution of occupied or unoccupied states.

• I think this did not answer the original question completely. Electrons do have a discrete energy, and the corresponding Fermi-Dirac distribution gives you the probability (= average occupancy, in this case) that a fermionic quantum state occupies a given (discrete) energy. But this is unhandy for calculations. Therefore one performs the so-called continuum limit where one treats discrete energies as quasi-continuous. Then the FD-distribution tells you the average occupation of a given quantum state with (continuous) energy. The rest is explained by engineer. – RogueDodecahedron Feb 18 '15 at 21:53

In a (perfect) semiconductor, there are no electronic states available in the band gap. Therefore, despite the fact that the Fermi-Dirac distribution "predicts" (or better: accounts for) electrons with energies lying in the band gap, they cannot exist there because no states are available.

If the Fermi level lies in the band gap, the undoped semiconductor behaves like an insulator because all electronic states in the valence band are occupied and the electrons can't move. If $E_\mathrm{F}$ was smaller than the highest energy level in the valence band, the material would become conductive because free states in the valence band become available. If $E_\mathrm{F}$ was larger than the lowest energy level in the conduction band, the material would also become conductive for the same reason.

The Fermi function or Fermi-Dirac distribution was developed as a quantum mechanical expansion of the Boltzmann distribution. With it, you can describe the free electron gas appropriately, whereas the Boltzmann distribution fails by predicting zero energy for all particles at absolute zero (see Pauli exclusion principle). The fermi-dirac distributiom arises from statistical mechanics considerations only and is not influenced by the density of states. Even if there is a probability that a state be occupied by a fermion within the bandgap, if there are no states to be occupied, what do you have?